TY - JOUR
AU - Chu,, Ming
AB - Abstract The performance of underwater acoustic communication system is affected seriously by inter-symbol interference caused by multipath effects. Therefore, a novel blind equalization algorithm based on constant modulus algorithm (CMA) and decision-directed least mean square (DD_LMS) is adopted to improve the equalization ability of the system. Firstly, the LMS algorithm is improved by introducing inverse hyperbolic sine function and three adjustment factors to control step-size and the appropriate parameter values are set through the simulation of three adjustment factors. Secondly, the error values of the step-size function are replaced with error expectations to improve the anti-noise performance. Finally, the improved step-size function is introduced into the CMA and DD_LMS algorithm and the difference of the iteration error of adjacent k times is used as the switching condition of the dual mode algorithm. The results show that the algorithm has good equalization and anti-noise performance at both high and low signal-to-noise ratio (SNR), especially at low SNR, its steady-state error is ~10 dB lower than the traditional CMA and its convergence speed is ~15% higher than the traditional CMA. This algorithm can be used to effectively improve the communication efficiency of the communication system of underwater robots, which has good application value. 1. Introduction Underwater robots can replace divers to perform the tasks of search and salvage in shallow sea. Relying on underwater acoustic communication technology, the remote control of underwater robots can be realized [1]. However, sound waves will not only be reflected by the sea surface and the sea floor but also be absorbed and refracted by seawater. The inter-symbol interference caused by this multipath propagation will lead to an increase in the bit error rate (BER) at the receiving end, which greatly reduces the communication efficiency of the communication system of underwater robots [2]. At present, the adaptive equalization technology is generally adopted to offset the interference of multipath channels, so as to reduce the BER of the communication and improve the communication efficiency of the system [3, 4]. The traditional adaptive equalization technology wastes the limited underwater acoustic channel bandwidth by transmitting the training sequence to adjust the weight coefficient of the equalizer. However, the blind equalization only uses the probability characteristics and statistical characteristics of the received signal to adjust the parameters, which saves the resources of the communication system [5, 6]. Constant modulus algorithm (CMA) is a classical and effective blind equalization algorithm, which is widely used due to its low computational complexity and easy implementation. However, its slow convergence speed and large steady-state mean square error result in high BER of restored signals [4, 7, 8]. In order to solve this problem, a series of improvements have been made to the CMA to achieve faster convergence speed and less steady-state error [5, 9]. Among them, the dual-mode blind equalization algorithm combining CMA and decision-directed least mean square (DD_LMS) algorithms is a typical improved method, which combines the advantages of CMA and DD_LMS, adopts CMA in the initial phase of communication and switches to DD_LMS algorithm after convergence to achieve a good equalization effect [9]. The switching conditions need to be set for the switching of dual mode equalization algorithm. The hard switching based on fixed threshold value in [10] is greatly affected by channel noise, which will lead to the false switching of the algorithm under the circumstance of low signal-to-noise ratio (SNR). In order to overcome the problems of hard switching, as well as to promote equalization performance, in [11], the method of convex combination of the filters is adopted to improve the performance of the equalization. In this method, the results of two filters with different settings and running independently are mixed so that the overall performance of the system is at least the same as the better performing filter in each iteration. Although this structure can achieve lower steady-state error than a single CMA equalizer, its components are all blind equalization filters, so the large residual errors still exist. In addition, the CMA and recursive least squares algorithm based on