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ARTICLE https://doi.org/10.1038/s41467-019-09380-x OPEN Partially coherent radar unties range resolution from bandwidth limitations 1 1 1 1,2 Rony Komissarov , Vitali Kozlov , Dmitry Filonov & Pavel Ginzburg It is widely believed that range resolution, the ability to distinguish between two closely situated targets, depends inversely on the bandwidth of the transmitted radar signal. Here we demonstrate a different type of ranging system, which possesses superior range resolution that is almost completely free of bandwidth limitations. By sweeping over the coherence length of the transmitted signal, the partially coherent radar experimentally demonstrates an improvement of over an order of magnitude in resolving targets, compared to standard coherent radars with the same bandwidth. A theoretical framework is developed to show that the resolution could be further improved without a bound, revealing a tradeoff between bandwidth and sweep time. This concept offers solutions to problems which require high range resolution and accuracy but available bandwidth is limited, as is the case for the autonomous car industry, optical imaging, and astronomy to name just few. 1 2 School of Electrical Engineering, Tel Aviv University, Tel Aviv 69978, Israel. Light-Matter Interaction Centre, Tel Aviv University, Tel Aviv 69978, Israel. These authors contributed equally: Rony Komissarov, Vitali Kozlov. Correspondence and requests for materials should be addressed to P.G. (email: pginzburg@post.tau.ac.il) NATURE COMMUNICATIONS | (2019) 10:1423 | https://doi.org/10.1038/s41467-019-09380-x | www.nature.com/naturecommunications 1 1234567890():,; ARTICLE NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-019-09380-x patial and temporal coherence of electromagnetic radiation modulated CW (FMCW), which transmit continuously, and manifest in the ability of the wave to interfere with itself coded pulse radars, which have nontransmitting periods. It is Sunder interferometric experiments (e.g., observation of important to underline that the word “coherent” in this report interference fringes) . This peculiar statistical property was does not refer to the integration method, which is commonly already utilized almost a century ago by Michelson for per- used in the context of standard radars, but rather to the property forming stellar imaging . Today, optical coherence tomography of the transmitted wave itself. At this point it may be asked why (OCT) turns the finite coherence length of light sources into an bother improving on the well-developed radar systems? While 3–5 advantage , performing imaging with deep submillimeter various radar signals offer advantages over others, to the best of resolution inside biological tissues. Distances to scattering objects the authors’ knowledge, all suffer from a link between range under investigation are deduced by sweeping over the delay resolution (the ability to distinguish between two closely situated between a transmitted and a reflected signal and then recovering targets) and transmitted signal bandwidth, leading to the opinion the peak of the coherence function. While control over the that it is an unbreakable relation. Furthermore, range accuracy, coherence length of optical sources is still a technological chal- the certainty with which the distance to a single target is known, lenge, the low-frequency part of the electromagnetic spectrum tends to have a similar inverse dependence on bandwidth as 18,19 (below 1 THz) has benefited from coherent sources since the well , (mostly in FMCW realizations). This forces expensive invention of the quartz resonator and the homodyne receiver over high-bandwidth implementations in applications where range 6,7 a century ago . Today, the availability of cheap and reliable accuracy and range resolution are crucial. Typical examples electronics allows unprecedented control over the shape of the include but are not limited to the automotive and security transmitted electromagnetic fields, as well as precise measure- industries, which can require over 1 GHz of bandwidth to achieve 20,21 ment of the reflected signals’ phase. These advantages lead to the resolution of better than a meter . The cost of high-bandwidth dominance of fully coherent sources in most radar implementa- hardware and the regulation of the allowed spectral bands push tions as we know them today . Partially coherent sources, on the toward reducing the beforehand mentioned dependence. A few 10,22–25 other hand, have remained largely unexplored below the optical ideas were proposed to achieve this goal , but they are frequency spectrum. A notable exception, termed “noise radar”, mostly limited to special conditions and only offer an improve- employs stochastic degrees of freedom to modulate the carrier ment by a relatively small factor, leaving the fundamental 9–16 wave, e.g., . However, the method of operation is different to dependence on bandwidth intact. the presented