Position estimation with a millimeter-wave massive MIMO system based on distributed steerable phased antenna arrays

Position estimation with a millimeter-wave massive MIMO system based on distributed steerable... In this paper, we propose a massive MIMO (multiple-input-multiple-output) architecture with distributed steerable phased antenna subarrays for position estimation in the mmWave range. We also propose localization algorithms and a multistage/multiresolution search strategy that resolve the problem of high side lobes, which is inherent in spatially coherent localization. The proposed system is intended for use in line-of-sight indoor environments. Time synchronization between the transmitter and the receiving system is not required, and the algorithms can also be applied to a multiuser scenario. The simulation results for the line-of-sight-only and specular multipath scenarios show that the localization error is only a small fraction of the carrier wavelength and that it can be achieved under reasonable system parameters including signal-to-noise ratios, antenna number/placement, and subarray apertures. The proposed concept has the potential of significantly improving the capacity and spectral/energy efficiency of future mmWave massive MIMO systems. Keywords: Direct position estimation, mmWave, Massive MIMO, Steerable phased antenna arrays, Wireless indoor localization 1 Introduction channels between pairs of antennas are assumed uncorre- Millimeter-wave (mmWave) communication and mas- lated, in massive MIMO systems there is a large number of sive MIMO (multiple-input-multiple-output) are disrup- antennas at a base station (BS). The antennas of the system tive technologies for cellular 5G (5th generation) systems. form beams toward low-cost user devices with spatially Not surprisingly, they have been in the focus of inten- separated single antennas [1]. Many antennas are required sive research efforts in both academia and industry in in the mmWave band because of the high pathloss and the last decade. The application of massive MIMO sys- the need for large antenna gains to obtain sufficiently high tems in themmWavebandrepresentsabigresearchand signal-to-noise ratios (SNRs). technological challenge. Since the work of Marzetta in Traditionally, beamforming by the antennas is realized 2010 [1], there have been many technical papers on this completely in the digital domain. This entails that every technology. Some address system issues [2–6], and others antenna has its own radio-frequency (RF) chain (a low- signal processing [7], analog and hybrid beamforming noise amplifier, a down-converter, an A/D converter at [8–17], propagation and channel modeling/measurement the receiving side, a D/A converter, up-converter, and a [18–20], technological aspects [21], and practical imple- power amplifier at the transmitting side), which renders mentations [22, 23]. the application of massive MIMO in mmWave impracti- Multi-user MIMO systems referred to as massive MIMO cal due to high cost and energy consumption. A promising systems were introduced in [1]. Unlike in conventional M solution to these problems lies in the concept of hybrid IMO systems for point-to-point communications where the transceivers, which use a combination of analog beam- forming in the RF domain and digital beamforming in the baseband to allow for RF circuits with a smaller number *Correspondence: vn135023p@student.etf.bg.ac.rs School of Electrical Engineering, University of Belgrade, Belgrade, Serbia of up/down conversion chains. In practice, a beamformer Full list of author information is available at the end of the article is usually implemented as an array of phase shifters with © The Author(s). 2018 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. Vukmirovic´ et al. EURASIP Journal on Advances in Signal Processing (2018) 2018:33 Page 2 of 17 only a discrete set of possible shifts (phase quantization) are more users) with greatly reduced interference levels [7]. Interest in hybrid transceivers has accelerated over to other users. This clearly suggests that accurate location the past 3 years (especially following [7]), and as a result, awareness enables location-aided communication. various structures have already been proposed. Our previous research has confirmed that in a spatially In the wide literature, there are only a few papers dealing coherent scenario (where the LoS component is dominant with localization with mmWave massive MIMO systems. and where the carrier phase changes predictably over dis- The authors of [24] surveyed applications of localiza- tance), a distributed antenna array and direct localization tion in massive MIMO systems and state that the 5G algorithms can achieve localization accuracy much bet- technology is expected to allow localization accuracy of ter than the carrier wavelength (by two to three orders of 1 cm, which is twice the carrier wavelength at 60 GHz magnitude). In [35], it was reported that accuracy of 30% (around 5 mm). In [25], high-accuracy localization with of carrier wavelength in RFID (radio frequency identifica- mmWave systems in applications related to assisted living tion) localization was achieved. Localization in a spatially and location awareness was considered. It was concluded coherent scenario was also addressed in [36, 37]. The that “future 5G mmWave communication systems could spatially coherent approach suffers from high side lobes be an ideal platform for achieving high-accuracy indoor in the criterion function (localization ambiguity). This localization.” The performance of localization based on problem of side lobes is similar in nature to the one of the RSSI (received signal strength indicator) principle side/grating lobes in direction of arrival estimation with applied to the mmWave range was investigated in [26], classical antenna arrays. In this paper, we aim at achieving a high localization and it was found that it was possible to achieve accu- accuracy with distributed antenna subarrays in mmWave, racy of around 1 m. A fingerprint-based localization was where the accuracy would be much better than the carrier presented in [27], and a method for direct localization wavelength. At the same time, we also resolve the problem was introduced in [28]. In [29], the authors presented an of localization ambiguity. New research problems arise mTrack system for high precision passive object tracking with this including designing an architecture of such sys- at 60 GHz and claimed that submillimeter accuracy could tem and formulating algorithms which achieve these two be achieved. This accuracy can provide location aware- goals. Even though the focus of this paper is localiza- ness in massive MIMO systems that can be exploited to tion with mmWave massive MIMO systems, the proposed improve communication and enable location-based ser- localization algorithms are applicable to cmWave bands vices. Performance limits of localization by beamforming as well. This is an important feature of the algorithms with mmWave systems was studied in [15]. The problem because the 3GPP (3rd Generation Partnership Project) of positioning and orientation of subarrays of user nodes group has started to define bands for 5G and the cmWave was investigated in [30, 31]. Papers [32]and [33]propose bandsare expectedtobeusedinthe firstphase of 5G a method for localization/tracking of moving terminals in networks [38]. The contributions of our paper are as dense urban environments in 5G based on intermediate follows: ToA/DoA (time of arrival/direction of arrival) estimates at base stations. The method consists of two steps and is 1. We propose an innovative mmWave massive MIMO implemented using extended Kalman filters and achieves architecture for accurate localization. In the proposed sub-meter accuracy in cmWave. This error is about five concept, the BS uses distributed “subarray units,” times larger than the carrier wavelength but is suffi- which are connected to the fusion center of the BS by cient for location aware communications [24]. In [34], calibrated wired or fiber-optic links. Each subarray a solution to non-cooperative transmitter localization is unit has one “omni antenna” and one phased antenna presented. The solution is based on sectorized antennas subarray (thus, there are two RF chains in total). The and intermediate DoA and RSS (received signal strength) distributed array composed of omni antennas is used estimates at base stations. That paper also provides the for the detection of signal presence (interception), CRBs (Cramér-Rao bounds) for DoA/RSS and localization estimation of time axes misalignment between the errors, and it shows that the methods achieve sub-meter UT and BS, and accurate coherent localization. The accuracy. antenna subarrays are used to estimate the location One may argue that localization, especially in coher- of the UT once its presence has been detected. ent LoS (line-of-sight) scenarios (typical of the mmWave 2. We propose coherent and non-coherent localization band), canhaveprofoundimplicationsonsystemcapac- algorithms. The algorithms are of maximum ity. Namely, if it is possible to localize a UT (user terminal) likelihood (ML)-type for single user and additive with an accuracy much better (by two orders of magni- white Gaussian noise scenarios, but can also be tude) than the carrier wavelength, then it is conceivable applied to multi-user settings because they are to focus energy from distributed transmitters to the loca- user-selective (a user’s code sequence is adopted in tion of the UT (and to possibly other locations, if there the criterion functions of the algorithms). Vukmirovic´ et al. EURASIP Journal on Advances in Signal Processing (2018) 2018:33 Page 3 of 17 3. We formulate a multistage/multiresolution searching error is a small fraction of the carrier wavelength, and and scanning strategy to achieve high localization also to solve the ambiguity problem, inherent to coher- accuracy, which is much better than the carrier ent position estimation. We have proposed an innovative wavelength. The strategy also circumvents the model of a massive MIMO system with distributed phased ambiguity problem. The idea is to split the antenna arrays, formulated a signal model for this system localization process into stages in which increasingly model, proposed a multistage/multiresolution localiza- accurate estimates are made over smaller and smaller tion strategy, and proposed new localization algorithms. domains. The performance of the proposed strategy and its algo- rithms is evaluated by running Monte Carlo simulations In the paper, we also demonstrate the performance in which the signals were generated according to the of the proposed algorithms with extensive simulations. proposed system and signal models, and then the loca- The numerical experiments were carried out to study the tion of the simulated transmitter was estimated using the performance in LoS-only and multipath (LoS + NLoS) proposed strategy. scenarios. The rest of this paper is organized as follows. Section 2.1 2.1 System model of mmWave massive MIMO with introduces the system architecture of the mmWave mas- distributed subarrays sive MIMO system with distributed subarrays, the mul- 2.1.1 System architecture tistage/multiresolution searching and scanning strategy Our system uses a distributed antenna array to selectively for localization, and the mathematical models of the sig- estimate the position of an independent RF transmitter, nals. In Section 2.2, we propose three different classes of Tx, based on its code sequence (known to the system). algorithms for multistage/multiresolution searching and All the antennas, including the transmitting one, are dis- scanning. In Section 3, we demonstrate the performance tributed indoors and are either stationary or slow-moving of the system and the methods with Monte Carlo simu- (see Fig. 1). The slow-moving requirement is needed to lations, and we discuss the obtained results. Concluding allow for neglecting Doppler effects. The receiving anten- remarks are given in Section 4. nas are grouped in M “subarrays.” The distances between the antennas within the same subarray are of the order of 2 Methods the carrier wavelength, λ . The aim of the research is to develop algorithms for coher- The mth subarray has L antennas with positions r = m m,l ent passive localization in massive MIMO systems with x , y , z , m ∈ {1, 2, ... , M},and l ∈ {1, 2, ... , L }. m,l m,l m,l m distributed phased antenna arrays, so that the localization Fig. 1 The system architecture Vukmirovic´ et al. EURASIP Journal on Advances in Signal Processing (2018) 2018:33 Page 4 of 17 The signals from those antennas are inputs to a beam- including the one of the Tx, must match the phase of former, which multiplies them by complex coefficients its local carrier to its clock. With the matching, the car- w that are electronically set in advance (see Fig. 2). rier phase would be 0 at each beginning of observation m,l The output of the mth beamformer is IQ (in-phase interval. quadrature-phase) demodulated and A/D (analog-to- In summary, every antenna unit in the proposed sys- digital) converted to obtain the (complex) samples of the tem includes one omni antenna and one phased antenna mth channel. Further, each subarray has an omnidirec- array (two receiving channels are needed at each antenna unit). Thus, we have two functionally independent, mutu- tional receiving antenna at r = x , y , z with m,0 m,0 m,0 m,0 ally synchronized distributed antenna systems in time and its own A/D converter. Thus, the digital signal processor frequency. (DSP) in the fusion center has access to 2M channels. Another option is to have A/D converters and pro- 2.1.2 Multistage/multiresolution searching and scanning cessing circuitry at the units. Then, they are digitally strategy connected to the fusion center. The system performs detection and location estimation of The Tx antenna is at an unknown position r = (x, y, z) , user transmitters in three stages, Fig. 3.Instage 1, thesys- whereas the three-dimensional positions of all the other tem runs a numerically low-intensive algorithm