adaptive forgetting factors in [5] can achieve smaller steady-state error, but the convergence speed is slower, and because it uses the structure of least squares, the calculation amount is increased. In order to further improve communication efficiency, the inverse hyperbolic sine function is used to optimize the variable step-size LMS algorithm to improve the convergence speed of the algorithm and reduce the steady-state error of the algorithm. What is more, the anti-noise performance of variable step-size LMS algorithm is enhanced to adapt to the underwater acoustic channel with serious multipath interference. Moreover, the improved step-size function is introduced into the CMA to solve the contradiction that the convergence speed and the steady-state error of CMA are difficult to balance. The switching condition based on the difference of iterative error is adopted to avoid the problem of incorrect switching of CMA+DD_LMS algorithm. This novel algorithm has a simpler structure and satisfactory effect of equalization, which is beneficial to real-time or burst communication. 2. Blind equalization algorithm The basic principle of blind equalization is shown in Fig. 1, where h(n) is the impulse response of the underwater transmission channel, n(n) is the Gaussian white noise with zero mean value, u(n) represents the input signal of the equalizer, w(n) is the weight coefficient of the equalizer, |$\tilde{x}(n)$| is the output signal of the equalizer and |$\hat{x}(n)$| is the output signal of the judge. FIGURE 1. Open in new tabDownload slide The basic principle of blind equalization. FIGURE 1. Open in new tabDownload slide The basic principle of blind equalization. When the parameter P = 2, the Godard algorithm is CMA that is a special case of the Godard blind equalization algorithm. Moreover, the iterative formula for the weight coefficient of the equalizer obtained by the stochastic gradient descent method is $$\begin{equation} \mathbf{w}\left(n+1\right)=\mathbf{w}(n)+\mu{e}_C(n){\mathbf{u}}^{\ast }(n), \end{equation}$$(1) where |$\mu$| is the step-size and |${e}_C(n)$|is the error signal of CMA, and the expression is $$\begin{equation} {e}_C(n)=\tilde{x}(n)\left({R}_2-{\left|\tilde{x}(n)\right|}^2\right), \end{equation}$$(2) where R2 is the norm, namely the mode of the input signal. DD_LMS algorithm combines decision pointing algorithm and LMS algorithm, and its updating formula of tap coefficient is $$\begin{equation} \mathbf{w}\left(n+1\right)=\mathbf{w}(n)+\mu{e}_D(n)\mathbf{u}(n), \end{equation}$$(3) where the error |$\mu{e}_D(n)$| is expressed as $$\begin{equation} {e}_D(n)=\hat{x}(n)-\tilde{x}(n). \end{equation}$$(4) 3. Improved variable step-size LMS algorithm 3.1. LMS algorithm The equalizer structure of traditional LMS algorithm is shown in Fig. 2. FIGURE 2. Open in new tabDownload slide Structure diagram of adaptive equalizer. FIGURE 2. Open in new tabDownload slide Structure diagram of adaptive equalizer. The iterative formula of the equalizer weight coefficient of the LMS algorithm is given by $$\begin{equation} \mathbf{w}\left(n+1\right)=\mathbf{w}(n)+2\mu e(n)\mathbf{u}(n), \end{equation}$$(5) where w(n + 1) and w(n), respectively, represent the weight coefficients of the next moment and the current moment, |$\mu$| is the step-size factor in the gradient descent method, which is used to control the convergence speed and stability of the algorithm. What is more, |$\mu$| is a constant whose range is: |$0<\mu <1/{\lambda}_{\mathrm{max}}$| where |${\lambda}_{\mathrm{max}}$| is the maximum eigenvalue of the auto-correlation function of the input signal of the equalizer. e(n) is the error signal between the expected signal d(n) and the equalizer output signal y(n). u(n) is the signal received by the equalizer. FIGURE 3. Open in new tabDownload slide The relationships between |$\mu (n)$| and e(n). FIGURE 3. Open in new tabDownload slide The relationships between |$\mu (n)$| and e(n). 