approach because it does not involve noise. Here, we propose and experimentally demonstrate a different In order to achieve high range and Doppler resolutions, many type of super-resolution ranging and detection system inspired by 8,17 types of coherent carrier modulations have been proposed , OCT, which is not limited by bandwidth, at the expense of longer resulting in different radar implementations, such as frequency acquisition time. The concept is depicted in Fig. 1, where gradual d L Antenna Targets Mixer Cross correlation Signal L d , coherence length c N Partially coh. source Fig. 1 Illustration of the partially coherent radar concept. Three different waves are shown: light color—smallest, purple—intermediate and blue—longest coherence lengths. The width of the beam is drawn differently for each wave solely for clarity of illustration. For the lightly colored wave, the reflected signal from the cars is no longer correlated with the still transmitting part of the signal, due to its short coherence length. The purple wave, reflected from the first car, is correlated with the transmitting signal, but the reflections from the second car are not, which allows to detect the distance of the first one. The blue wave has the longest coherence length that correlates with reflections from both objects, allowing the detection of the second car as well. The coherence length (or time) of the radar is swept from shortest to longest, scanning the location of targets along the line of sight. Inset—Schematic representation of the radar system. An oscillator with controllable coherence time τ is transmitted and mixed with the reflections from the targets. The phase is switched N times and the output of the mixer is averaged over a window of length Nτ . Repeating the process by sweeping over the coherence length produces the cross-correlation as a function of coherence length. The location of the targets is extracted from this data 2 NATURE COMMUNICATIONS | (2019) 10:1423 | https://doi.org/10.1038/s41467-019-09380-x | www.nature.com/naturecommunications NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-019-09380-x ARTICLE increase of the coherence length of a CW radiation allows map- 1 (see Fig. 2 for an illustration) ping a road scenario, as a representative example. nτ þτ N1 Z ωτ 1 SST E C E cos φ φ þ ωτ dt m n;m n1;m Results 2Nτ n¼0 nτ Theory and implementation. In contrast to optical sources, ðÞ nþ1 τ where coherence is governed by internal noise (typically Gaus- Z þ cosðÞ ωτ ddt : sian), radio frequency (RF) technology allows control over the coherence almost on demand. This permits an all analogue nτ þτ implementation that can quickly sweep over the coherence length ð3Þ and recover the cross-correlation function between the trans- The first integral is over the uncorrelated window, where mitted and received signals. In order to implement this partially coherent source, the phase of the carrier can be switched uni- φ ≠φ , and so the expectation value will vanish. The second n;m n1;m formly in the range of½ 0; 2π , where the time between switching term is over the correlated window and will contribute to the final events is distributed exponentially with a mean time that is result. For τ <τ, i.e., the target is not within the current coherent related to the desired coherence length (as in optical sources) .A window, there will be no correlated part and the expectation value complementary approach, undertaken here, has technological will vanish completely. It is convenient to rewrite the final result advantages in RF implementations and suggests generating a in terms of the spatial coherence length ðl ¼ cτ ; l ¼ cτÞ, m m SST 100% duty cycle pulse train (CW), where the random switching SST where c is the speed of light, as well as defining C ¼ l C in m m m time is replaced with constant coherence intervals. This archi- order to linearize the dependence of the cross-correlation on the tecture corresponds to deterministic time between random phase coherence length jumps, which possess similar cross-correlation properties when ðÞ ðÞ l l cos kl if l >l sweeping over the coherence length. Schematic representation of SST m m E C ðÞ l ¼ : ð4Þ m m an implementation of a partially coherent oscillator is shown 0 otherwise latter and will be discussed after describing the basic signal pro- The standard deviation of the cross-correlation around the mean cessing formalism. The proposed radar signal is given by Eq. (1): can be calculated in a similar manner using the considerations StðÞ ¼ cosðÞ ωt þ φðtÞ ; leading up to Eq. (3). In the absence of noise the variance is 2 0 nτ þτ N1 M1 N1 m X X X t nτ T m m SST 4 @ φðÞ t ¼ rect φ ; ð1Þ Var C ¼ Var cos φ φ þ ωτ dt nm m n;m n1;m 2Nτ m m n¼0 m¼0 n¼0 nτ where rectðÞ t ¼ f10 t 10o:w:, φ are uniformly distributed ðÞ nþ1 τ nm m Δτ independent and identically distributed phases, τ ¼ τ þ m A5 m 0 M1 þ cosðÞ ωτ dt : is the length of each constant phase pulse (or coherent time nτ þτ duration, which increases after N pulses were ð5Þ m1 sent),T ¼ N τ m 10o:w: is the time that passed from m q This time the second integral does not contribute, as it is not a q¼0 random variable. Since the different cosines in the sum are the beginning of the scan until iteration m,ðÞ l ; l þ Δl¼ 0 0 independent, the variance is simply the sum of variances ðÞ cτ ; cτ þ cΔτ is the scanned range along the line of sight and 0 0 N1 2 Anτ A τ ω ¼ ck is the frequency of the carrier. An illustration of the SST Var C ¼ Var cos φ φ þ ωτ ¼ : n;m n1;m transmitted signal is shown on Fig. 2. 