to detect antennas in the system are known. All the receiving chan- the presence of RF transmissions and to obtain approx- nels are time, phase, and frequency synchronized to each imate estimates of the transmitters’ locations. Only the other. Time synchronization between the Tx and our sys- omni antennas are employed in stage 1, and they can be tem is not required. However, it is assumed that they both used all the time. To start the estimation, the algorithm use the same (known) carrier frequency. To perform the has to wait only for a single period of the Tx sequence. most accurate position estimation, each of the channels, Each omni antenna channel has a bank of as many cross- correlators as there are user sequences of interest. When at least three cross-correlators detect the presence of a sequence s for two-dimensional localization (or four for three-dimensional localization), the algorithm performs coarse localization of this user (with sequence s)overa grid that spans the entire area of interest. The resulting inaccuracy of the estimated locations is expected to be of the order of 10λ or more. In stage 2, another algorithm refines the search of the previous stage by scanning the area around the previous estimates using the subarrays. Since each subarray can only operate with a single set of coefficients w at a m,l time, more than one observation period is needed for a single estimate. The length of the period corresponds to the period of the user sequence. Also, there must be time intervals between the periods so that the beamformers can change their coefficients. Stage 2 can be split into steps 2a, 2b, etc., each cor- responding to beamformers with different beam widths, resolutions, and scan areas. The number of steps depends on the ratio of the resulting root-mean-squared error (RMSE) of stage 1 and the required RMSE of stage 2. The larger the ratio, the more steps should be used to keep the number of observation intervals down. The coefficients in stage 2a are chosen to create relatively wide (sector) beams for the subarrays in order to decrease the num- ber of points on the scan grid, while still providing an SNR (signal-to-noise-ratio) gain compared to that of the omnidirectional antennas. This translates into a smaller number of sequence periods required for estimation. The last step of stage 2 uses the narrowest possible Fig. 2 A phased antenna subarray unit beams for the given subarrays, and it scans the smallest Vukmirovic´ et al. EURASIP Journal on Advances in Signal Processing (2018) 2018:33 Page 5 of 17 Fig. 3 The block scheme of the multistage/multiresolution search strategy area. Each scan point requires a new sequence period. The better. When the Tx is localized with this accuracy and it scan grid needs to be sufficiently fine so that the result- moves, it can be tracked by continuously running the same ing location error is below λ . The overall purpose of this algorithm. stage is to shrink enough the search area so that in the third stage one can solve the so called ambiguity problem, 2.1.3 Signal model discussed later in the text, which is inherent to the applied The Tx prepares a periodic training signal in the following algorithm. way. A complex sequence s = s , s , ... , s , assigned [ ] 0 1 N −1 In stage 3, only one sequence period is needed and only to a user, is repeated multiple times and D/A (digital-to- the signals from the omni antennas are used. The algo- analog) converted with sampling frequency ν . The result- rithm in this stage relies on the phase relations among ing periodic continuous-time signal is s(t),where the the different channels to make the most accurate esti- time variable t in the mathematical model is normalized mates. The search grid is small but very fine because the with 1/ν . For compatibility between the discrete-time resulting error is expected to be of the order of λ /100 or and continuous-time domains, we use normalization of c Vukmirovic´ et al. EURASIP Journal on Advances in Signal Processing (2018) 2018:33 Page 6 of 17 time values with 1/ν and frequencies with ν throughout shift, and F is a modified DFT (discrete Fourier trans- s s −1 H the paper. The real and imaginary components of s(t) are form) matrix such that F = F and whose rows are upconverted to the carrier frequency ν with quadrature sorted by their corresponding natural RF frequencies. carriers. The resulting RF signal is periodic with period More formally, N /ν and its bandwidth is B. The signals in all the channels 2π −jω τ are sampled at the Nyquist rate, which implies B = ν . D = e Diag exp −j τk , (14) s τ The RF signal of the Tx propagates at c = 3 × 10 m/s. 1 2π The lth antenna in the mth subarray receives the signal F = √ exp −j k · n , (15) whose baseband equivalent is N N N u (t) = s (t) + η (t),(1) where n = [0, 1, ... , N − 1] , k = − , − + 1, ... , m,l m,l m,l 2 2 −jω (t +τ ) c 0 m,l − 1 , exp() is the element-by-element exponential s (t) = a e s t − t − τ ,(2) m,l m,l 0 m,l 2 function, and Diag{} is a diagonal matrix with the given where m ∈ {1, 2, ... , M}, l ∈ {0, 1, ... , L }. The index l = elements on its main diagonal. 0 denotes the omni antenna associated with the appropri- ate subarray; a is an unknown real-valued attenuation m,l 2.2 Direct position estimation algorithms coefficient; ω = 2πf and f = ν /ν are normalized c c c c s In this subsection, we describe algorithms for estimating carrier frequencies in radians per sample and cycles per the position of a user with a code sequence s,where the sample, respectively; t is an unknown delay of the start algorithms have different levels of accuracy and numerical of the transmission of a period of the Tx signal rela- complexity. The algorithms are derived for a single-user tive to the receiving system’s time axis; τ = d ν /c m,l m,l scenario; however, if the code sequences of the other users is the propagation delay from the Tx to the appropriate are orthogonal to s, the algorithms can also be applied in receiving antenna where d =r −r ; η (t) is inde- m,l m,l m,l multi-user settings. If the sequences are not orthogonal pendent complex Gaussian noise in the frequency range and the users are sufficiently separated from each other in (−1/2, 1/2). The baseband equivalent of the signal at the space, the algorithms should still work well. output of the mth beamformer is 2.2.1 Coherent algorithms u (t) = s (t) + η (t),(3) m m m First, we discuss coherent algorithms, which rely on dif- ferences of carrier phases among signals from different −jω t +τ c( 0 ) m,l s (t) = w a e s t − t − τ ,(4) m m,l m,l 0 m,l channels and on differences of complex envelopes. We l=1 point out that information about the Tx location is also present in the signal amplitudes; however, we will not use η (t) = w η (t).(5) m m,l m,l it here. l=1 The coherent algorithms only use the signals from the The DSP has access to the samples u (n) and u (n) m m,0 omni antennas; therefore, the available data for process- for m ∈ {1, 2, ... , M} and n ∈ {0, 1, ... , N − 1}. ing include the time samples u (n) for 1 ≤ m ≤ M, m,0 The discrete-time matrix baseband model derived from 0 ≤ n ≤ N − 1. We assume that the noises in the channels (1)–(5)isgiven by have the same power, which is known, so that η (n) has m,0 a circularly symmetric Gaussian probability density func- u = s + η,(6) m,0 m,0 m,0 tion (PDF) with mean 0 and variance σ ,or η (n) ∼ m,0 s = a F D Fs,(7) m,0 m,0 t +τ 2 0 m,0 CN 0, σ , ∀m. In practice, if the noisy data have differ- u = s + η,(8) m m ent powers, they can be scaled by different factors to make L this condition hold. The PDF of the observed data is s = w a F D Fs,(9) m t +τ M m,l m,l 0 m,l 2 2 l=1 f (u ) ∝ exp −u − s  /σ , (16) 0 m,0 m,0 m=1 where where · denotes the Frobenius norm. We want to esti- u = u (0), u (1), ... , u (N − 1) , (10) m,0 m,0 m,0 m,0 mate the unknown parameters of s , ∀m, from which we m,0 η = η (0), η (1), ... , η (N − 1) , (11) m,0 m,0 m,0 can estimate the location of Tx. m,0 According to the ML method, we maximize the u = [u (0), u (1), ... , u (N − 1)] , (12) m m m m likelihood function (also given by (16)) with respect η = η (0), η (1), ... , η (N − 1) , (13) [ ] m m m to the unknown parameters, a , ... , a , t , x, y, z . 1,0 M,0 0 This maximization is equivalent to the minimization of are all N × 1 complex vectors, D is a time-delay-by-τ u − s  , or more specifically of operator that also models the appropriate carrier phase m,0 m,0 m=1 Vukmirovic´ et al. EURASIP Journal on Advances in Signal Processing (2018) 2018:33 Page 7 of 17 H H t = arg max u F D Fs , 1,r t 1,0 1,r 2 2 H H g = a s − 2a Re u F D Fs . t ∈R 1 m,0 t +τ 1,r m,0 m,0 0 m,0 (23) m=1 R = t − 0.5, t + 0.5 . 1,int 1,int (17) In the third step, we estimate with the highest accuracy Note that the propagation times τ implicitly depend m,0 t , by searching in the smallest interval around t ,now 1 1,r on the coordinates of the Tx, x, y, z. relying also on the carrier phase and employing (20). The minimization can be first carried out over Finally, once we obtain t ,weestimatethe location of a (∀m) and then over (t , x, y, z).For given t , x, y, z, m,0 0 0 Tx from the ML estimate of a is given by m,0 H H 2 2 H H ( x, y, z) =arg max max 0,Re u F D Fs . a = arg min a s −2a Re u F D Fs m,0 m,0 t +τ m,0 τ −τ +t m,0 m,0 0 m,0 m,0 1,0 1 x,y,z a ∈ 0,+∞ [ ) m,0 m=1 (24) H H = max 0, Re u F D Fs . t +τ m,0 0 m,0 This is the algorithm we will use in stage 3 of the esti- (18) mation process. Note that this final search grid does not include the t dimension and that the calculation of the Note that negative values are not allowed for the ampli- firstterminthesum(m = 1) can be omitted because it tude a and that the function being minimized is a m,0 is constant. Also, in practice, channel 1 may sometimes second-degree polynomial of a . After substituting (18) m,0 have low SNR, and therefore, another channel should be in (17), we obtain the estimates of t , x, y,and z from selected as a reference. One inherent disadvantage of the coherent algorithms H H is that there are many high and narrow lobes in the cri- t , x, y, z =arg max max 0, Re u F D Fs . 0 t +τ m,0 0 m,0 t ,x,y,z terion function near the true location of the Tx. This is m=1 often referred to as the “ambiguity problem.” Stage 3 relies (19) on stage 2 of the localization to correctly identify the main The above steps represent the coherent ML algorithm. lobe from the side lobes. The search for the best values of (t , x, y, z) must be very 0 Besides the ambiguity problem in the spatial domain, fine, but this would result in high numerical complexity. there is also an ambiguity problem in the estimation of t As an alternative, we propose a statistically suboptimal in the time domain. The resulting effect is an additional approach but numerically much more efficient. Without error which is an integer multiple of 1/f .Thiserror is loss of generality, we select the first channel to be the ref- equal across the channels and (x, y, z). For narrowband erence channel. In a preprocessing step, we estimate the signals, its impact on the localization accuracy is negligi- total delay in that channel, t = t + τ from 1 0 1,0 ble. For wideband signals, on average, this error is smaller than for narrowband signals. H H t = arg max Re u F D Fs . (20) 1 t 1,0 2.2.2 Non-coherent algorithms Now, we discuss algorithms that discard carrier phase dif- This maximization can further be simplified by breaking ferences between signals from different channels, unlike it down into three steps. First, we estimate an integer- the coherent algorithms that exploit these phase differ- valued delay t , dismissing the carrier phase, from 1,int ences. The algorithms use the same data as the ones H H t = arg max u F D Fs , (21) 1,int t 1,0 1,int in Section 2.2.1; however, their criterion functions do 1,int not fluctuate nearly as much over x, y, z and as a result ( ) their estimates are much less accurate. Convenient conse- which reduces to quences of this are that the search grid can be made much t = arg max u s(N − t ), ... , s(N − 1), coarser and that the ambiguity problem does not exist. 1,int 1,int 1,0 t ,int We assume completely unknown phase terms in each channel, ψ ,and write m,0 s(0), ... , s(N − t − 1)  . 1,int jψ H m,0 (22) s = a e F D Fs. (25) m,0 m,0 t +τ 0 m,0 In the second step, we find a fractional, but still a rela- We follow the same reasoning as in Section 2.2.1,except tively rough estimate t by searching in a smaller interval, that negative values are allowed for a since we choose 1,r m,0 say, t ∈ t − 0.5, t + 0.5 , also dismissing the the best phase ψ anyway, and formulate the optimiza- 1 1,int 1,int m,0 carrier phase and using (21), or tion problem as Vukmirovic´ et al. EURASIP Journal on Advances in Signal Processing (2018) 2018:33 Page 8 of 17 ψ , ... , ψ , t , x, y, z 1,0 M,0 0 2, 3, ... , M). Also note that there is no need for the esti- M mate t to be as accurate as in the implementation of the jψ H H m,0 = arg max Re e u F D Fs . coherent algorithm. Therefore, one can skip step 3 of the t +τ m,0 0 m,0 ψ ,...,ψ 1,0 M,0 m=1 method for estimating t accurately. Instead of t ,one can 1 1 t ,x,y,z use t . 