3.2. Variable step-size LMS algorithm based on inverse hyperbolic sine function The convergence speed and steady-state error of traditional LMS algorithm are difficult to be taken into account at the same time. In recent years, the improvement of the LMS algorithm mainly focuses on the step-size adjustment. By selecting an appropriate step-size iterative formula, the big step-size is used to speed up the convergence at the initial stage of the algorithm; then, when the algorithm tends to steady state, the step-size factor needs to be reduced to reduce the steady-state mean square error of the algorithm [12–14]. Considering the complex characteristics of underwater acoustic channel, the LMS algorithm with fixed step-size is improved by introducing inverse hyperbolic sine function. The function expression of step-size |$\mu (n)$| changing with error signal e(n) is $$\begin{equation} \mu (n)=\beta \times \arcsin \mathrm{h}\ \left(\alpha{\left|e(n)\right|}^{\gamma}\right), \end{equation}$$(6) where e(n) is the error signal between the expected signal d(n) and the output signal y(n) of the equalizer. β, α, γ are the adjustment parameters. Among them, β is the parameter that controls the value range of the step-size factor, α is the parameter that controls the overall shape of the curve and γ is the parameter that controls the steady-state mean square error range as the step-size factor tends to be zero. Three parameters are introduced in order to make the nonlinear function relation between step-size factor and error signal more controllable. When parameter β changes, the relationship curve between |$\mu (n)$| and e(n) is shown in Fig. 3(a). The larger β is, the larger the value range of step-size factor |$\mu (n)$| is and the faster the convergence speed is. Therefore, it is necessary to choose the appropriate β according to the actual situation. When parameter α changes, the relationship curve between |$\mu (n)$| and e(n) is shown in Fig. 3(b). The influence of parameter α on the relationship curve is mainly reflected in the degree of curve bending, which means that α is mainly used to control the sensitivity of step-size change. When α is small, the step-size is small and the sensitivity of the change is low, which will lead to slow convergence speed of the algorithm. When α is large, the sensitivity of the step-size change is high, which may lead to the steady-state maladjustment of the communication system. Therefore, it is necessary to select the appropriate α according to the actual situation. When parameter γ changes, the relationship curve between |$\mu (n)$| and e(n) is shown in Fig. 3(c). When γ = 1, the bottom of the curve is sharp, which indicates that when the communication system tends to converge, the sensitivity of step-size change is extremely high, which may lead to the steady-state imbalance. As γ increases, the bottom of the curve is smooth, but when γ is large, there is a case where the step-size factor is extremely small and the error is still large, which will reduce the convergence speed of the algorithm. Moreover，since γ is a power of |$\Big|e(n)\Big|$|⁠, it should not be too large, otherwise it will lead to a sharp increase in the amount of calculation. Therefore, γ = 2 or γ = 3 should be selected. In this paper, γ = 2 is selected for the convenience of calculation. Therefore, the initial improved variable step-size LMS algorithm can be expressed as follows: $$\begin{equation}\hskip4pt e(n)=d(n)-{\mathbf{u}}^T(n)\mathbf{w}(n), \end{equation}$$(7) $$\begin{equation}\hskip23pt \mu (n)=\beta \times ar \ \sinh \left(\alpha{\left|e(n)\right|}^2\right), \end{equation}$$(8) $$\begin{equation} \mathbf{w}\left(n+1\right)=\mathbf{w}(n)+2\mu (n)e(n)\mathbf{u}(n). \end{equation}$$(9) 3.3. Improvement of anti-noise performance In underwater acoustic communication system, additive noise can be regarded as Gaussian white noise with zero mean value. When the algorithm converges, the interference of additive noise will cause the step-size |$\mu (n)$| to fall short of the optimal value, which will affect the steady-state error of the algorithm. The error signal e(n) consists of additive noise and equalizer noise, and the expression is $$\begin{equation} e(n)=N(n)+{\mathbf{u}}^T(n)\varDelta \mathbf{W}(n), \end{equation}$$(10) where N(n) is the additive white noise with zero mean value in the system and |$\varDelta \mathbf{W}(n)$| is the difference between the optimal weight coefficient of the equalizer and the current weight coefficient. When the weight coefficient of the equalizer tends to the optimal weight coefficient, only the additive noise is left in e(n), so the expression of e(n) is $$\begin{equation} e(n)=N(n). \end{equation}$$(11) In this case, |$E[e(n)]=0$|⁠, where |$E[e(n)]$| is the mean of the error signal. However, in Equation (8), γ = 2 is selected in this paper and |$E\big[{e}^2(n)\big]$| is not zero, which results in that when the algorithm converges, the