2Nτ 8N τ m m n¼0 The signal in Eq. (1) can be thought of as a random phase pulse ð6Þ code, which is distinct from the well-known “pseudo random 21,27 noise” , by effectively having 100% duty cycle (CW), as well The above result considers τ >τ, otherwise there is no correlated part and the variance does not directly depend on the delay to the as possessing completely random phases and varying pulse repetition frequency. Since in this implementation the coherence target (it still depends on the attenuation A, which increases with target distance). In addition, if the target were very far away, the length corresponds to pulse width, the detection method could also be thought of as a type of “pulse width modulation radar”. delay would be so large that for the first transmitting “pulses” there are no echoes to mix with, and so the variance in Eq. (6) will be diminished. This, however, is not considered ahead in order to Single stationary target detection. The process of detection in avoid cumbersome formulas. The noise term can be incorporated the presence of a single stationary target (SST) is described in into the variance by introducing the signal to noise ratio at the Fig. 2 and Fig. 3a. For a given coherence time τ (which is related receiving channel to coherence length cτ ), the expectation value of the cross- SST T 2 correlation of the signal C with its echo, delayed by time τ, 2 1 M A jj StðÞ dt 0 A M ð7Þ attenuated by factor A, and immersed in white Gaussian noise SNR ¼ ¼ ; 2 2 σ 2σ nðtÞ, is given by 2 3 where σ is the band limited power spectral density of the noise. T þNτ m m The standard deviation can finally be written in full form using SST 4 5 EC ¼ E StðÞðÞ StðÞ τþ nðtÞ dt : ð2Þ the above results Nτ T 8 rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 l 1 Considering the case τ >τ (i.e., the target is within the coherent þ if l >l m A m 2N l SNR σ SST ¼ : ð8Þ window), the signal in Eq. (1) is substituted into Eq. (2) (see qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 > 1 1 Supplementary Note 1). Noting that the signal is uncorrelated : þ otherwise 2N SNR with the noise, the expression can be broken down into two parts, further simplified by trigonometric identities and the fact ωτ Eqs. (4) and (8) allow to numerically estimate the cross- NATURE COMMUNICATIONS | (2019) 10:1423 | https://doi.org/10.1038/s41467-019-09380-x | www.nature.com/naturecommunications 3 ∫ ARTICLE NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-019-09380-x 2 M M M 1 1 1 2 2 1N 22 2N M1 M 2 MN 11 12 21 … … … M M M 1 1 1 2 2 2 1N 2N 11 12 21 22 M1 M 2 MN … … C C C 1 2 M Fig. 2 Illustration of the proposed detection method. The transmitted signal consists of a CW wave with a phase that is switched randomly every τ seconds, corresponding to opening a coherent window of length cτ . If a target exists within the coherent window, the reflected signal will be delayed by time τ and can be divided into two parts—the first is of duration ðτ τÞ, which is correlated with the still transmitting signal (i.e., the same phase), the other part is of duration τ and is uncorrelated with the transmitting signal. By switching the phase N times and averaging the product of the reflected and transmitting signal over a window of length Nτ , the cross-correlation C , which is the cross-correlation for coherence time interval τ , is measured. The m m cross-correlation averages to 0 if the target is not within the coherence length. For a target within the coherent window, however, the average increases as the target becomes closer. By increasing the coherent window and repeating the process, the cross-correlation as a function of coherence length can be obtained (see Fig. 3). 0.3 n (t ) ∼ [arb] f = 2.004 GHz 1 f A + f = 2.006 GHz m C f = 2.007 GHz T +N m m N 1 S (t ) f = 2.008 GHz × [ ]dt m f T 5 f = 2.010 GHz –0.3 5 22 25 27 l , coherence length [m] 0.03 0.3 c d = 0 km/h [arb] [arb] = 36 km/h f = 2.015 GHz 2 = 70 km/h = 200 km/h 3 22 23.6 25.4 27 10 30 55 l , coherence length [m] l , coherence length [m] m m Fig. 3 Simulation results and schematics. a Schematic representation of the partially coherent radar operation. A continuous wave signal is generated with N phase jumps that are randomly produced to provide a constant (controllable) coherence time τ (time between phase switching events). Each pulse has a random phase (φ or vector φ), which is kept constant for the pulse duration. The signal reflects from a target that is situated