1,r (26) 2.2.3 Semi-coherent algorithms We can find the solutions for ψ separately. Namely, m,0 The difference between the coherent and non-coherent for given t , x, y, z, the solutions for ψ are given by 0 m,0 algorithms is in the way how the summation in the cri- H H terion function is used; in the coherent algorithm, it is ψ =− arg u F D Fs , m = 1, 2, ... , M. m,0 t +τ m,0 0 m,0 the real component of the sum that is applied whereas (27) in the non-coherent algorithm, it is the absolute values When these solutions are substituted in (26), we opti- of its terms that are exploited (cf. (24)and (29)). By tak- mize over (t , x, y, z),or ing absolute values, the constant phase differences among channels are lost. We can use this idea to formulate a H H semi-coherent algorithm by taking the appropriate abso- t , x, y, z = arg max u F D Fs . (28) 0 t +τ m,0 0 m,0 lute values before summing over the channels (over m), t ,x,y,z m=1 but after summing over the antennas in each subarray We refer to the algorithm based on the solutions in (over l). In this way, the phase differences between the (27) and the optimization in (28) as the noncoherent ML antennas of the same subarray are preserved, whereas the algorithm. phase differences between subarrays are lost. We also propose a noncoherent ML algorithm with Let us choose a scan grid inside a given area of inter- reduced computational complexity. As in the coherent est, see Figs. 4 and 5.Let r be the position of the SGp algorithm, we first estimate the total delay in channel 1 pth point on the scan grid. Unlike the coherent and non- and use the obtained estimate to search for the coordi- coherent algorithms, for each point on the scan grid, a nates of Tx, or (p) new N-sample-long signal segment, u , ∀m ,isreceived ( ) by the beamformers whose beams have been directed to H H ( x, y, z) = arg max u F D Fs . (29) m,0 τ −τ +t this point. The beams are formed by setting their coeffi- m,0 1,0 1 x,y,z m=1 cients w . The 3 dB widths of the beams are chosen to m,l be greater than the distance between adjacent scan-grid This is the algorithm we will use in stage 1 of the esti- points to avoid degradation due to the grid. The objective mation process. The first term in the sum is constant, so is to estimate p and t by it can be omitted (the index m can take just the values Fig. 4 Stage 2a scanning Vukmirovic´ et al. EURASIP Journal on Advances in Signal Processing (2018) 2018:33 Page 9 of 17 Fig. 5 Stage 2b scanning M L Geometry G consists of five antenna subarrays, each sub- (p)H H (B) (p, t ) = arg max u F D D Fs  , 0 m t 0 τ array having the geometry of an 18-element acoustic cam- m,l p,t m=1 l=1 era scaled down by a factor of 3 [39]. One omni antenna is (30) added to the center of each subarray. The centers are in the (B) plane, z = 0. The omni antennas have the following coor- 2π where D = Diag exp −j τk denotes a baseband dinates x and y in meters: (−2.20, −1.24), (0.18, −2.64), signal time delay matrix without a carrier phase shift, (2.96, −1.06), (2.53, 2.21),and (−2.18, 2.24). They are rep- unlike D . The position estimate of Tx is then r =r . SGp ˆ resented by white triangles in the figures in this section. As before, we can avoid estimating t by estimating t 0 m The positions of the subarrays were chosen by hand in for each omni antenna in preprocessing and then maxi- order to be irregular. The distances between subarrays mizing over p, i.e., were selected to correspond to subarrays placed on the wallsofaroom.The subarrayshaveplanargeometryin M L (p)H H (B) vertical plains, rotated around their vertical axes so that p = arg max u F D D Fs  . ˆ τ t −τ m m,0 m,l their broadside directions (approximately) point to the m=1 l=1 center of the area between subarrays (the room). Geom- (31) etry G is formed from G by scaling up by a factor of 2 1 This is the algorithm we will use in stage 2 of the estima- five the antenna positions in the subarrays with respect tion process. to their centers (omni antennas). The simulations were If the signals are narrowband, the expressions (30)and carried out using a known deterministic sequence, the (31)reduceto(32)and (33), respectively: first of the modulatable orthogonal sequences proposed in [40] for a given N. The parameters were as follows: (p)H −jω t ν = 60 GHz B = 10 MHz, and SNR = 10 dB (if c 0 c 0 ( p, t ) = arg max u e s , (32) 0 m p,t not stated otherwise), where SNR denotes the SNR in m=1 a virtual channel whose antenna is at a distance of 1 m (p)H −jω (t −τ ) c m m,0 from the transmitting antenna. Throughout this section, p = arg max u e s . (33) we assume that the signal power decreases with squared m=1 distance from the transmitter. 3 Numerical results and discussion In the multipath scenario, we simulated a specular mul- This section provides numerical results obtained by the tipath. We simulated only first-order reflected paths off presented algorithms with Monte Carlo simulations for four vertical planes (x =−2.4 m, y =−2.85 m, two scenarios—a LoS-only scenario and a multipath sce- x = 3.15 m, and y = 2.45 m), which represented walls of a nario. We experimented with two distributed receiver room, so that the subarrays are attached to them (at a dis- antenna array geometries for each of the two scenarios. tance of about 20 cm). As in [41], we assumed a ratio of Vukmirovic´ et al. EURASIP Journal on Advances in Signal Processing (2018) 2018:33 Page 10 of 17 LoS component power and the sum of reflected compo- nent powers (the Rice factor) of at least 10 dB. According to the ray-tracing method, the reflected components were modeled as if they were sent by virtual images of the Tx (w.r.t. the walls) according to the LoS model (7) (which includes a time shift, a carrier phase shift, and an attenu- ation). The reflected components were then phase shifted by π, and their sum at each receiving antenna was scaled to get the specified Rice factor. 3.1 Qualitative characterization of the criterion functions This subsection shows the qualitative behavior of the cri- terion functions of the respective algorithms for each of the three localization stages. The Tx was at (0, 0, 0),near the “center” of either G or G .Since stages 1and 3employ 1 2 only omni antennas, the choice of subarray geometry does not matter. The criterion functions are shown over areas lying in the plane z = 0. In Figs. 6, 7, 8, 9, 10,and 11,the true Tx location is marked by a circle with a cross and the estimated location by a square. Fig. 7 Criterion function of stage 1, given by (29) with N = 1024 In order to localize the Tx with accuracy much better than λ , we use the coherent algorithm. Its criterion func- tion has high side lobes and requires a very fine search grid Figure 8 shows the LoS-only criterion function of stage 2 (see Fig. 6). Therefore, we cannot work with it immedi- over an area inside the antenna array for G for N = 1024. ately, but instead we resort to a multistage/multiresolution We have also generated the corresponding criterion func- search. tion for N = 16, but it is not shown because it has the Figure 7 shows the LoS-only criterion function of stage same shape. It also has no side lobes but shows more vari- 1(givenby(29)) over an area inside the antenna array for ations across space compared to the criterion function N = 1024. The function does not have side lobes, it is of stage 1. This function offers better estimation accu- not influenced by carrier phases, it is immune to phase synchronization errors, and it varies slowly across space, racy. Figure 9 shows the same results over a smaller area which suggests that a coarse grid can be used. for geometry G . The figures suggest that the plane wave Fig. 6 The criterion function of stage 3, given by (24) with N = 1024 Fig. 8 Criterion function of stage 2, given by (31) for G with N = 1024 1 Vukmirovic´ et al. EURASIP Journal on Advances in Signal Processing (2018) 2018:33 Page 11 of 17 Fig. 9 Criterion function of stage 2 for G with N = 1024 Fig. 11 Criterion function for stage 2, G , Rice factor 10 dB, and N = 1024 with ray-tracing assumption would not be justified because of the size of subarray apertures. Figure 10 shows the LoS-only criterion function of stage peak of the lobe it has been initialized on (the initializa- 3for N = 1024 over an area around the transmitter tion point is the estimate obtained in stage 2). Clearly, to spanning a little more than the main lobe. As the used prevent the algorithm from converging to a side lobe, the algorithm is coherent (utilizes information in the phase of localization in stage 2 must produce an estimate inside the carrier for localization), the criterion function has side the main lobe of the criterion function of stage 3. In other lobes, separated by approximately 2λ /3. Since we use an words, if the localization error of stage 2 is smaller than adaptive search grid in this stage, the algorithm finds the approximately λ /3, the ambiguity problem is resolved, because the displacement of the center of the main lobe in stage 3 due to noise is small compared to its width without noise. Figure 11 shows the criterion function of stage 2 in the multipath scenario for N = 1024 over an area inside the antenna array for G , along with wall positions and the “rays” from the ray-tracing method. The Rice factor was 10 dB. The figure shows that the localization algorithm is robust w.r.t. the multipath propagation since the lobes corresponding to the reflected rays cannot be seen. The criterion functions for stage 1 and 3 with multipath prop- agation are not given because they are almost identical to the LoS-only ones. 3.2 Quantitative characterization of the algorithms In this subsection, we evaluate the accuracy of the algo- rithms of each stage. As performance metrics, we used both the MSE (mean squared error) and RMSE of the estimates. In Fig. 12, we display the histogram of the SNRs at the antennas of array G (it is similar for G ) for all simulated 1 2 transmitter locations (points of the Tx grid) for SNR = Fig. 10 Criterion function of stage 3, given by (24) with N = 1024 10 dB. Most of the SNRs are between −5and 10dB. Vukmirovic´ et al. EURASIP Journal on Advances in Signal Processing (2018) 2018:33 Page 12 of 17 Fig. 12 Distribution of SNRs at the antennas for simulated Tx locations for SNR = 10 dB The contour plots in the rest of the section were gen- Fig. 14 RMSE/λ of stage 2 for G and N = 1024 erated over a Tx grid of 16 × 16 points that covers most c 1 of the area inside the array to show the error distribution across space. The grid has uniformly spaced points in the plane z = 0. estimate of this stage is far away from the reference In Fig. 13, we plotted the LoS-only RMSEs relative to antenna, another antenna can be adopted as the refer- the carrier wavelength, λ , for stage 1 for N = 1024. For c ence and the process is repeated. Stage 3 could benefit every Tx grid point, we performed 100 Monte Carlo runs from choosing a better reference antenna even more. The and averaged out the results. Note that the accuracy is RMSE of stage 1 varies between 6 and 12 λ in the given generally better near the first antenna because it is used area. These values determine how narrow the search grid as the reference antenna for estimating t .Ifthe position 1 in the next stage can be for a given Tx position, because Fig. 13 RMSE/λ for stage 1 and N = 1024 Fig. 15 RMSE/λ for stage 2 for G and N = 16 c c 2 Vukmirovic´ et al. EURASIP Journal on Advances in Signal Processing (2018) 2018:33 Page 13 of 17 Fig. 16 RMSE/λ of stage 2 for G and N = 1024 c 2 Fig. 18 RMSE/λ of stage 3 and N = 1024 when the main lobe is not missed the grid should include the real Tx position. If the esti- mation errors have Gaussian distributions, the search grid Monte Carlo simulations for every Tx grid point and for the next stage should span an area that is ±2standard computed from them the RMSEs. The same results but deviations of the current stage along each dimension in for G ,and N = 16 and N = 1024, are presented in order to include the real location with probability of 0.95. Figs. 15 and 16. These results are better because of the The LoS-only RMSEs relative to λ for stage 2 for G c 1 increased space between the antennas in the subarrays. and N = 1024 is shown in Fig. 14. Again, we ran 100 Fig. 17 Probability of missing the main lobe in stage 3 due to the Fig. 19 MSE/CRB of stage 3 and N = 1024 when the main lobe is not error in stage 2, for G used in stage 2 and N = 1024 missed Vukmirovic´ et al. EURASIP Journal on Advances in Signal Processing (2018) 2018:33 Page 14 of 17 miss−distance [λ ] −4 −3 −2 −1 0 1 10 10 10 10 10 10 1 1 0.9 0.9 Main lobe G init. 0.8 0.8 G init. 0.7 0.7 0.6 0.6 0.5 0.5 0.4 0.4 0.3 0.3 0.2 0.2 0.1 0.1 0 0 −7 −6 −5 −4 −3 −2 −1 10 10 10 10 10 10 10 miss−distance [m] Fig. 20 Stage 3 error CDF curves for different initializations The increased space produces “narrower beams,” i.e., bet- main lobe has not been missed. Figure 20 shows LoS-only ter spatial selectivity. For N = 1024 and G ,the RMSE CDF (cumulative density function) curves of the stage 3 is below λ /6 over a significant part of the area inside localization error for N = 1024 for three cases: (1) the the array. This allows the search in stage 3 to start some- main lobe is not missed, (2) the stage 3 algorithm is ini- where within the main lobe of its criterion function with a tialized by the results of the stage 2 algorithm for G (see probability of 0.95. Thus, we can argue that the ambiguity Fig. 16), and (3) the stage 3 algorithm is initialized by the problem is avoided with high probability. The simulations results of the stage 2 algorithm for G (see Fig. 14). The in which the analog beamformers had phase quantization CDF curves were obtained for the same Tx grid as for the with a resolution of 3 were also carried out. The results contour plots (e.g., Fig. 13) with five runs for each grid are not shown here because they were almost identical to point. As predicted, the algorithm in case (2) misses the the ones without phase quantization. main lobe only 2% of the time. On the other hand, the The LoS-only results for stage 3 for N = 1024 are plot- algorithm in case (3) misses the main lobe 78% of the time. ted in Figs. 17, 18,and 19. In this experiment, for every Tx For easier comparison of the numerical results for the grid point, we had 1000 Monte Carlo runs. In Fig. 17,we LoS-only scenario, we provide them in Table 1.The first see how the probability of obtaining an estimate from a row shows the RMSE averaged over the Tx grid, the sec- side lobe (or that the main lobe was missed) varies across ond row the RMSE at a point near the center of the the Tx grid. This probability depends on the estimate of array (roughly (0, 0, 0)), and the third row the value not stage2becausethe algorithmofstage 3usesanadaptive exceeded by the RMSE of 80% of the points on the Tx grid. grid that converges to the maximum of the lobe on which The results are for the case when the main lobe in stage 3 it has been initialized. Figure 18 shows the RMSE across is not missed. the Tx grid provided that the main lobe has not been Figure 21 shows CDF curves