step-size fluctuates around the optimal value and the steady-state mean square error also increases. Therefore, the LMS algorithm based on inverse hyperbolic sine function is improved. In Equation (11), |${\big|e(n)\big|}^2$| is replaced by |$\big|E\big[e(n)\big]\big|\big|e(n)\big|$|⁠, so Equation (11) becomes $$\begin{equation} {\mu}_1(n)=\beta \times ar \ \sinh \left(\alpha \left|E\left[e(n)\right]\right|\left|e(n)\right|\right). \end{equation}$$(12) In Equation (12), |$E\big[e(n)\big]=0$| when the weight coefficient of the equalizer tends to the optimal weight coefficient. Therefore, when the algorithm converges, the step-size is in a stable state and is no longer affected by additive white noise, which improves the anti-noise performance of the algorithm and reduces the steady-state error of the algorithm to some extent. Therefore, the iterative formula of the variable step-size LMS algorithm based on the inverse hyperbolic sine function after improving the anti-noise performance is $$\begin{equation} \mathbf{w}\left(n\!+\!1\right)\!=\!\mathbf{w}(n)+2\left[\beta \times ar \ \sinh \left(\alpha \left|e(n)\right|\left|E\left[e(n)\right]\right|\right)\right]e(n)\mathbf{u}(n). \end{equation}$$(13) 4. Novel CMA+DD_LMS blind equalization algorithm 4.1. Variable step-size CMA+DD_LMS algorithm The variable step-size LMS algorithm given in Section 3 is used to replace the fixed step-size LMS algorithm in DD_LMS algorithm, so the update formula of weight coefficient of the variable step-size DD_ LMS blind equilibrium algorithm is $$\begin{align}& {\mathbf{w}}_D\left(n+1\right)\\ &\ =\!{\mathbf{w}}_D(n)\!+\!2\left[\beta \!\times\! ar \ \sinh \left(\alpha \left|{e}_D(n)\right|\left|E\left[{e}_D(n)\right]\right|\right)\right]{e}_D(n){\mathbf{u}}_D(n).\nonumber \end{align}$$(14) Similarly, considering the contradiction between the convergence rate and steady-state error of CMA, Equation (12) is substituted into Equation (1). Therefore, the update formula of weight coefficient of the variable-step CMA is expressed as $$\begin{align}& {\mathbf{w}}_C\left(n+1\right)\\ &\ =\!{\mathbf{w}}_C(n)+2\left[\beta \!\times\! ar \ \sinh \left(\alpha \left|{e}_C(n)\right|\left|E\left[{e}_C(n)\right]\right|\right)\right]{e}_C(n){\mathbf{u}}_C^{\ast }(n). \nonumber\end{align}$$(15) 4.2. Switching method based on the difference of iterative error The hard switching based on fixed threshold of CMA+DD_LMS algorithm is greatly affected by channel noise, so it will cause false switching of the algorithm in low SNR environment. In order to avoid this problem, a switching method based on the difference of iterative error is proposed. The principle of the improved CMA+DD_LMS algorithm is shown in Fig. 4. FIGURE 4. Open in new tabDownload slide Schematic diagram of CMA+DD_LMS algorithm based on the difference of iterative error. FIGURE 4. Open in new tabDownload slide Schematic diagram of CMA+DD_LMS algorithm based on the difference of iterative error. The switching condition of this improved algorithm is controlled by the difference of the error signal of CMA with variable step-size, and the difference is $$\begin{equation} {e}_{\varDelta }(n)={e}_C(n)-{e}_C\left(n-k\right), \end{equation}$$(16) where |${e}_C(n)$| is the current error signal of CMA with variable step-size, |${e}_C\Big(n-k\Big)$| is the error signal before k times of CMA algorithm and |${e}_{\varDelta }(n)$| is the difference of the iteration error of adjacent k times of CMA algorithm with variable step-size. The value of k should be set according to the actual channel environment. Assuming that the switching threshold value of the algorithm is ε1, then the update formula of weight coefficient of the improved CMA+DD_LMS algorithm is $$\begin{equation} \left\{\!\!\begin{array}{l}{\mathbf{w}}_C\left(n+1\right)=\mathbf{w}(n)+\left[\beta \times ar \ \sinh \left(\alpha \left|{e}_C(n)\right|\left|E\left[{e}_C(n)\right]\right|\right)\right]\\\ \quad{e}_C(n){\mathbf{u}}_C^{\ast }(n) \ {e}_{\varDelta }(n)>{\varepsilon}_1\\{}{\mathbf{w}}_D\left(n+1\right)=\mathbf{w}(n)+\left[\beta \times ar \ \sinh \left(\alpha \left|{e}_D(n)\right|\left|E\left[{e}_D(n)\right]\right|\right)\right]\\\ \quad{e}_D(n){\mathbf{u}}_D^{\ast }(n) \ {e}_{\varDelta }(n)\le{\varepsilon}_1,\end{array}\right. \end{equation}$$(17) where the value of ε2 should be set according to actual needs. 