at a distance related to the delay, attenuated by a factor A and received along with additive white noise. The output of the receiver is mixed with the still transmitting signal and averaged over the duration of the transmission time Nτ (the averaging starts at the same time as the signal begins transmitting). The result of the integration is multiplied by the coherence time τ . The result is termed the cross-correlation and denoted as C . The process is repeated for M coherence points (lengths of constant coherence). M and N define the performances of the system (range resolution and range accuracy). Monte Carlo simulations in high SNR (30 dB) scenarios: b Cross-correlation as a function of coherence length for a single target located 25 away, drawn for different carrier frequencies using Eq. (4). c Cross-correlation for two targets located at coherence lengths of 23.6 and 25.4 corresponding to Eq. (9). d Cross-correlation of a single target moving at different velocities along the line of sight, corresponding to Eq. (14) 4 NATURE COMMUNICATIONS | (2019) 10:1423 | https://doi.org/10.1038/s41467-019-09380-x | www.nature.com/naturecommunications S(t) – trans. S(t–) – ref. NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-019-09380-x ARTICLE correlation versus coherence length as shown in Fig. 3,by frequency that avoids cross-correlation nulls for both targets, it is assuming each point to be Gaussian distributed with a corre- theoretically possible to distinguish uncoupled point targets sponding mean and standard deviation. The detection of targets located arbitrarily close to each other. This separation is only is made by plotting the cross-correlation as a function of corre- limited by the standard deviation of Eq. (10), which can be made lation length (or correlation time). The resulting graph is piece- arbitrarily small by increasing the number of phase switches N wise linear and the location of the target corresponds to the and the SNR. As will be shown in the following section, the breakpoint (see Fig. 3b, c for the theory and Fig.5 for the required bandwidth depends entirely on the initial scanned range experiment hereafter), which can be retrieved with the help of (the closest point scanned on the line of sight), meaning that the linear regression methods that were developed for the needs of range resolution of the proposed system (the ability to distinguish stock market analysis . Briefly, the approach here is to assume close targets) does not depend on bandwidth. some point to be the breakpoint and then calculate the least squares fit to a linear function for the data on the right and Sweep-time and bandwidth tradeoff. For N pulses, M coherence separately on the left of that point. Repeating the process for all sweep points that begin at τ and scan a range Δτ of coherence points and choosing the one that produced the least squares time, the total scan time is allows finding the breakpoint. More complex methods may be M1 applied to further increase the accuracy of the breakpoint esti- ðÞ 2τ þ Δτ T ¼ N τ ¼ NM: ð11Þ tot m mation as well as decrease the computational cost. m¼0 It is important to note that the choice of the carrier frequency is important in avoiding cross-correlation zeroes when cosðÞ kl ¼ Eq. (11) shows a trade-off between the range accuracy and total 0 in Eq. (4), as can be seen on Fig. 3b. This encourages an sweep time, where a good precision requires high M and N, which additional sweep over the carrier (frequency hopping for prolongs the scan time. The maximal transmitted signal band- example) to insure detectability at any range. This additional width (defined as the spectral distance between zeroes in the sweep bandwidth is at most Δf ¼ , which is between 5 and 7.5 2τ “sinc” function, which is the Fourier transform of the rectangular MHz for targets that are 15–10 m away from the radar, as is the envelopes, defined in Eq. (1)) depends entirely on the starting case in our experiment and future relevant applications. This coherence length time, BW ¼ , allowing to rewrite Eq. (11) max τ additional bandwidth, which becomes even smaller for targets in the following form located further away, will be shown to be a relatively small addition. The impact of the carrier frequency choice on the cross- BW ¼ : ð12Þ max correlation is shown on Fig. 3b—while the location of the tot Δτ NM 2 breakpoint does not change, the slope of the correlation function strongly depends on the carrier. Eq. (2) shows clearly that the proposed partially coherent radar is trading maximal transmitted bandwidth for sweep time, showing Multiple stationary targets detection. For multiple stationary an inverse dependence. targets (MST) the expectation value of the cross-correlation becomes a sum. Using similar arguments as for the single target, Effects of moving targets. In order to account for the effects of the cross-correlation can be reduced to a sum of single target moving targets, the delay τ in Eq. (2) should be replaced with a terms in the