for different Rice factors missed. As for stage 1, the effect of choosing the reference for all three localization stages for N = 1024. For each antenna can be seen (because the accuracy is better near the reference antenna). In this case, the obtained accuracy Table 1 RMSEs for search/scan stages (G and N = 1024) is of the order of λ /100. For comparison reasons, we have Stage 1 Stage 2 Stage 3 also run simulations for SNR = 20 dB, and the RMSE avg. RMSE 7.56λ (37.8 mm) 0.162λ (0.81 mm) 0.00365λ (0.0182 mm) c c c for the Tx at (0, 0, 0) is λ /963. In Fig. 19,weobserve the cent. RMSE 6.74λ (33.7 mm) 0.16λ (0.8 mm) 0.00317λ (0.0159 mm) c c c statistical efficiency measured as the ratio of MSE and 80% RMSE 8.61λ (43.1 mm) 0.176λ (0.88 mm) 0.00419λ (0.021 mm) c c c Cramér-Rao bound for the stage 3 algorithm when the Probability Vukmirovic´ et al. EURASIP Journal on Advances in Signal Processing (2018) 2018:33 Page 15 of 17 miss−distance [λ ] −4 −3 −2 −1 0 1 2 10 10 10 10 10 10 10 1 1 LoS−only 0.9 0.9 LoS+NLoS (Rice f. 15 dB) LoS+NLoS (Rice f. 10 dB) 0.8 0.8 0.7 0.7 0.6 0.6 0.5 0.5 0.4 0.4 0.3 0.3 0.2 0.2 0.1 0.1 0 0 −7 −6 −5 −4 −3 −2 −1 0 10 10 10 10 10 10 10 10 miss−distance [m] Fig. 21 CDF curves of localization errors for different stages and Rice factors for SNR = 10 dB stage, we show a CDF curve for LoS-only and Rice factor times for Rice factors 15 and 10 dB, respectively. In stage 2, values of 15 and 10 dB. Geometry G was used (in stage 2). the error is increased 1.2 and 1.3 times. In stage 3, the Again, these results hold for outcomes when the main errorincreaseis6and10times.Stage 2isthe leastaffected lobe in stage 3 is not missed. In stage 1, compared to the by multipath propagation thanks to the beam directivity of LoS-only curve, the error is increased roughly 2.5 and 4.3 the subarrays. The vertical line at λ /3 shows whether the miss−distance [λ ] −5 −4 −3 −2 −1 0 1 2 10 10 10 10 10 10 10 10 1 1 LoS−only 0.9 0.9 LoS+NLoS (Rice f. 15 dB) LoS+NLoS (Rice f. 10 dB) 0.8 0.8 0.7 0.7 0.6 0.6 0.5 0.5 0.4 0.4 0.3 0.3 0.2 0.2 0.1 0.1 0 0 −8 −7 −6 −5 −4 −3 −2 −1 0 10 10 10 10 10 10 10 10 10 miss−distance [m] Fig. 22 CDF curves of localization errors for different stages and Rice factors for SNR = 20 dB Probability Probability Vukmirovic´ et al. EURASIP Journal on Advances in Signal Processing (2018) 2018:33 Page 16 of 17 stage 2 estimate is within the main lobe of stage 3 or not. Acknowledgements This work was supported by national project TR32028 “Advanced Techniques This is a critical value for solving the ambiguity problem. for Efficient Use of Spectrum in Wireless Systems.” Even for a Rice factor of 10 dB, the ambiguity problem is solved 90% of the time. Authors’ contributions All authors read and approved the final manuscript. Figure 22 shows the appropriate CDF curves for SNR = 20 dB (instead of 10 dB as in Fig. 21). As expected, the Competing interests results for the LoS-only scenario are better. However, the The authors declare that they have no competing interests. results for the multipath environment are practically the Publisher’s Note same. Therefore, the adverse effect of multipath propaga- Springer Nature remains neutral with regard to jurisdictional claims in tion is greater for higher SNR values. published maps and institutional affiliations. To summarize, as opposed to the existing methods men- tioned in Section 1, which achieve a submeter localization Author details School of Electrical Engineering, University of Belgrade, Belgrade, Serbia. accuracy, the proposed methods improve that accuracy to Innovation Center of School of Electrical Engineering, University of Belgrade, a small fraction of the carrier wavelength, which enables Belgrade, Serbia. Department of Electrical and Computer Engineering, Stony the shift from location-based services to location-based Brook University, New York City, NY, USA. communication for dramatic improvement of a 5G system Received: 5 January 2018 Accepted: 22 May 2018 performance. 4Conclusions References In this paper, we addressed indoor position estimation 1. T Marzetta, Noncooperative cellular wireless with unlimited numbers of base station antennas. IEEE Trans. Wireless Commun. 9(11), 3590–3600 with a millimeter-wave massive MIMO system. We pro- (2010) posed an architecture with distributed antenna units, a 2. E Torkildson, U Madhow, M Rodwell, Indoor millimeter wave MIMO: multistage/multiresolution strategy, and three classes of feasibility and performance. IEEE Trans. Wireless Comunn. 10(12), 4150–4160 (2011) localization algorithms that together achieve RMSE of 3. Z Pi, F Khan, An introduction to millimeter-wave mobile broadband up to three orders better than the carrier wavelength, systems. IEEE Commun. Mag. 49(6), 101–107 (2011) and solve the ambiguity problem, inherent to coherent 4. TS Rappaport, S Sun, R Mayzus, H Zhao, Y Azar, K Wang, GN Wong, JK Schulz, M Samimi, F Gutierrez, Millimeter wave mobile communications algorithms. In the LoS-only scenario, the localization for 5G cellular: It will work! IEEE Access. 1, 335–349 (2013) error is by two to three orders better than the carrier 5. EG Larsson, O Edfors, F Tufvesson, TL Marzetta, Massive MIMO for next wavelength, whereas in the specular multipath scenario, generation wireless systems. IEEE Commun. Mag. 52(2), 186–195 (2014) 6. AL Swindlehurst, E Ayanoglu, P Heydari, F Capolino, Millimeter-wave it is up to 10 times worse for realistic Rice factors, massive MIMO: the next wireless revolution. IEEE Commun. Mag. 52(9), but still well below the carrier wavelength. The strat- 56–62 (2014) egy does not require channel-state information and is 7. RW Heath, N González-Prelcic Rangan, W Roh, A Sayeed, An overview of signal processing techniques for millimeter wave MIMO systems. IEEE J. applicable in multi-user scenarios, but requires domi- Sel. Topics Signal Process. 10(3), 436–453 (2016) nant LoS propagation. The studied signal model is inher- 8. V Venkateswaran, AJ van der Veen, Analog beamforming in mimo ently wideband, and it assumes spherical wavefronts. communications with phase shift networks and online channel estimation. IEEE Trans. Signal Process. 58(8), 4131–4143 (2010) The execution of the algorithms can be partially dis- 9. J Brady, N Behdad, AM Sayeed, Beamspace MIMO for millimeter-wave tributed among the subarray units. The obtained accuracy communications: system architecture, modeling, analysis, and allows the base station array to focus energy to the posi- measurements. IEEE Trans. Antennas Propag. 61(7), 3814–3827 (2013) 10. S Hur, T Kim, DJ Love, JV Krogmeier, TA Thomas, A Ghosh, Millimeter wave tion of the localized user terminal on downlink and to beamforming for wireless backhaul and access in small cell networks. receive its uplink signal emitted with decreased power. IEEE Trans. Commun. 61(10), 4391–4403 (2013) This can dramatically improve the overall capacity of the 11. A Alkhateeb, J Mo, N Gonzalez-Prelcic, RW Heath, MIMO precoding and combining solutions for millimeter-wave systems. IEEE Commun. Mag. millimeter-wave massive MIMO system. An open issue is 52(12), 122–131 (2014) positioning of the BS antennas with accuracy greater than 12. S Han, I Chih-Lin, Z Xu, C Rowell, Large-scale antenna systems with hybrid that of the localization, including the orientation of the analog and digital beamforming for millimeter wave 5G. IEEE Commun. Mag. 53(1), 186–194 (2015) subarrays. 13. J Li, L Xiao, X Xu, S Zhou, Robust and low complexity hybrid beamforming for uplink multiuser mmwave MIMO systems. IEEE Commun. Lett. 20(6), Abbreviations 1140–1143 (2016) 3GPP: 3rd Generation Partnership Project; 5G: 5th generation; A/D: Analog-to-digital; 14. JC Chen, Hybrid beamforming with discrete phase shifters for BS: Base station; CDF: Cumulative density function; DoA: Direction of arrival; millimeter-wave massive MIMO systems. IEEE Trans. Veh. Technol. 66(8), CRB: Cramér-rao bound; D/A: Digital-to-analog; DFT: Discrete Fourier transform; 7604–7608 (2017) DSP: Digital signal processor; IQ: In-phase quadrature-phase; LoS: Line-of-sight; 15. A Guerra, F Guidi, D Dardari, On the impact of beamforming strategy on MIMO: Multiple-input-multiple-output; ML: Maximum likelihood; MSE: Mean mm-wave localization performance limits. Presented at 2017 IEEE Int. squared error; NLoS: Non-line-of-sight; PDF: Probability density function; RF: Conf. Commun. Workshops, Paris, 21-25 May 2017 Radio frequency; RFID: Radio frequency identification; RMSE: Root mean 16. Y Zhu, T Yang, Low complexity hybrid beamforming for uplink multiuser squared error; RSS: Received signal strength; RSSI: Received signal strength mmwave MIMO systems. Presented at 2017 IEEE Wireless Commun. indicator; SNR: Signal-to-noise-ratio; ToA: Time of arrival; Tx: Transmitter; UT: Netw. Conf. (WCNC), San Francisco, 19-22 Mar 2017 User terminal Vukmirovic´ et al. EURASIP Journal on Advances in Signal Processing (2018) 2018:33 Page 17 of 17 17. AF Molisch, VV Ratnam, S Han, Z Li, SLH Nguyen, L Li, K Haneda, Hybrid 38. J Lee, E Tejedor, K Ranta-aho, H Wang, K Lee, E Semaan, E Mohyeldin, beamforming for massive MIMO: A survey. IEEE Commun. Mag. 55(9), J Song, C Bergljung, S Jung, Spectrum for 5G: Global status, challenges, 134–141 (2017) and enabling technologies. IEEE Commun. Mag. 56(3), 12–18 (2018) 18. TS Rappaport, F Gutierrez, E Ben-Dor, JN Murdock, Y Qiao, JI Tamir, 39. PULSE Beamforming System with 18-channel sector wheel array based Broadband millimeter-wave propagation measurements and models on beamforming type 8608 Bruel Kjoer Product information. https:// using adaptive-beam antennas for outdoor urban cellular www.bksv.com/~/media/literature/Product%20Data/bn1467.ashx. communications. IEEE Trans. Antennas Propag. 61(4), 1850–1859 (2013) Accessed 30 May 2018 19. N Iqbal, C Schneider, J Luo, D Dupleich, RS Thöma, Modeling of 40. N Suehiro, M Hatory, Modulatable orthogonal sequences and their directional fading channels for millimeter wave systems. Presented at application to SSMA systems. IEEE Trans. Inf. Theory. 34(1), 93–100 (1988) 2017 IEEE 86th Veh. Technol. Conf. (VTC Fall), Toronto, 24-27 Sept 2017 41. H Xu, V Kukshya, TS Rappaport, Spatial and temporal characterization of 20. N Iqbal, J Luo, Y Xin, R Müller, S Haefner, RS Thöma, Measurements based 60 GHz indoor channels. Presented at Fall 2000 IEEE Veh. Technol. Conf., interference analysis at millimeter wave frequencies in an indoor Boston, 24-28 Sept 2000 scenario. Presented at 2017 IEEE Globecom, Singapore, 4-8 Dec 2017 21. TS Rappaport, JN Murdock, F Gutierrez, State of the art in 60-Ghz integrated circuits and systems for wireless communications. Proc. IEEE. 99(8), 1390–1436 (2011) 22. W Roh, JY Seol, J Park, B Lee, J Lee, Y Kim, Y Cho, K Cheun, F Aryanfar, Millimeter-wave beamforming as an enabling technology for 5G cellular communications: theoretical feasibility and prototype results. IEEE Commun. Mag. 52(2), 106–113 (2014) 23. S Malkowsky, J Vieira, L Liu, P Harris, K Nieman, N Kundargi, IC Wong, F Tufvesson, V Öwall, O Edfors, The worlds first real-time testbed for massive MIMO: Design, implementation, and validation. IEEE Access. 5, 9073–9088 (2017) 24. R Di Taranto, S Muppirisetty, R Raulefs, D Slock, T Svensson, H Wymeersch, Location-aware communications for 5G networks: how location information can improve scalability, latency, and robustness of 5G. IEEE Signal Process. Mag. 31(6), 102–112 (2014) 25. K Witrisal, P Meissner, E Leitinger, Y Shen, C Gustafson, F Tufvesson, K Haneda, D Dardari, A Molisch, A Conti, MZ Win, High-accuracy localization for assisted living: 5G systems will turn multipath channels from foe to friend. IEEE Signal Process. Mag. 33(2), 59–70 (2016) 26. M Vari, D Cassioli, mmWaves RSSI indoor network localization. Presented at 2014 IEEE Int. Conf. Commun. Workshops (ICC), Sydney, 10-14 June 27. V Savic, EG Larsson, Fingerprinting-based positioning in distributed massive MIMO systems. Presented at IEEE 82nd Veh. Technol. Conf. (VTC Fall), Boston, 6-19 Sept 2015 28. N Garcia, H Wymeersch, EG Larsson, AM Haimovich, M Coulon, Direct localization for massive MIMO. IEEE Trans. Signal Process. 65(10), 2475–2487 (2017) 29. T Wei, X Zhang, mTrack: high-precision passive tracking using millimeter wave radios. Presented at (2015) 21st Annual Int. Conf. Mobile Comput. Netw. Mobicom ’15, Paris, 7-11 Sept 2015 30. A Guerra, F Guidi, D Dardari, Position and orientation error bound for wideband massive antenna arrays. Presented at 2015 IEEE Int. Conf. Commun. Workshops (ICC), London, 8-12 June 2015 31. A Shahmansoori, G Garcia, G Destino, G Seco-Granados, H Wymeersch, 5G position and orientation estimation through millimeter wave MIMO. Presented at (2015) IEEE Globecom Workshops, San Diego, 6-10 Dec 2015 32. M Koivisto, M Costa, J Werner, K Heiska, J Talvitie, K Leppänen, V Koivunen, M Valkama, Joint device positioning and clock synchronization in 5G ultra-dense networks. IEEE Trans. Wireless Commun. 16(5), 2866–2881 (2017) 33. M Koivisto, A Hakkarainen, M Costa, P Kela, K Leppänen, M Valkama, High-efficiency device positioning and location-aware communications in dense 5G networks. IEEE Commun. Mag. 55(8), 188–195 (2017) 34. J Werner, J Wang, A Hakkarainen, D Cabric, M Valkama, Performance and Cramer-Rao bounds for DoA/RSS estimation and transmitter localization using sectorized antennas. IEEE Trans. Veh. Technol. 65(5), 3255–3270 (2016) 35. M Scherhäufl, M Pichler, A Stelzer, UHF RFID localization based on phase evaluation of passive tag arrays. IEEE Trans. Instrum. Meas. 64(14), 913–922 (2015) 36. M Oispuu, U Nickel, 3D passive source localization by a multi-array network: Noncoherent vs.coherent processing. Presented at Int. ITG Workshop Smart Antennas, Bremen, 23-24 Feb 2010 37. N Hadaschik, B Sackenreuter, M Schäfer, M Faßbinder, Direct positioning with multiple antenna arrays. Presented at (2015). Int. Cong. Indoor Posit. Indoor Navig. (IPIN), Bremen, 13-16 Oct 2015 http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png EURASIP Journal on Advances in Signal Processing Springer Journals

Position estimation with a millimeter-wave massive MIMO system based on distributed steerable phased antenna arrays