4.3. Algorithm flow (i) Initialize variable step-size CMA, mainly to initialize the weight coefficient. (ii) In the initial stage of the algorithm, variable step-size CMA is used for iterative operation. Compared with CMA with fixed step-size, variable step-size CMA has a faster convergence rate and can quickly make the algorithm reach the convergence state. (iii) Calculate the iterative error of adjacent k times of the CMA with variable step-size. When the difference is less than or equal to ε1, the variable step-size CMA is already in a convergence state. At this time, the algorithm will be switched to the variable step-size DD_LMS algorithm. (iv) Calculate the iterative error of the adjacent k times of the DD_LMS algorithm with variable step-size. When the difference is less than or equal to ε2, the algorithm is in a convergence state. At this time, the mean square error reaches the minimum value and the whole communication system has been working in a stable state, then the algorithm ends up running. ε2 mentioned in this part is the end threshold of the algorithm and needs to be set according to actual requirements. 5. Simulation and analysis In the simulation experiment, the input signals are binary sequences with equal probability and quadrature phase shift keying (QPSK) modulation mode is adopted. The adding noise is Gauss white noise with zero mean, and SNR is set to 18 dB. The length of the equalizer is 21. What is more, a typical shallow seawater acoustic channel is adopted in this simulation and the channel model has been verified by the sea experiment. The parameters of the channel model are set as follows: The transmission baud rate is 1000 symbol/s; the channel bandwidth is 2 kHz; the carrier frequency is 10 kHz; and the transmitter and receiver are located at 10 meters underwater, with a distance of 5000 meters. The parameters of eight rays of the channel models are listed in Table 1 [5, 15]. Finally, it is determined that the optimal parameters of the algorithm in this simulation environment are |$\alpha=0.034, \ \gamma=2, \ \mathrm{k}=20, \ {\varepsilon}_1=3\times{10}^{-2}, \ {\varepsilon}_2=2\times{10}^{-3}$|⁠. TABLE 1. The parameters of eight rays of the channel models. Ray number . Time delay(t/ms) . Sound pressure normalized amplitude . Ray number . Time delay(t/ms) . Sound pressure normalized amplitude . 1 0.000 1.0000 5 0.100 0.3286 2 0.026 −1.0000 6 0.240 −0.3286 3 0.026 −0.3286 7 0.420 −0.1080 4 0.100 0.3286 8 0.420 0.1080 Ray number . Time delay(t/ms) . Sound pressure normalized amplitude . Ray number . Time delay(t/ms) . Sound pressure normalized amplitude . 1 0.000 1.0000 5 0.100 0.3286 2 0.026 −1.0000 6 0.240 −0.3286 3 0.026 −0.3286 7 0.420 −0.1080 4 0.100 0.3286 8 0.420 0.1080 Open in new tab TABLE 1. The parameters of eight rays of the channel models. Ray number . Time delay(t/ms) . Sound pressure normalized amplitude . Ray number . Time delay(t/ms) . Sound pressure normalized amplitude . 1 0.000 1.0000 5 0.100 0.3286 2 0.026 −1.0000 6 0.240 −0.3286 3 0.026 −0.3286 7 0.420 −0.1080 4 0.100 0.3286 8 0.420 0.1080 Ray number . Time delay(t/ms) . Sound pressure normalized amplitude . Ray number . Time delay(t/ms) . Sound pressure normalized amplitude . 1 0.000 1.0000 5 0.100 0.3286 2 0.026 −1.0000 6 0.240 −0.3286 3 0.026 −0.3286 7 0.420 −0.1080 4 0.100 0.3286 8 0.420 0.1080 Open in new tab The CMA, CMA+DD_LMS algorithm and the novel CMA+DD_LMS algorithm are compared, and the simulation results are shown in Fig. 5(a). The convergence speed of the novel CMA+DD_LMS algorithm is the fastest. Compared with CMA, it can enter the convergence state about 25 times in advance, and compared with CMA+DD_LMS algorithm, it can enter the convergence state about 400 times in advance. In terms of steady-state error, the steady-state property of the novel CMA+DD_LMS algorithm is better because its steady-state mean square error is ~3 dB lower than CMA+DD_LMS algorithm and ~18 dB lower than CMA algorithm. The above results show that the proposed algorithm has good equalization performance and anti-noise performance. FIGURE 5. Open in new tabDownload slide Comparison of algorithm performance under two kinds of input SNR. FIGURE 5. Open in new tabDownload slide Comparison of algorithm performance under two kinds of input SNR. Considering the complex channel environment of underwater acoustic communication, it is necessary to verify the performance of the proposed algorithm under the condition of low SNR, so the SNR is changed to 9 dB. The DD_LMS algorithm, CMA and the