following form function of time. Assuming a single-moving target (SMT) with speed v along the line of sight, the delay between the transmitted K mþ1 and received signals is now τðÞ t ¼ τ þ 2 t, where the factor of 2 MST ~ c E C ðÞ l ¼ l A E½ StðÞ τðÞ StðÞþ ntðÞ dt m m m i i is due to the back and forth travel time of the wave, accounting for the classical Doppler effect in monostatic radars. Since the ð9Þ coherence time τ is short (typically less than a microsecond) it ðÞ l l cosðÞ kl ; m 2 m i i i2D ¼ can be assumed, as normally done in radar analysis, that the target remains stationary during this period and that the Doppler effect 0if D ¼; results merely in the phase accumulation between adjacent “pul- where A is the attenuation related to the distance and scattering i ses”. Further simplification can (but does not have to) be made by cross section of the ith point-like target, l ¼ cτ is twice the i i assuming that the target does not move much during the sweep- physical distance to target i, c the speed of light, K the number of time-per-point Nτ , and that the target only changes its range targets and D ¼fg i : l >l is the set of all target indices that are m i when the coherence length is switched at the next iteration m. The within the coherence length of the signal. The standard deviation last simplification allows obtaining a compact solution, which at each coherence length point m will depend on the amount of otherwise will be cumbersome. This approximation can be justi- targets within the coherence length. Since the echoes are additive, fied by considering low-target velocities of around 200 km/h, and the standard deviation in the presence of K targets is a sweep-time-per-point of under a millisecond (corresponding to vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi N < 10,000). In such a case the target will have moved by about 6 K 2 uX cm, which is around the accuracy of many radars including the MST K K SST; i i ð10Þ σ l ;fg l ; fg A ¼ σ ; A : m i i¼1 i i¼1 ~ i C C experimental system described ahead. Finally, an assumption i¼1 about the scanning mechanism needs to be made. For simplicity, consider a sequential scanning algorithm, which starts from the Eq. (9) reveals that for multiple targets along the line of sight, shortest coherence length and monotonically increases towards several breakpoints on the cross-correlation graph are expected to the final length scanned along the line of sight. In such a scenario, appear. The location of the breakpoints on the plot identifies the the target location is moving monotonically along the line of sight, physical position of the reflecting targets (see Fig. 3d for the presenting a different delay at each coherence length. The above theoretical plot and Fig.5e for the experimental result hereafter). discussion is applied to Eq. (3) by replacing τ ! τ þ 2nτ inside The distance between the targets is half the distance between the c the integral and considering only the correlated part. When the breakpoints due to the monostatic operation of the radar. By performing a finer scan of the range and choosing an appropriate target is within the current coherence length, i.e., τ > τ þ NATURE COMMUNICATIONS | (2019) 10:1423 | https://doi.org/10.1038/s41467-019-09380-x | www.nature.com/naturecommunications 5 ARTICLE NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-019-09380-x ðÞ M1ðÞ τ τ m 0 in the process. The carrier frequency was chosen to avoid zeros in 2 N τ the equation reads Δτ |fflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflffl} the cross-correlation (see discussion at the end of section A “Single Stationary Target” in “theory and implementation“). 2 3 Using Eq. (11) the sweep time is 204 ms under optimal condi- ðÞ nþ1 τ N1 Z ωτ 1 A v tions, which can be reduced by performing less phase jumps and SMT 4 5 EC E cos ωτ þ 2 nτ dt : m m 2Nτ c taking fewer sweep points, as well as implementing an advanced n¼0 nτ þτ search algorithm (for example, a binary search instead of the ð13Þ brute force sequential sweep described in the “effects of moving targets” section). Figure 4a shows the photograph of the practical As before, if the target is not inside the coherent window, the implementation of the partially coherent oscillator. This imple- cross-correlation is expected to vanish. The solution to Eq. (3) mentation was chosen over a simple phase shifter to allow for a could now be written in terms of range rather than delay and faster switching time of the phase. Panel b demonstrates the multiplied by the coherence length as done in Eqs. (4) and (9) actual transmitted bandwidth of the signal, which was used to kl v sin N < ðÞ obtain the experimental results depicted on Fig. 5a. ðÞ N1 v c A v ðÞ l l cos kðl þ l Þ if l >l þ 2mN l SMT kl v 2 m c m m m c m N sinðÞ EC ¼ : c Figure 5 shows the results for scenarios where either a single 0o:w target, no target or both targets are present. When no target is present, a slight downward slope can be observed due to a small ð14Þ DC bias