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Copyright © 2018 by The Author(s)
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Engineering; Signal,Image and Speech Processing; Quantum Information Technology, Spintronics
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Abstract

In this paper, we propose a massive MIMO (multiple-input-multiple-output) architecture with distributed steerable phased antenna subarrays for position estimation in the mmWave range. We also propose localization algorithms and a multistage/multiresolution search strategy that resolve the problem of high side lobes, which is inherent in spatially coherent localization. The proposed system is intended for use in line-of-sight indoor environments. Time synchronization between the transmitter and the receiving system is not required, and the algorithms can also be applied to a multiuser scenario. The simulation results for the line-of-sight-only and specular multipath scenarios show that the localization error is only a small fraction of the carrier wavelength and that it can be achieved under reasonable system parameters including signal-to-noise ratios, antenna number/placement, and subarray apertures. The proposed concept has the potential of significantly improving the capacity and spectral/energy efficiency of future mmWave massive MIMO systems. Keywords: Direct position estimation, mmWave, Massive MIMO, Steerable phased antenna arrays, Wireless indoor localization 1 Introduction channels between pairs of antennas are assumed uncorre- Millimeter-wave (mmWave) communication and mas- lated, in massive MIMO systems there is a large number of sive MIMO (multiple-input-multiple-output) are disrup- antennas at a base station (BS). The antennas of the system tive technologies for cellular 5G (5th generation) systems. form beams toward low-cost user devices with spatially Not surprisingly, they have been in the focus of inten- separated single antennas [1]. Many antennas are required sive research efforts in both academia and industry in in the mmWave band because of the high pathloss and the last decade. The application of massive MIMO sys- the need for large antenna gains to obtain sufficiently high tems in themmWavebandrepresentsabigresearchand signal-to-noise ratios (SNRs). technological challenge. Since the work of Marzetta in Traditionally, beamforming by the antennas is realized 2010 [1], there have been many technical papers on this completely in the digital domain. This entails that every technology. Some address system issues [2–6], and others antenna has its own radio-frequency (RF) chain (a low- signal processing [7], analog and hybrid beamforming noise amplifier, a down-converter, an A/D converter at [8–17], propagation and channel modeling/measurement the receiving side, a D/A converter, up-converter, and a [18–20], technological aspects [21], and practical imple- power amplifier at the transmitting side), which renders mentations [22, 23]. the application of massive MIMO in mmWave impracti- Multi-user MIMO systems referred to as massive MIMO cal due to high cost and energy consumption. A promising systems were introduced in [1]. Unlike in conventional M solution to these problems lies in the concept of hybrid IMO systems for point-to-point communications where the transceivers, which use a combination of analog beam- forming in the RF domain and digital beamforming in the baseband to allow for RF circuits with a smaller number *Correspondence: vn135023p@student.etf.bg.ac.rs School of Electrical Engineering, University of Belgrade, Belgrade, Serbia of up/down conversion chains. In practice, a beamformer Full list of author information is available at the end of the article is usually implemented as an array of phase shifters with © The Author(s). 2018 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. Vukmirovic´ et al. EURASIP Journal on Advances in Signal Processing (2018) 2018:33 Page 2 of 17 only a discrete set of possible shifts (phase quantization) are more users) with greatly reduced interference levels [7]. Interest in hybrid transceivers has accelerated over to other users. This clearly suggests that accurate location the past 3 years (especially following [7]), and as a result, awareness enables location-aided communication. various structures have already been proposed. Our previous research has confirmed that in a spatially In the wide literature, there are only a few papers dealing coherent scenario (where the LoS component is dominant with localization with mmWave massive MIMO systems. and where the carrier phase changes predictably over dis- The authors of [24] surveyed applications of localiza- tance), a distributed antenna array and direct localization tion in massive MIMO systems and state that the 5G algorithms can achieve localization accuracy much bet- technology is expected to allow localization accuracy of ter than the carrier wavelength (by two to three orders of 1 cm, which is twice the carrier wavelength at 60 GHz magnitude). In [35], it was reported that accuracy of 30% (around 5 mm). In [25], high-accuracy localization with of carrier wavelength in RFID (radio frequency identifica- mmWave systems in applications related to assisted living tion) localization was achieved. Localization in a spatially and location awareness was considered. It was concluded coherent scenario was also addressed in [36, 37]. The that “future 5G mmWave communication systems could spatially coherent approach suffers from high side lobes be an ideal platform for achieving high-accuracy indoor in the criterion function (localization ambiguity). This localization.” The performance of localization based on problem of side lobes is similar in nature to the one of the RSSI (received signal strength indicator) principle side/grating lobes in direction of arrival estimation with applied to the mmWave range was investigated in [26], classical antenna arrays. In this paper, we aim at achieving a high localization and it was found that it was possible to achieve accu- accuracy with distributed antenna subarrays in mmWave, racy of around 1 m. A fingerprint-based localization was where the accuracy would be much better than the carrier presented in [27], and a method for direct localization wavelength. At the same time, we also resolve the problem was introduced in [28]. In [29], the authors presented an of localization ambiguity. New research problems arise mTrack system for high precision passive object tracking with this including designing an architecture of such sys- at 60 GHz and claimed that submillimeter accuracy could tem and formulating algorithms which achieve these two be achieved. This accuracy can provide location aware- goals. Even though the focus of this paper is localiza- ness in massive MIMO systems that can be exploited to tion with mmWave massive MIMO systems, the proposed improve communication and enable location-based ser- localization algorithms are applicable to cmWave bands vices. Performance limits of localization by beamforming as well. This is an important feature of the algorithms with mmWave systems was studied in [15]. The problem because the 3GPP (3rd Generation Partnership Project) of positioning and orientation of subarrays of user nodes group has started to define bands for 5G and the cmWave was investigated in [30, 31]. Papers [32]and [33]propose bandsare expectedtobeusedinthe firstphase of 5G a method for localization/tracking of moving terminals in networks [38]. The contributions of our paper are as dense urban environments in 5G based on intermediate follows: ToA/DoA (time of arrival/direction of arrival) estimates at base stations. The method consists of two steps and is 1. We propose an innovative mmWave massive MIMO implemented using extended Kalman filters and achieves architecture for accurate localization. In the proposed sub-meter accuracy in cmWave. This error is about five concept, the BS uses distributed “subarray units,” times larger than the carrier wavelength but is suffi- which are connected to the fusion center of the BS by cient for location aware communications [24]. In [34], calibrated wired or fiber-optic links. Each subarray a solution to non-cooperative transmitter localization is unit has one “omni antenna” and one phased antenna presented. The solution is based on sectorized antennas subarray (thus, there are two RF chains in total). The and intermediate DoA and RSS (received signal strength) distributed array composed of omni antennas is used estimates at base stations. That paper also provides the for the detection of signal presence (interception), CRBs (Cramér-Rao bounds) for DoA/RSS and localization estimation of time axes misalignment between the errors, and it shows that the methods achieve sub-meter UT and BS, and accurate coherent localization. The accuracy. antenna subarrays are used to estimate the location One may argue that localization, especially in coher- of the UT once its presence has been detected. ent LoS (line-of-sight) scenarios (typical of the mmWave 2. We propose coherent and non-coherent localization band), canhaveprofoundimplicationsonsystemcapac- algorithms. The algorithms are of maximum ity. Namely, if it is possible to localize a UT (user terminal) likelihood (ML)-type for single user and additive with an accuracy much better (by two orders of magni- white Gaussian noise scenarios, but can also be tude) than the carrier wavelength, then it is conceivable applied to multi-user settings because they are to focus energy from distributed transmitters to the loca- user-selective (a user’s code sequence is adopted in tion of the UT (and to possibly other locations, if there the criterion functions of the algorithms). Vukmirovic´ et al. EURASIP Journal on Advances in Signal Processing (2018) 2018:33 Page 3 of 17 3. We formulate a multistage/multiresolution searching error is a small fraction of the carrier wavelength, and and scanning strategy to achieve high localization also to solve the ambiguity problem, inherent to coher- accuracy, which is much better than the carrier ent position estimation. We have proposed an innovative wavelength. The strategy also circumvents the model of a massive MIMO system with distributed phased ambiguity problem. The idea is to split the antenna arrays, formulated a signal model for this system localization process into stages in which increasingly model, proposed a multistage/multiresolution localiza- accurate estimates are made over smaller and smaller tion strategy, and proposed new localization algorithms. domains. The performance of the proposed strategy and its algo- rithms is evaluated by running Monte Carlo simulations In the paper, we also demonstrate the performance in which the signals were generated according to the of the proposed algorithms with extensive simulations. proposed system and signal models, and then the loca- The numerical experiments were carried out to study the tion of the simulated transmitter was estimated using the performance in LoS-only and multipath (LoS + NLoS) proposed strategy. scenarios. The rest of this paper is organized as follows. Section 2.1 2.1 System model of mmWave massive MIMO with introduces the system architecture of the mmWave mas- distributed subarrays sive MIMO system with distributed subarrays, the mul- 2.1.1 System architecture tistage/multiresolution searching and scanning strategy Our system uses a distributed antenna array to selectively for localization, and the mathematical models of the sig- estimate the position of an independent RF transmitter, nals. In Section 2.2, we propose three different classes of Tx, based on its code sequence (known to the system). algorithms for multistage/multiresolution searching and All the antennas, including the transmitting one, are dis- scanning. In Section 3, we demonstrate the performance tributed indoors and are either stationary or slow-moving of the system and the methods with Monte Carlo simu- (see Fig. 1). The slow-moving requirement is needed to lations, and we discuss the obtained results. Concluding allow for neglecting Doppler effects. The receiving anten- remarks are given in Section 4. nas are grouped in M “subarrays.” The distances between the antennas within the same subarray are of the order of 2 Methods the carrier wavelength, λ . The aim of the research is to develop algorithms for coher- The mth subarray has L antennas with positions r = m m,l ent passive localization in massive MIMO systems with x , y , z , m ∈ {1, 2, ... , M},and l ∈ {1, 2, ... , L }. m,l m,l m,l m distributed phased antenna arrays, so that the localization Fig. 1 The system architecture Vukmirovic´ et al. EURASIP Journal on Advances in Signal Processing (2018) 2018:33 Page 4 of 17 The signals from those antennas are inputs to a beam- including the one of the Tx, must match the phase of former, which multiplies them by complex coefficients its local carrier to its clock. With the matching, the car- w that are electronically set in advance (see Fig. 2). rier phase would be 0 at each beginning of observation m,l The output of the mth beamformer is IQ (in-phase interval. quadrature-phase) demodulated and A/D (analog-to- In summary, every antenna unit in the proposed sys- digital) converted to obtain the (complex) samples of the tem includes one omni antenna and one phased antenna mth channel. Further, each subarray has an omnidirec- array (two receiving channels are needed at each antenna unit). Thus, we have two functionally independent, mutu- tional receiving antenna at r = x , y , z with m,0 m,0 m,0 m,0 ally synchronized distributed antenna systems in time and its own A/D converter. Thus, the digital signal processor frequency. (DSP) in the fusion center has access to 2M channels. Another option is to have A/D converters and pro- 2.1.2 Multistage/multiresolution searching and scanning cessing circuitry at the units. Then, they are digitally strategy connected to the fusion center. The system performs detection and location estimation of The Tx antenna is at an unknown position r = (x, y, z) , user transmitters in three stages, Fig. 3.Instage 1, thesys- whereas the three-dimensional