novel CMA+DD_LMS algorithm are compared, and the simulation results are shown in Fig. 5(b). It can be seen that under the condition of low SNR, the DD_LMS algorithm approximates the divergence state and cannot equalize the communication system. Although CMA can enter a convergence state, its steady-state error and fluctuation are large. However, the steady-state error of the improved algorithm is ~10 dB lower than that of CMA and its convergence speed is ~15% higher than that of CMA. Therefore, the novel CMA+DD_LMS can work stably in low SNR environment. FIGURE 6. Open in new tabDownload slide The constellations of QPSK symbols through the shallow seawater acoustic channel without equalization. FIGURE 6. Open in new tabDownload slide The constellations of QPSK symbols through the shallow seawater acoustic channel without equalization. Figures 6 and 7 are the constellations of symbols before and after blind equalization under the SNR of 18 dB. Through the comparison of Fig. 6, Fig. 7(a) and (b), it can be seen that compared with CMA+DD_LMS, after using the proposed algorithm, the signals are stable in four phases and the decision error of the equalizer is smaller. Therefore, the novel CMA+DD_LMS can cancel the influence of multipath and noise to a certain extent and achieve reliable communication. FIGURE 7. Open in new tabDownload slide The constellations of equalized QPSK symbols through the shallow seawater acoustic channel by using (a) CMA+DD_LMS and (b) the proposed algorithm. FIGURE 7. Open in new tabDownload slide The constellations of equalized QPSK symbols through the shallow seawater acoustic channel by using (a) CMA+DD_LMS and (b) the proposed algorithm. Figure 8 shows the BER of the system before equalization, after CMA+DD_LMS equalization and after novel CMA+DD_LMS equalization. It verifies the receiving performance of the novel CMA+DD_LMS under the different SNRs of the shallow water acoustic channel model. It can be seen from Fig. 8 that with the increase of SNR, the BER of the system presents a downward trend before equalization, after CMA+DD_LMS equalization and after the novel CMA + DD_LMS equalization. When the SNR is low, the BER of the three cases is similar. With the increase of SNR, the BER of the system before equalization decreases slowly, while the BER of the system after equalization decreases obviously, and after using CMA+DD_LMS equalization and using the novel CMA + DD_LMS equalization, the BER difference of the system gradually becomes larger and the proposed algorithm has the lowest BER. FIGURE 8. Open in new tabDownload slide Performances of equalization under different SNRs. FIGURE 8. Open in new tabDownload slide Performances of equalization under different SNRs. 6. Conclusion The variable step-size method is introduced into the CMA + DD_LMS algorithm, and the error values of the step-size function are replaced with error expectations. In addition, the difference of the iteration error of adjacent k times is used as the switching condition of the CMA+DD_LMS algorithm. Therefore, the improved algorithm has good equalization and anti-noise performance under both high and low SNR, which can effectively reduce the BER of underwater acoustic communication system. When the input SNR is 9 dB, the steady-state error of the improved algorithm is ~10 dB lower than that of CMA and its convergence speed is ~15% higher than that of the CMA. As a result, the novel CMA+DD_LMS blind equalization algorithm can be effectively applied in the communication system of the underwater robots of shallow sea. Conflict of Interest: The authors declare no conflict of interest. References [1] Page , B.R. , Ziaeefard , S., Pinar , A.J. and Mahmoudian , N. ( 2016 ) Highly maneuverable low-cost underwater glider: Design and development . IEEE Robot. Auto. Lett. , 2 , 344 – 349 . 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For permissions, please e-mail: journals.permissions@oup.com This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model (https://academic.oup.com/journals/pages/open_access/funder_policies/chorus/standard_publication_model)
TI - A Novel CMA+DD_LMS Blind Equalization Algorithm for Underwater Acoustic Communication
JF - The Computer Journal
DO - 10.1093/comjnl/bxaa013
DA - 2020-06-18
UR - https://www.deepdyve.com/lp/oxford-university-press/a-novel-cma-dd-lms-blind-equalization-algorithm-for-underwater-g0FHnhZ79X
SP - 974
VL - 63
IS - 6
DP - DeepDyve
ER -