present in the experiment, which is due to imperfect kl v sin N ðÞ isolation between the transmitting and receiving antennas, as well For low velocities the term in Eq. (14) tends to unity, kl v N sin ðÞ c as reflections from various components. In Fig. 5b, c, it is leaving a solution that is similar in form to Eq. (4). The difference observed that for coherence lengths shorter than the distance to is found in the appearance of an oscillatory term as a function of the target, the line is slowly sloping downward due to the same coherence length l , which is due to phase accumulation between m DC bias. As soon as the coherence length of the source achieves constant coherence iterations n, as well as an updated condition the back and forth distance to the target, a breakpoint occurs and that considers the movement of the target between varying the cross-correlation between the transmitted and received signals coherence length iterations m. Figure 3(d) depicts the cross- starts to rise linearly, as predicted by Eq. (4) and shown on the correlation as a function of coherence length for a moving target theoretical Fig. 3b. The different slopes in Fig. 5b, c are the result at different speeds, starting at a distance of 30 m. For low velocity of target location and illumination frequency, determining the (36 km/h) the linear increase following the breakpoint deviates sign of cosðÞ kl for each target in Eq. (4). In Fig. 5d, one can see slightly from the stationary case. When the velocity increases the response when both targets are present, with slopes further (70 and 200 km/h) the breakpoint can be seen to recede corresponding to the previous figures and in accordance with from the stationary solution, due to the movement of the target, Eq. (10) and the theoretical Fig. 3c. The distance between the as described by the updated condition in Eq. (14). resulting breakpoints is interpreted as twice the distance between Eq. (14) proves that the proposed detection method would only the targets. By repeating the sweep numerous times and obtaining need a small adjustment in order to cope with slowly moving the location of the breakpoints each time, it is possible to estimate targets, by fitting the cross-correlation as a function of coherence the probability densities of target range, shown as Gaussian insets length to an oscillatory, rather than linear function. Under the in Fig. 4. The standard deviation of the probability density is the above approximations, the movement of the target has no effect accuracy of the range, which is obtained to be about 10 cm. The on the standard deviation around the expected value, as can be distance between the targets from Fig. 5d is calculated as 35 cm, deduced by adding a phase factor to the cosine in Eq. (6). The which is close to the actual physical distance (32 cm). Remark- same arguments that were used to derive Eq. (14) could be ably, when both targets are present, a shift of the first target’s applied together with the considerations leading up to Eq. (9) and range can be observed from Fig. 5b, d, which is the result of (10) in order to derive the cross-correlation of multiple moving multiple reflections between the closely placed objects, which is targets. Finally, it is important to note that the phase changes not considered in the simple point target model leading up to Eqs. between adjacent ‘pulses’ of constant coherence time could be (4) and (9). Figure 4b shows the measured spectrum of the signals used in order to estimate the velocity of the target in the same at chosen coherence lengths, showing the maximum transmitted manner as performed by standard pulsed radars , allowing for a bandwidth to be 27.2 MHz. While this bandwidth is enough to quick estimation of the velocity before the end of the full resolve two targets 32 cm apart using the proposed method, the coherence sweep. This velocity may be used in order to better fit same bandwidth would only suffice to resolve targets separated by the target location using Eq. (14) and extrapolation formulas in several meters using FMCW or pulsed radars, which is an future applications. improvement of more than an order of magnitude over standard systems. This improvement can be increased if the targets are Experimental results. In order to demonstrate the performance located further away, as the highest bandwidth depends entirely of the system, a pair of scatterers were placed one in front of the on the starting point of the coherence length sweep. The starting other on the line of sight inside an anechoic chamber. Square point of the scan can be made arbitrarily far away artificially, by plates were chosen in order to avoid ambiguity in measuring the using delay lines (here coaxial cables were used as discussed distance between the targets, which was 32 cm with the first before), finally untying range resolution from bandwidth object placed 2 m away from the transmitting antenna. The limitations. transmitting antenna was connected with a long cable to the radar