positions of all the other tem runs a numerically low-intensive algorithm to detect antennas in the system are known. All the receiving chan- the presence of RF transmissions and to obtain approx- nels are time, phase, and frequency synchronized to each imate estimates of the transmitters’ locations. Only the other. Time synchronization between the Tx and our sys- omni antennas are employed in stage 1, and they can be tem is not required. However, it is assumed that they both used all the time. To start the estimation, the algorithm use the same (known) carrier frequency. To perform the has to wait only for a single period of the Tx sequence. most accurate position estimation, each of the channels, Each omni antenna channel has a bank of as many cross- correlators as there are user sequences of interest. When at least three cross-correlators detect the presence of a sequence s for two-dimensional localization (or four for three-dimensional localization), the algorithm performs coarse localization of this user (with sequence s)overa grid that spans the entire area of interest. The resulting inaccuracy of the estimated locations is expected to be of the order of 10λ or more. In stage 2, another algorithm refines the search of the previous stage by scanning the area around the previous estimates using the subarrays. Since each subarray can only operate with a single set of coefficients w at a m,l time, more than one observation period is needed for a single estimate. The length of the period corresponds to the period of the user sequence. Also, there must be time intervals between the periods so that the beamformers can change their coefficients. Stage 2 can be split into steps 2a, 2b, etc., each cor- responding to beamformers with different beam widths, resolutions, and scan areas. The number of steps depends on the ratio of the resulting root-mean-squared error (RMSE) of stage 1 and the required RMSE of stage 2. The larger the ratio, the more steps should be used to keep the number of observation intervals down. The coefficients in stage 2a are chosen to create relatively wide (sector) beams for the subarrays in order to decrease the num- ber of points on the scan grid, while still providing an SNR (signal-to-noise-ratio) gain compared to that of the omnidirectional antennas. This translates into a smaller number of sequence periods required for estimation. The last step of stage 2 uses the narrowest possible Fig. 2 A phased antenna subarray unit beams for the given subarrays, and it scans the smallest Vukmirovic´ et al. EURASIP Journal on Advances in Signal Processing (2018) 2018:33 Page 5 of 17 Fig. 3 The block scheme of the multistage/multiresolution search strategy area. Each scan point requires a new sequence period. The better. When the Tx is localized with this accuracy and it scan grid needs to be sufficiently fine so that the result- moves, it can be tracked by continuously running the same ing location error is below λ . The overall purpose of this algorithm. stage is to shrink enough the search area so that in the third stage one can solve the so called ambiguity problem, 2.1.3 Signal model discussed later in the text, which is inherent to the applied The Tx prepares a periodic training signal in the following algorithm. way. A complex sequence s = s , s , ... , s , assigned [ ] 0 1 N −1 In stage 3, only one sequence period is needed and only to a user, is repeated multiple times and D/A (digital-to- the signals from the omni antennas are used. The algo- analog) converted with sampling frequency ν . The result- rithm in this stage relies on the phase relations among ing periodic continuous-time signal is s(t),where the the different channels to make the most accurate esti- time variable t in the mathematical model is normalized mates. The search grid is small but very fine because the with 1/ν . For compatibility between the discrete-time resulting error is expected to be of the order of λ /100 or and continuous-time domains, we use normalization of c Vukmirovic´ et al. EURASIP Journal on Advances in Signal Processing (2018) 2018:33 Page 6 of 17 time values with 1/ν and frequencies with ν throughout shift, and F is a modified DFT (discrete Fourier trans- s s −1 H the paper. The real and imaginary components of s(t) are form) matrix such that F = F and whose rows are upconverted to the carrier frequency ν with quadrature sorted by their corresponding natural RF frequencies. carriers. The resulting RF signal is periodic with period More formally, N /ν and its bandwidth is B. The signals in all the channels 2π −jω τ are sampled at the Nyquist rate, which implies B = ν . D = e Diag exp −j τk , (14) s τ The RF signal of the Tx propagates at c = 3 × 10 m/s. 1 2π The lth antenna in the mth subarray receives the signal F = √ exp −j k · n , (15) whose baseband equivalent is N N N u (t) = s (t) + η (t),(1) where n = [0, 1, ... , N − 1] , k = − , − + 1, ... , m,l m,l m,l 2 2 −jω (t +τ ) c 0 m,l − 1 , exp() is the element-by-element exponential s (t) = a e s t − t − τ ,(2) m,l m,l 0 m,l 2 function, and Diag{} is a diagonal matrix with the given where m ∈ {1, 2, ... , M}, l ∈ {0, 1, ... , L }. The index l = elements on its main diagonal. 0 denotes the omni antenna associated with the appropri- ate subarray; a is an unknown real-valued attenuation m,l 2.2 Direct position estimation algorithms coefficient; ω = 2πf and f = ν /ν are normalized c c c c s In this subsection, we describe algorithms for estimating carrier frequencies in radians per sample and cycles per the position of a user with a code sequence s,where the sample, respectively; t is an unknown delay of the start algorithms have different levels of accuracy and numerical of the transmission of a period of the Tx signal rela- complexity. The algorithms are derived for a single-user tive to the receiving system’s time axis; τ = d ν /c m,l m,l scenario; however, if the code sequences of the other users is the propagation delay from the Tx to the appropriate are orthogonal to s, the algorithms can also be applied in receiving antenna where d =r −r ; η (t) is inde- m,l m,l m,l multi-user settings. If the sequences are not orthogonal pendent complex Gaussian noise in the frequency range and the users are sufficiently separated from each other in (−1/2, 1/2). The baseband equivalent of the signal at the space, the algorithms should still work well. output of the mth beamformer is 2.2.1 Coherent algorithms u (t) = s (t) + η (t),(3) m m m First, we discuss coherent algorithms, which rely on dif- ferences of carrier phases among signals from different −jω t +τ c( 0 ) m,l s (t) = w a e s t − t − τ ,(4) m m,l m,l 0 m,l channels and on differences of complex envelopes. We l=1 point out that information about the Tx location is also present in the signal amplitudes; however, we will not use η (t) = w η (t).(5) m m,l m,l it here. l=1 The coherent algorithms only use the signals from the The DSP has access to the samples u (n) and u (n) m m,0 omni antennas; therefore, the available data for process- for m ∈ {1, 2, ... , M} and n ∈ {0, 1, ... , N − 1}. ing include the time samples u (n) for 1 ≤ m ≤ M, m,0 The discrete-time matrix baseband model derived from 0 ≤ n ≤ N − 1. We assume that the noises in the channels (1)–(5)isgiven by have the same power, which is known, so that η (n) has m,0 a circularly symmetric Gaussian probability density func- u = s + η,(6) m,0 m,0 m,0 tion (PDF) with mean 0 and variance σ ,or η (n) ∼ m,0 s = a F D Fs,(7) m,0 m,0 t +τ 2 0 m,0 CN 0, σ , ∀m. In practice, if the noisy data have differ- u = s + η,(8) m m ent powers, they can be scaled by different factors to make L this condition hold. The PDF of the observed data is s = w a F D Fs,(9) m t +τ M m,l m,l 0 m,l 2 2 l=1 f (u ) ∝ exp −u − s  /σ , (16) 0 m,0 m,0 m=1 where where · denotes the Frobenius norm. We want to esti- u = u (0), u (1), ... , u (N − 1) , (10) m,0 m,0 m,0 m,0 mate the unknown parameters of s , ∀m, from which we m,0 η = η (0), η (1), ... , η (N − 1) , (11) m,0 m,0 m,0 can estimate the location of Tx. m,0 According to the ML method, we maximize the u = [u (0), u (1), ... , u (N − 1)] , (12) m m m m likelihood function (also given by (16)) with respect η = η (0), η (1), ... , η (N − 1) , (13) [ ] m m m to the unknown parameters, a , ... , a , t , x, y, z . 1,0 M,0 0 This maximization is equivalent to the minimization of are all N × 1 complex vectors, D is a time-delay-by-τ u − s  , or more specifically of operator that also models the appropriate carrier phase m,0 m,0 m=1 Vukmirovic´ et al. EURASIP Journal on Advances in Signal Processing (2018) 2018:33 Page 7 of 17 H H t = arg max u F D Fs , 1,r t 1,0 1,r 2 2 H H g = a s − 2a Re u F D Fs . t ∈R 1 m,0 t +τ 1,r m,0 m,0 0 m,0 (23) m=1 R = t − 0.5, t + 0.5 . 1,int 1,int (17) In the third step, we estimate with the highest accuracy Note that the propagation times τ implicitly depend m,0 t , by searching in the smallest interval around t ,now 1 1,r on the coordinates of the Tx, x, y, z. relying also on the carrier phase and employing (20). The minimization can be first carried out over Finally, once we obtain t ,weestimatethe location of a (∀m) and then over (t , x, y, z).For given t , x, y, z, m,0 0 0 Tx from the ML estimate of a is given by m,0 H H 2 2 H H ( x, y, z) =arg max max 0,Re u F D Fs . a = arg min a s −2a Re u F D Fs m,0 m,0 t +τ m,0 τ −τ +t m,0 m,0 0 m,0 m,0 1,0 1 x,y,z a ∈ 0,+∞ [ ) m,0 m=1 (24) H H = max 0, Re u F D Fs . t +τ m,0 0 m,0 This is the algorithm we will use in stage 3 of the esti- (18) mation process. Note that this final search grid does not include the t dimension and that the calculation of the Note that negative values are not allowed for the ampli- firstterminthesum(m = 1) can be omitted because it tude a and that the function being minimized is a m,0 is constant. Also, in practice, channel 1 may sometimes second-degree polynomial of a . After substituting (18) m,0 have low SNR, and therefore, another channel should be in (17), we obtain the estimates of t , x, y,and z from selected as a reference. One inherent disadvantage of the coherent algorithms H H is that there are many high and narrow lobes in the cri- t , x, y, z =arg max max 0, Re u F D Fs . 0 t +τ m,0 0 m,0 t ,x,y,z terion function near the true location of the Tx. This is m=1 often referred to as the “ambiguity problem.” Stage 3 relies (19) on stage 2 of the localization to correctly identify the main The above steps represent the coherent ML algorithm. lobe from the side lobes. The search for the best values of (t , x, y, z) must be very 0 Besides the ambiguity problem in the spatial domain, fine, but this would result in high numerical complexity. there is also an ambiguity problem in the estimation of t As an alternative, we propose a statistically suboptimal in the time domain. The resulting effect is an additional approach but numerically much more efficient. Without error which is an integer multiple of 1/f .Thiserror is loss of generality, we select the first channel to be the ref- equal across the channels and (x, y, z). For narrowband erence channel. In a preprocessing step, we estimate the signals, its impact on the localization accuracy is negligi- total delay in that channel, t = t + τ from 1 0 1,0 ble. For wideband signals, on average, this error is smaller than for narrowband signals. H H t = arg max Re u F D Fs . (20) 1 t 1,0 2.2.2 Non-coherent algorithms Now, we discuss algorithms that discard carrier phase dif- This maximization can further be simplified by breaking ferences between signals from different channels, unlike it down into three steps. First, we estimate an integer- the coherent algorithms that exploit these phase differ- valued delay t , dismissing the carrier phase, from 1,int ences. The algorithms use the same data as the ones H H t = arg max u F D Fs , (21) 1,int t 1,0 1,int in Section 2.2.1; however, their criterion functions do 1,int not fluctuate nearly as much over x, y, z and as a result ( ) their estimates are much less accurate. Convenient conse- which reduces to quences of this are that the search grid can be made much t = arg max u s(N − t ), ... , s(N − 1), coarser and that the ambiguity problem does not exist. 1,int 1,int 1,0 t ,int We assume completely unknown phase terms in each channel, ψ ,and write m,0 s(0), ... , s(N − t − 1)  . 1,int jψ H m,0 (22) s = a e F D Fs. (25) m,0 m,0 t +τ 0 m,0 In the second step, we find a fractional, but still a rela- We follow the same reasoning as in Section 2.2.1,except tively rough estimate t by searching in a smaller interval, that negative values are allowed for a since we choose 1,r m,0 say, t ∈ t − 0.5, t + 0.5 , also dismissing the the best phase ψ anyway, and formulate the optimiza- 1 1,int 1,int m,0 carrier phase and using (21), or tion problem as Vukmirovic´ et al. EURASIP Journal on Advances in Signal Processing (2018) 2018:33 Page 8 of 17 ψ , ... , ψ , t , x, y, z 1,0 M,0 0 2, 3, ... , M). Also note that there is no need for the esti- M mate t to be as accurate as in the implementation of the jψ H H m,0 = arg max Re e u F D Fs . coherent algorithm. Therefore, one can skip step 3 of the t +τ m,0 0 m,0 ψ ,...,ψ 1,0 M,0 m=1 method for estimating t accurately. Instead of t ,one can 1 1 t ,x,y,z use t . 