system, adding additional delay to the target in order to reduce the required bandwidth. Note, that a cable adds a deterministic Comparison between partially coherent radar and existing effective distance to the target, and hence it effectively increases approaches. The vast majority of modern radar signals can be the duration of probing “pulses”, reducing the bandwidth as divided into two main groups: continuous wave (CW), trans- shown in Eq. (12). The coherence length was swept electronically mitting continuously, and pulsed signals that transmit for rela- from 22 to 27 meters with M = 500 coherence length points and tively short periods. While both techniques improved N = 5000 phase jumps per point, recording the cross-correlation significantly in the last few decades, none of them meet all the 6 NATURE COMMUNICATIONS | (2019) 10:1423 | https://doi.org/10.1038/s41467-019-09380-x | www.nature.com/naturecommunications NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-019-09380-x ARTICLE Tunable coherence-time oscillator Cos() Tx 0° and 90° splitter Isolator Splitter Isolators Mixers Combiner Isolator Rx Frequency tunable Mixer Sin() oscillator IF to A\D 11.1 MHz –5 –10 –15 –20 –25 2.04 25 2.02 1.98 1.96 Coherence length, m Frequency, GHz Fig. 4 Experimental implementation and transmitted bandwidth measurements. a Photograph of the partially coherent oscillator implementation. A carrier is split into two quadratures, where one arm is phase delayed by 90°. Each arm is multiplied by an appropriate sine or cosine term of the desired random phase output at time t, and the two arms are combined together to reveal a single carrier with the desired phase jumps, implementing and IQ vector modulator. b Measured half-bandwidth of the radar as it sweeps from coherence length of 22–27 m, corresponding to transmitted bandwidths of between 27.2 and 22 MHz. The peaks of the “sinc” function are lowered with increasing bandwidth, conserving the transmitted power throughout the sweep. These signals were used to explore the scenarios shown in Fig. 5a demands in the field of target detection and radar imaging owing demanding extremely expensive G (IEEE) band or even larger to inherent limitations and trade-offs. mm wave frequencies in order to separate several distant targets 32,33 The majority of CW radar implementations are frequency that are close to each other . modulated CW (FMCW) radars, which are widely used in many Pulsed and pulsed Doppler radars are widely used for long- applications today. The detection technique is based on mixing distance detection, air traffic control being one of the main between a transmitted chirp signal and the received echo, which applications. These systems radiate short pulses and switch off the allows estimating the distance and velocity of a target . FMCW transmitter while waiting for echoes. This results in implementa- 29,30 radars are implemented all across the frequency spectrum . tions that have an inherent blindness for short range targets. Many chirp modulation schemes are available (with increasing Compression techniques are used to cope with this problem with and then decreasing frequency, saw tooth modulation and great success, but they still require large bandwidth and smarter others), however, additional smart signal processing algorithms signal processing at the receiver end . are needed to prevent severe problems of ghost target Another type of ranging system that receives considerable 31 15 appearance . FMCW schemes are commonly used in short interest is the noise radar , which does not fall into any of the range application in order to avoid the “blindness” problem that beforehand mentioned classifications. The most basic type of pulsed radars usually experience. Furthermore, there is an noise radar cross correlates a random transmitted waveform with intrinsic relation between range resolution and bandwidth, its received echo in order to determine the distance to the target. NATURE COMMUNICATIONS | (2019) 10:1423 | https://doi.org/10.1038/s41467-019-09380-x | www.nature.com/naturecommunications 7 13.6 MHz Magnitude, dB ARTICLE NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-019-09380-x ab d 2 2 0 0 –2 –2 0.08 –4 –4 Free space Target 2 25.64 Coh. l. –6 –6 ce 6 4 0.07 0.1 Target 1 4 2 24.95 Coh. l. 25.1 Coh. l. Target 2 Target 1 Horns 2 0 0.13 0 –2 Target 1 and 2 25.65 Cor. l. –2 –4 22 23 24 25 26 27 22 23 24 25 26 27 l , coherence length, m l , coherence length, m m m Fig. 5 Detection and separation of two objects with narrowband signals—more than an order of magnitude below standard limitations. a Photograph of the experimental layout where two square plates were placed at a separation of 32 cm away from each other. b–e Plots of cross-correlation as a function of the coherence length. Experimental data—blue points, piece-wise linear fit—red solid lines. Insets—uncertainty in target locations. b Free space scan—empty room. c, d Single targets without the presence of the other, in accordance with the