1,r (26) 2.2.3 Semi-coherent algorithms We can find the solutions for ψ separately. Namely, m,0 The difference between the coherent and non-coherent for given t , x, y, z, the solutions for ψ are given by 0 m,0 algorithms is in the way how the summation in the cri- H H terion function is used; in the coherent algorithm, it is ψ =− arg u F D Fs , m = 1, 2, ... , M. m,0 t +τ m,0 0 m,0 the real component of the sum that is applied whereas (27) in the non-coherent algorithm, it is the absolute values When these solutions are substituted in (26), we opti- of its terms that are exploited (cf. (24)and (29)). By tak- mize over (t , x, y, z),or ing absolute values, the constant phase differences among channels are lost. We can use this idea to formulate a H H semi-coherent algorithm by taking the appropriate abso- t , x, y, z = arg max u F D Fs . (28) 0 t +τ m,0 0 m,0 lute values before summing over the channels (over m), t ,x,y,z m=1 but after summing over the antennas in each subarray We refer to the algorithm based on the solutions in (over l). In this way, the phase differences between the (27) and the optimization in (28) as the noncoherent ML antennas of the same subarray are preserved, whereas the algorithm. phase differences between subarrays are lost. We also propose a noncoherent ML algorithm with Let us choose a scan grid inside a given area of inter- reduced computational complexity. As in the coherent est, see Figs. 4 and 5.Let r be the position of the SGp algorithm, we first estimate the total delay in channel 1 pth point on the scan grid. Unlike the coherent and non- and use the obtained estimate to search for the coordi- coherent algorithms, for each point on the scan grid, a nates of Tx, or (p) new N-sample-long signal segment, u , ∀m ,isreceived ( ) by the beamformers whose beams have been directed to H H ( x, y, z) = arg max u F D Fs . (29) m,0 τ −τ +t this point. The beams are formed by setting their coeffi- m,0 1,0 1 x,y,z m=1 cients w . The 3 dB widths of the beams are chosen to m,l be greater than the distance between adjacent scan-grid This is the algorithm we will use in stage 1 of the esti- points to avoid degradation due to the grid. The objective mation process. The first term in the sum is constant, so is to estimate p and t by it can be omitted (the index m can take just the values Fig. 4 Stage 2a scanning Vukmirovic´ et al. EURASIP Journal on Advances in Signal Processing (2018) 2018:33 Page 9 of 17 Fig. 5 Stage 2b scanning M L Geometry G consists of five antenna subarrays, each sub- (p)H H (B) (p, t ) = arg max u F D D Fs  , 0 m t 0 τ array having the geometry of an 18-element acoustic cam- m,l p,t m=1 l=1 era scaled down by a factor of 3 [39]. One omni antenna is (30) added to the center of each subarray. The centers are in the (B) plane, z = 0. The omni antennas have the following coor- 2π where D = Diag exp −j τk denotes a baseband dinates x and y in meters: (−2.20, −1.24), (0.18, −2.64), signal time delay matrix without a carrier phase shift, (2.96, −1.06), (2.53, 2.21),and (−2.18, 2.24). They are rep- unlike D . The position estimate of Tx is then r =r . SGp ˆ resented by white triangles in the figures in this section. As before, we can avoid estimating t by estimating t 0 m The positions of the subarrays were chosen by hand in for each omni antenna in preprocessing and then maxi- order to be irregular. The distances between subarrays mizing over p, i.e., were selected to correspond to subarrays placed on the wallsofaroom.The subarrayshaveplanargeometryin M L (p)H H (B) vertical plains, rotated around their vertical axes so that p = arg max u F D D Fs  . ˆ τ t −τ m m,0 m,l their broadside directions (approximately) point to the m=1 l=1 center of the area between subarrays (the room). Geom- (31) etry G is formed from G by scaling up by a factor of 2 1 This is the algorithm we will use in stage 2 of the estima- five the antenna positions in the subarrays with respect tion process. to their centers (omni antennas). The simulations were If the signals are narrowband, the expressions (30)and carried out using a known deterministic sequence, the (31)reduceto(32)and (33), respectively: first of the modulatable orthogonal sequences proposed in [40] for a given N. The parameters were as follows: (p)H −jω t ν = 60 GHz B = 10 MHz, and SNR = 10 dB (if c 0 c 0 ( p, t ) = arg max u e s , (32) 0 m p,t not stated otherwise), where SNR denotes the SNR in m=1 a virtual channel whose antenna is at a distance of 1 m (p)H −jω (t −τ ) c m m,0 from the transmitting antenna. Throughout this section, p = arg max u e s . (33) we assume that the signal power decreases with squared m=1 distance from the transmitter. 3 Numerical results and discussion In the multipath scenario, we simulated a specular mul- This section provides numerical results obtained by the tipath. We simulated only first-order reflected paths off presented algorithms with Monte Carlo simulations for four vertical planes (x =−2.4 m, y =−2.85 m, two scenarios—a LoS-only scenario and a multipath sce- x = 3.15 m, and y = 2.45 m), which represented walls of a nario. We experimented with two distributed receiver room, so that the subarrays are attached to them (at a dis- antenna array geometries for each of the two scenarios. tance of about 20 cm). As in [41], we assumed a ratio of Vukmirovic´ et al. EURASIP Journal on Advances in Signal Processing (2018) 2018:33 Page 10 of 17 LoS component power and the sum of reflected compo- nent powers (the Rice factor) of at least 10 dB. According to the ray-tracing method, the reflected components were modeled as if they were sent by virtual images of the Tx (w.r.t. the walls) according to the LoS model (7) (which includes a time shift, a carrier phase shift, and an attenu- ation). The reflected components were then phase shifted by π, and their sum at each receiving antenna was scaled to get the specified Rice factor. 3.1 Qualitative characterization of the criterion functions This subsection shows the qualitative behavior of the cri- terion functions of the respective algorithms for each of the three localization stages. The Tx was at (0, 0, 0),near the “center” of either G or G .Since stages 1and 3employ 1 2 only omni antennas, the choice of subarray geometry does not matter. The criterion functions are shown over areas lying in the plane z = 0. In Figs. 6, 7, 8, 9, 10,and 11,the true Tx location is marked by a circle with a cross and the estimated location by a square. Fig. 7 Criterion function of stage 1, given by (29) with N = 1024 In order to localize the Tx with accuracy much better than λ , we use the coherent algorithm. Its criterion func- tion has high side lobes and requires a very fine search grid Figure 8 shows the LoS-only criterion function of stage 2 (see Fig. 6). Therefore, we cannot work with it immedi- over an area inside the antenna array for G for N = 1024. ately, but instead we resort to a multistage/multiresolution We have also generated the corresponding criterion func- search. tion for N = 16, but it is not shown because it has the Figure 7 shows the LoS-only criterion function of stage same shape. It also has no side lobes but shows more vari- 1(givenby(29)) over an area inside the antenna array for ations across space compared to the criterion function N = 1024. The function does not have side lobes, it is of stage 1. This function offers better estimation accu- not influenced by carrier phases, it is immune to phase synchronization errors, and it varies slowly across space, racy. Figure 9 shows the same results over a smaller area which suggests that a coarse grid can be used. for geometry G . The figures suggest that the plane wave Fig. 6 The criterion function of stage 3, given by (24) with N = 1024 Fig. 8 Criterion function of stage 2, given by (31) for G with N = 1024 1 Vukmirovic´ et al. EURASIP Journal on Advances in Signal Processing (2018) 2018:33 Page 11 of 17 Fig. 9 Criterion function of stage 2 for G with N = 1024 Fig. 11 Criterion function for stage 2, G , Rice factor 10 dB, and N = 1024 with ray-tracing assumption would not be justified because of the size of subarray apertures. Figure 10 shows the LoS-only criterion function of stage peak of the lobe it has been initialized on (the initializa- 3for N = 1024 over an area around the transmitter tion point is the estimate obtained in stage 2). Clearly, to spanning a little more than the main lobe. As the used prevent the algorithm from converging to a side lobe, the algorithm is coherent (utilizes information in the phase of localization in stage 2 must produce an estimate inside the carrier for localization), the criterion function has side the main lobe of the criterion function of stage 3. In other lobes, separated by approximately 2λ /3. Since we use an words, if the localization error of stage 2 is smaller than adaptive search grid in this stage, the algorithm finds the approximately λ /3, the ambiguity problem is resolved, because the displacement of the center of the main lobe in stage 3 due to noise is small compared to its width without noise. Figure 11 shows the criterion function of stage 2 in the multipath scenario for N = 1024 over an area inside the antenna array for G , along with wall positions and the “rays” from the ray-tracing method. The Rice factor was 10 dB. The figure shows that the localization algorithm is robust w.r.t. the multipath propagation since the lobes corresponding to the reflected rays cannot be seen. The criterion functions for stage 1 and 3 with multipath prop- agation are not given because they are almost identical to the LoS-only ones. 3.2 Quantitative characterization of the algorithms In this subsection, we evaluate the accuracy of the algo- rithms of each stage. As performance metrics, we used both the MSE (mean squared error) and RMSE of the estimates. In Fig. 12, we display the histogram of the SNRs at the antennas of array G (it is similar for G ) for all simulated 1 2 transmitter locations (points of the Tx grid) for SNR = Fig. 10 Criterion function of stage 3, given by (24) with N = 1024 10 dB. Most of the SNRs are between −5and 10dB. Vukmirovic´ et al. EURASIP Journal on Advances in Signal Processing (2018) 2018:33 Page 12 of 17 Fig. 12 Distribution of SNRs at the antennas for simulated Tx locations for SNR = 10 dB The contour plots in the rest of the section were gen- Fig. 14 RMSE/λ of stage 2 for G and N = 1024 erated over a Tx grid of 16 × 16 points that covers most c 1 of the area inside the array to show the error distribution across space. The grid has uniformly spaced points in the plane z = 0. estimate of this stage is far away from the reference In Fig. 13, we plotted the LoS-only RMSEs relative to antenna, another antenna can be adopted as the refer- the carrier wavelength, λ , for stage 1 for N = 1024. For c ence and the process is repeated. Stage 3 could benefit every Tx grid point, we performed 100 Monte Carlo runs from choosing a better reference antenna even more. The and averaged out the results. Note that the accuracy is RMSE of stage 1 varies between 6 and 12 λ in the given generally better near the first antenna because it is used area. These values determine how narrow the search grid as the reference antenna for estimating t .Ifthe position 1 in the next stage can be for a given Tx position, because Fig. 13 RMSE/λ for stage 1 and N = 1024 Fig. 15 RMSE/λ for stage 2 for G and N = 16 c c 2 Vukmirovic´ et al. EURASIP Journal on Advances in Signal Processing (2018) 2018:33 Page 13 of 17 Fig. 16 RMSE/λ of stage 2 for G and N = 1024 c 2 Fig. 18 RMSE/λ of stage 3 and N = 1024 when the main lobe is not missed the grid should include the real Tx position. If the esti- mation errors have Gaussian distributions, the search grid Monte Carlo simulations for every Tx grid point and for the next stage should span an area that is ±2standard computed from them the RMSEs. The same results but deviations of the current stage along each dimension in for G ,and N = 16 and N = 1024, are presented in order to include the real location with probability of 0.95. Figs. 15 and 16. These results are better because of the The LoS-only RMSEs relative to λ for stage 2 for G c 1 increased space between the antennas in the subarrays. and N = 1024 is shown in Fig. 14. Again, we ran 100 Fig. 17 Probability of missing the main lobe in stage 3 due to the Fig. 19 MSE/CRB of stage 3 and N = 1024 when the main lobe is not error in stage 2, for G used in stage 2 and N = 1024 missed Vukmirovic´ et al. EURASIP Journal on Advances in Signal Processing (2018) 2018:33 Page 14 of 17 miss−distance [λ ] −4 −3 −2 −1 0 1 10 10 10 10 10 10 1 1 0.9 0.9 Main lobe G init. 0.8 0.8 G init. 0.7 0.7 0.6 0.6 0.5 0.5 0.4 0.4 0.3 0.3 0.2 0.2 0.1 0.1 0 0 −7 −6 −5 −4 −3 −2 −1 10 10 10 10 10 10 10 miss−distance [m] Fig. 20 Stage 3 error CDF curves for different initializations The increased space produces “narrower beams,” i.e., bet- main lobe has not been missed. Figure 20 shows LoS-only ter spatial selectivity. For N = 1024 and G ,the RMSE CDF (cumulative density function) curves of the stage 3 is below λ /6 over a significant part of the area inside localization error for N = 1024 for three cases: (1) the the array. This allows the search in stage 3 to start some- main lobe is not missed, (2) the stage 3 algorithm is ini- where within the main lobe of its criterion function with a tialized by the results of the stage 2 algorithm for G (see probability of 0.95. Thus, we can argue that the ambiguity Fig. 16), and (3) the stage 3 algorithm is initialized by the problem is avoided with high probability. The simulations results of the stage 2 algorithm for G (see Fig. 14). The in which the analog beamformers had phase quantization CDF curves were obtained for the same Tx grid as for the with a resolution of 3 were also carried out. The results contour plots (e.g., Fig. 13) with five runs for each grid are not shown here because they were almost identical to point. As predicted, the algorithm in case (2) misses the the ones without phase quantization. main lobe only 2% of the time. On the other hand, the The LoS-only results for stage 3 for N = 1024 are plot- algorithm in case (3) misses the main lobe 78% of the time. ted in Figs. 17, 18,and 19. In this experiment, for every Tx For easier comparison of the numerical results for the grid point, we had 1000 Monte Carlo runs. In Fig. 17,we LoS-only scenario, we provide them in Table 1.The first see how the probability of obtaining an estimate from a row shows the RMSE averaged over the Tx grid, the sec- side lobe (or that the main lobe was missed) varies across ond row the RMSE at a point near the center of the the Tx grid. This probability depends on the estimate of array (roughly (0, 0, 0)), and the third row the value not stage2becausethe algorithmofstage 3usesanadaptive exceeded by the RMSE of 80% of the points on the Tx grid. grid that converges to the maximum of the lobe on which The results are for the case when the main lobe in stage 3 it has been initialized. Figure 18 shows the RMSE across is not missed. the