theoretical plot in Fig. 3b. e Both targets present at the same locations as before. The measured distance between the targets is 35 cm, and it is close to the actual physical value (32 cm) . The correlation length in b–d includes the physical distance to targets (as seen in (a)) as well as added distance due to cables and delays in other electronic components Table 1 Comparison between widely used radar implementations and the partially coherent radar Inherent differences between common radar technologies and Partially Coherent Radar Pulsed radar FMCW radar Noise radar Partially coherent radar c c c Range resolution Or even worse when ✓ Free of bandwidth limitations 2BW 2BW 2BW dependence on using windowing techniques bandwidth Short-range target Requires large bandwidth for ✓ Does not suffer from blind Requires large bandwidth ✓ Does not require large detection short range detection, and range due to its simultaneous for short range detection, bandwidth due to smart thus fast ADC (analog-to- transmit and receive and thus very fast ADC, or correlation detection algorithm 35 29,35 14,35 digital converter) scheme low-dynamic range Long-range target Demands compression Has a built in trade-off ✓ Has no restrictions on ✓ Has no restrictions on range detection techniques to be used for between range and range long range, and thus use resolution, which cannot be larger bandwidth, making it improved more vulnerable to manmade noise Exploiting Doppler ✓ Widely used to extract ✓ Widely used to extract Cannot be used for high ✓ Can be used to extract Doppler effect for Doppler information. Fast Doppler information. Fast speed targets in the same manner as pulsed and measurement of targets do not severely affect targets do not severely affect FMCW radars. Fast targets (over moving targets range accuracy range accuracy 200 km/h) can affect performance and require smarter algorithms Other limitations/ Leakage from FMCW signal Most applications require ✓ Can be used even in sub 1 GHz advantages can impair the receiver precise controlled delay implementations especially at low received lines, which have high signal levels. Phase noise insertion loss and are 35 38 degrades performance frequency depended This approach has several advantages over conventional radars between the range resolution and the bandwidth of the trans- thanks to its random nature of electromagnetic radiation, which mitted signals. In particular, a new type of electromagnetic source includes high immunity to noise and low probability of intercept with controllable coherence length was implemented and which are relevant for military and urban applications. It does, employed, demonstrating a ranging system possessing super however, demand high-precision controllable delay lines, which resolution. Furthermore, this radar system is achieving a product are expensive and hard to implement at mm waves as well as of range resolution to bandwidth that is experimentally shown to having high-insertion loss . Moreover, its range resolution still be better by more than an order of magnitude compared with depends on the bandwidth, making it hard to implement an other radar technologies. In particular, it is shown that the range 13,16 energy efficient and high-range resolution noise radar . Table 1 resolution can be virtually unrelated to the transmitted signal presents a comparison between the commonly used radar bandwidth, trading this quantity for longer sweep time. The new implementations and the new partially coherent radar. system could be utilized to make bandwidth efficient, low power, and physically compact systems for ranging purposes, integrated into existing beamforming and scanning systems. Therefore, Discussion autonomous cars, airborne radar systems, aerospace imaging Statistical properties of electromagnetic radiation have been along with other field of science and practical applications might employed in order to remove the commonly accepted relation 8 NATURE COMMUNICATIONS | (2019) 10:1423 | https://doi.org/10.1038/s41467-019-09380-x | www.nature.com/naturecommunications Cross- Cross- correlation, a.u. correlation, a.u. 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Identification of regulation or exceeds the permitted use, you will need to obtain permission directly from parametric underspread linear systems and super-resolution radar. IEEE the copyright holder. To view a copy of this license, visit http://creativecommons.org/ Trans. Signal Process. 59, 2548–2561 (2011). licenses/by/4.0/. 26. Svelto, O. Princeipels of Lasers, 5th ed. (2010). 27. Zhang, H., Li, L. & Wu, K. 24GHz software-defined radar system for automotive applications. In 10th European Conference on Wireless Technology, © The Author(s) 2019 pp. 138–141 (2007). NATURE COMMUNICATIONS | (2019) 10:1423 | https://doi.org/10.1038/s41467-019-09380-x | www.nature.com/naturecommunications 9
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Published: Mar 29, 2019
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