Tx grid provided that the main lobe has not been Figure 21 shows CDF curves for different Rice factors missed. As for stage 1, the effect of choosing the reference for all three localization stages for N = 1024. For each antenna can be seen (because the accuracy is better near the reference antenna). In this case, the obtained accuracy Table 1 RMSEs for search/scan stages (G and N = 1024) is of the order of λ /100. For comparison reasons, we have Stage 1 Stage 2 Stage 3 also run simulations for SNR = 20 dB, and the RMSE avg. RMSE 7.56λ (37.8 mm) 0.162λ (0.81 mm) 0.00365λ (0.0182 mm) c c c for the Tx at (0, 0, 0) is λ /963. In Fig. 19,weobserve the cent. RMSE 6.74λ (33.7 mm) 0.16λ (0.8 mm) 0.00317λ (0.0159 mm) c c c statistical efficiency measured as the ratio of MSE and 80% RMSE 8.61λ (43.1 mm) 0.176λ (0.88 mm) 0.00419λ (0.021 mm) c c c Cramér-Rao bound for the stage 3 algorithm when the Probability Vukmirovic´ et al. EURASIP Journal on Advances in Signal Processing (2018) 2018:33 Page 15 of 17 miss−distance [λ ] −4 −3 −2 −1 0 1 2 10 10 10 10 10 10 10 1 1 LoS−only 0.9 0.9 LoS+NLoS (Rice f. 15 dB) LoS+NLoS (Rice f. 10 dB) 0.8 0.8 0.7 0.7 0.6 0.6 0.5 0.5 0.4 0.4 0.3 0.3 0.2 0.2 0.1 0.1 0 0 −7 −6 −5 −4 −3 −2 −1 0 10 10 10 10 10 10 10 10 miss−distance [m] Fig. 21 CDF curves of localization errors for different stages and Rice factors for SNR = 10 dB stage, we show a CDF curve for LoS-only and Rice factor times for Rice factors 15 and 10 dB, respectively. In stage 2, values of 15 and 10 dB. Geometry G was used (in stage 2). the error is increased 1.2 and 1.3 times. In stage 3, the Again, these results hold for outcomes when the main errorincreaseis6and10times.Stage 2isthe leastaffected lobe in stage 3 is not missed. In stage 1, compared to the by multipath propagation thanks to the beam directivity of LoS-only curve, the error is increased roughly 2.5 and 4.3 the subarrays. The vertical line at λ /3 shows whether the miss−distance [λ ] −5 −4 −3 −2 −1 0 1 2 10 10 10 10 10 10 10 10 1 1 LoS−only 0.9 0.9 LoS+NLoS (Rice f. 15 dB) LoS+NLoS (Rice f. 10 dB) 0.8 0.8 0.7 0.7 0.6 0.6 0.5 0.5 0.4 0.4 0.3 0.3 0.2 0.2 0.1 0.1 0 0 −8 −7 −6 −5 −4 −3 −2 −1 0 10 10 10 10 10 10 10 10 10 miss−distance [m] Fig. 22 CDF curves of localization errors for different stages and Rice factors for SNR = 20 dB Probability Probability Vukmirovic´ et al. EURASIP Journal on Advances in Signal Processing (2018) 2018:33 Page 16 of 17 stage 2 estimate is within the main lobe of stage 3 or not. Acknowledgements This work was supported by national project TR32028 “Advanced Techniques This is a critical value for solving the ambiguity problem. for Efficient Use of Spectrum in Wireless Systems.” Even for a Rice factor of 10 dB, the ambiguity problem is solved 90% of the time. Authors’ contributions All authors read and approved the final manuscript. Figure 22 shows the appropriate CDF curves for SNR = 20 dB (instead of 10 dB as in Fig. 21). As expected, the Competing interests results for the LoS-only scenario are better. However, the The authors declare that they have no competing interests. results for the multipath environment are practically the Publisher’s Note same. Therefore, the adverse effect of multipath propaga- Springer Nature remains neutral with regard to jurisdictional claims in tion is greater for higher SNR values. published maps and institutional affiliations. To summarize, as opposed to the existing methods men- tioned in Section 1, which achieve a submeter localization Author details School of Electrical Engineering, University of Belgrade, Belgrade, Serbia. accuracy, the proposed methods improve that accuracy to Innovation Center of School of Electrical Engineering, University of Belgrade, a small fraction of the carrier wavelength, which enables Belgrade, Serbia. Department of Electrical and Computer Engineering, Stony the shift from location-based services to location-based Brook University, New York City, NY, USA. communication for dramatic improvement of a 5G system Received: 5 January 2018 Accepted: 22 May 2018 performance. 4Conclusions References In this paper, we addressed indoor position estimation 1. T Marzetta, Noncooperative cellular wireless with unlimited numbers of base station antennas. IEEE Trans. Wireless Commun. 9(11), 3590–3600 with a millimeter-wave massive MIMO system. We pro- (2010) posed an architecture with distributed antenna units, a 2. E Torkildson, U Madhow, M Rodwell, Indoor millimeter wave MIMO: multistage/multiresolution strategy, and three classes of feasibility and performance. IEEE Trans. Wireless Comunn. 10(12), 4150–4160 (2011) localization algorithms that together achieve RMSE of 3. Z Pi, F Khan, An introduction to millimeter-wave mobile broadband up to three orders better than the carrier wavelength, systems. IEEE Commun. Mag. 49(6), 101–107 (2011) and solve the ambiguity problem, inherent to coherent 4. TS Rappaport, S Sun, R Mayzus, H Zhao, Y Azar, K Wang, GN Wong, JK Schulz, M Samimi, F Gutierrez, Millimeter wave mobile communications algorithms. In the LoS-only scenario, the localization for 5G cellular: It will work! IEEE Access. 1, 335–349 (2013) error is by two to three orders better than the carrier 5. EG Larsson, O Edfors, F Tufvesson, TL Marzetta, Massive MIMO for next wavelength, whereas in the specular multipath scenario, generation wireless systems. IEEE Commun. Mag. 52(2), 186–195 (2014) 6. AL Swindlehurst, E Ayanoglu, P Heydari, F Capolino, Millimeter-wave it is up to 10 times worse for realistic Rice factors, massive MIMO: the next wireless revolution. IEEE Commun. Mag. 52(9), but still well below the carrier wavelength. The strat- 56–62 (2014) egy does not require channel-state information and is 7. RW Heath, N González-Prelcic Rangan, W Roh, A Sayeed, An overview of signal processing techniques for millimeter wave MIMO systems. IEEE J. applicable in multi-user scenarios, but requires domi- Sel. Topics Signal Process. 10(3), 436–453 (2016) nant LoS propagation. The studied signal model is inher- 8. V Venkateswaran, AJ van der Veen, Analog beamforming in mimo ently wideband, and it assumes spherical wavefronts. communications with phase shift networks and online channel estimation. IEEE Trans. Signal Process. 58(8), 4131–4143 (2010) The execution of the algorithms can be partially dis- 9. J Brady, N Behdad, AM Sayeed, Beamspace MIMO for millimeter-wave tributed among the subarray units. The obtained accuracy communications: system architecture, modeling, analysis, and allows the base station array to focus energy to the posi- measurements. IEEE Trans. Antennas Propag. 61(7), 3814–3827 (2013) 10. S Hur, T Kim, DJ Love, JV Krogmeier, TA Thomas, A Ghosh, Millimeter wave tion of the localized user terminal on downlink and to beamforming for wireless backhaul and access in small cell networks. receive its uplink signal emitted with decreased power. IEEE Trans. Commun. 61(10), 4391–4403 (2013) This can dramatically improve the overall capacity of the 11. A Alkhateeb, J Mo, N Gonzalez-Prelcic, RW Heath, MIMO precoding and combining solutions for millimeter-wave systems. IEEE Commun. Mag. millimeter-wave massive MIMO system. An open issue is 52(12), 122–131 (2014) positioning of the BS antennas with accuracy greater than 12. S Han, I Chih-Lin, Z Xu, C Rowell, Large-scale antenna systems with hybrid that of the localization, including the orientation of the analog and digital beamforming for millimeter wave 5G. IEEE Commun. Mag. 53(1), 186–194 (2015) subarrays. 13. J Li, L Xiao, X Xu, S Zhou, Robust and low complexity hybrid beamforming for uplink multiuser mmwave MIMO systems. IEEE Commun. Lett. 20(6), Abbreviations 1140–1143 (2016) 3GPP: 3rd Generation Partnership Project; 5G: 5th generation; A/D: Analog-to-digital; 14. JC Chen, Hybrid beamforming with discrete phase shifters for BS: Base station; CDF: Cumulative density function; DoA: Direction of arrival; millimeter-wave massive MIMO systems. IEEE Trans. Veh. Technol. 66(8), CRB: Cramér-rao bound; D/A: Digital-to-analog; DFT: Discrete Fourier transform; 7604–7608 (2017) DSP: Digital signal processor; IQ: In-phase quadrature-phase; LoS: Line-of-sight; 15. A Guerra, F Guidi, D Dardari, On the impact of beamforming strategy on MIMO: Multiple-input-multiple-output; ML: Maximum likelihood; MSE: Mean mm-wave localization performance limits. Presented at 2017 IEEE Int. squared error; NLoS: Non-line-of-sight; PDF: Probability density function; RF: Conf. Commun. Workshops, Paris, 21-25 May 2017 Radio frequency; RFID: Radio frequency identification; RMSE: Root mean 16. Y Zhu, T Yang, Low complexity hybrid beamforming for uplink multiuser squared error; RSS: Received signal strength; RSSI: Received signal strength mmwave MIMO systems. Presented at 2017 IEEE Wireless Commun. indicator; SNR: Signal-to-noise-ratio; ToA: Time of arrival; Tx: Transmitter; UT: Netw. Conf. (WCNC), San Francisco, 19-22 Mar 2017 User terminal Vukmirovic´ et al. EURASIP Journal on Advances in Signal Processing (2018) 2018:33 Page 17 of 17 17. AF Molisch, VV Ratnam, S Han, Z Li, SLH Nguyen, L Li, K Haneda, Hybrid 38. J Lee, E Tejedor, K Ranta-aho, H Wang, K Lee, E Semaan, E Mohyeldin, beamforming for massive MIMO: A survey. IEEE Commun. Mag. 55(9), J Song, C Bergljung, S Jung, Spectrum for 5G: Global status, challenges, 134–141 (2017) and enabling technologies. IEEE Commun. Mag. 56(3), 12–18 (2018) 18. TS Rappaport, F Gutierrez, E Ben-Dor, JN Murdock, Y Qiao, JI Tamir, 39. PULSE Beamforming System with 18-channel sector wheel array based Broadband millimeter-wave propagation measurements and models on beamforming type 8608 Bruel Kjoer Product information. https:// using adaptive-beam antennas for outdoor urban cellular www.bksv.com/~/media/literature/Product%20Data/bn1467.ashx. communications. IEEE Trans. Antennas Propag. 61(4), 1850–1859 (2013) Accessed 30 May 2018 19. N Iqbal, C Schneider, J Luo, D Dupleich, RS Thöma, Modeling of 40. N Suehiro, M Hatory, Modulatable orthogonal sequences and their directional fading channels for millimeter wave systems. Presented at application to SSMA systems. IEEE Trans. Inf. Theory. 34(1), 93–100 (1988) 2017 IEEE 86th Veh. Technol. Conf. (VTC Fall), Toronto, 24-27 Sept 2017 41. H Xu, V Kukshya, TS Rappaport, Spatial and temporal characterization of 20. N Iqbal, J Luo, Y Xin, R Müller, S Haefner, RS Thöma, Measurements based 60 GHz indoor channels. Presented at Fall 2000 IEEE Veh. Technol. Conf., interference analysis at millimeter wave frequencies in an indoor Boston, 24-28 Sept 2000 scenario. Presented at 2017 IEEE Globecom, Singapore, 4-8 Dec 2017 21. TS Rappaport, JN Murdock, F Gutierrez, State of the art in 60-Ghz integrated circuits and systems for wireless communications. Proc. IEEE. 99(8), 1390–1436 (2011) 22. W Roh, JY Seol, J Park, B Lee, J Lee, Y Kim, Y Cho, K Cheun, F Aryanfar, Millimeter-wave beamforming as an enabling technology for 5G cellular communications: theoretical feasibility and prototype results. IEEE Commun. Mag. 52(2), 106–113 (2014) 23. S Malkowsky, J Vieira, L Liu, P Harris, K Nieman, N Kundargi, IC Wong, F Tufvesson, V Öwall, O Edfors, The worlds first real-time testbed for massive MIMO: Design, implementation, and validation. IEEE Access. 5, 9073–9088 (2017) 24. R Di Taranto, S Muppirisetty, R Raulefs, D Slock, T Svensson, H Wymeersch, Location-aware communications for 5G networks: how location information can improve scalability, latency, and robustness of 5G. IEEE Signal Process. Mag. 31(6), 102–112 (2014) 25. K Witrisal, P Meissner, E Leitinger, Y Shen, C Gustafson, F Tufvesson, K Haneda, D Dardari, A Molisch, A Conti, MZ Win, High-accuracy localization for assisted living: 5G systems will turn multipath channels from foe to friend. IEEE Signal Process. Mag. 33(2), 59–70 (2016) 26. M Vari, D Cassioli, mmWaves RSSI indoor network localization. Presented at 2014 IEEE Int. Conf. Commun. Workshops (ICC), Sydney, 10-14 June 27. V Savic, EG Larsson, Fingerprinting-based positioning in distributed massive MIMO systems. Presented at IEEE 82nd Veh. Technol. Conf. (VTC Fall), Boston, 6-19 Sept 2015 28. N Garcia, H Wymeersch, EG Larsson, AM Haimovich, M Coulon, Direct localization for massive MIMO. IEEE Trans. Signal Process. 65(10), 2475–2487 (2017) 29. T Wei, X Zhang, mTrack: high-precision passive tracking using millimeter wave radios. Presented at (2015) 21st Annual Int. Conf. Mobile Comput. Netw. Mobicom ’15, Paris, 7-11 Sept 2015 30. A Guerra, F Guidi, D Dardari, Position and orientation error bound for wideband massive antenna arrays. Presented at 2015 IEEE Int. Conf. Commun. Workshops (ICC), London, 8-12 June 2015 31. A Shahmansoori, G Garcia, G Destino, G Seco-Granados, H Wymeersch, 5G position and orientation estimation through millimeter wave MIMO. Presented at (2015) IEEE Globecom Workshops, San Diego, 6-10 Dec 2015 32. M Koivisto, M Costa, J Werner, K Heiska, J Talvitie, K Leppänen, V Koivunen, M Valkama, Joint device positioning and clock synchronization in 5G ultra-dense networks. IEEE Trans. Wireless Commun. 16(5), 2866–2881 (2017) 33. M Koivisto, A Hakkarainen, M Costa, P Kela, K Leppänen, M Valkama, High-efficiency device positioning and location-aware communications in dense 5G networks. IEEE Commun. Mag. 55(8), 188–195 (2017) 34. J Werner, J Wang, A Hakkarainen, D Cabric, M Valkama, Performance and Cramer-Rao bounds for DoA/RSS estimation and transmitter localization using sectorized antennas. IEEE Trans. Veh. Technol. 65(5), 3255–3270 (2016) 35. M Scherhäufl, M Pichler, A Stelzer, UHF RFID localization based on phase evaluation of passive tag arrays. IEEE Trans. Instrum. Meas. 64(14), 913–922 (2015) 36. M Oispuu, U Nickel, 3D passive source localization by a multi-array network: Noncoherent vs.coherent processing. Presented at Int. ITG Workshop Smart Antennas, Bremen, 23-24 Feb 2010 37. N Hadaschik, B Sackenreuter, M Schäfer, M Faßbinder, Direct positioning with multiple antenna arrays. Presented at (2015). Int. Cong. Indoor Posit. Indoor Navig. (IPIN), Bremen, 13-16 Oct 2015

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EURASIP Journal on Advances in Signal ProcessingSpringer Journals

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