1069-1073In this paper, a MATLAB based smart antenna testbed that efficiently localizes the line-of-sight (LOS) source in the presence of multipath signals is developed. By exploiting the consistent amplitude nature of the LOS signal, a variant of Constant Modulus Algorithm, namely Multitarget-Least Square Constant Modulus Algorithm is employed to adapt and update the weights of the smart antenna for estimation of the direction-of-arrival (DOA) of the of the LOS and multipath interference signals. Performance is compared with the conventional and recently proposed algorithms in the same testbed with alike considerations. Simulation result shows that the proposed method of DOA estimation performs better in terms of probability of resolution and root mean square error

Ganguly, Saurav

Ghosh, Jayanta

Kumar, Puli Kishore

Mukhopadhyay, Mainak

NOPR

Journal of Scientific & Industrial Research Vol. 79, December 2020, pp. 1069-1073 An Efficient Source Localization Method in Presence of Multipath using Smart Antenna System Saurav Ganguly1*, Jayanta Ghosh1, Puli Kishore Kumar2 and Mainak Mukhopadhyay31National Institute of Technology Patna, Patna 800 005, India 2National Institute of Technology Andhra Pradesh, Tadepalligudem 534 102, India 3Birla Institute of Technology, Mesra, Deoghar Campus, Deoghar 814 142, India Received 11 May 2020; revised 12 October 2020; accepted 06 November 2020 In this paper, a MATLAB based smart antenna testbed that efficiently localizes the line-of-sight (LOS) source in the presence of multipath signals is developed. By exploiting the consistent amplitude nature of the LOS signal, a variant of Constant Modulus Algorithm, namely Multitarget-Least Square Constant Modulus Algorithm is employed to adapt and update the weights of the smart antenna for estimation of the direction-of-arrival (DOA) of the of the LOS and multipath interference signals. Performance is compared with the conventional and recently proposed algorithms in the same testbed with alike considerations. Simulation result shows that the proposed method of DOA estimation performs better in terms of probability of resolution and root mean square error. Keywords: Array processing, DOA estimation, LOS, LS-CMA, Multipath transmission, Smart antennas Introduction Accurate source localization in a multipath environment always remains a challenge for researchers and engineers for decades. The perception of smart antenna, which uses an antenna array with an adaptive signal processor that can adjust its own beam pattern to put emphasis on signals of interest (SOI) and minimize signals, not of interest (SNOI) have aided to enhance direction finding capabilities and mitigate multipath interference. Blind adaptive algorithms always have advantages over non-blind counterparts, as the requisite training signal is not required, which reduces the spectral efficiency of the system. Constant Modulus Algorithm (CMA) proposed by Godard and later improved by Treichler and Agee1 is a blind deconvolution iterative approach that inclines to preserve the envelope of the beam forming output at a nearly constant level, so it can separate the SOI from the SNOI. Least Square CM algorithm (LSCMA) that was proposed by Agee2, uses the least square method and minimizes the cost function over a single block of data vectors which are updated on a block by block basis. Thus, LSCMA obtain faster convergence rate3 and global stability as compared to conventional CMA. In this paper, we make use of the Multi-target LSCMA (MT-LSCMA) based adaptive array system to estimate the direction-of-arrival (DOA) of the LOS source signal (SOI) in a multipath environment. A quasi-stationary source is assumed at the far-field region of the receiver smart antenna. MT-LSCMA exploits the constant amplitude property of the envelope of the narrowband received signals and extracts the SOI and suppresses the multipath (SNOI) or non-LOS (NLOS) signals by generating two sets of weights. Each set of weights selects one of the received signals as the SOI, rejecting the other as SNOI. This reduces the possibility of estimating a strong SNOI and rejecting an SOI, thus increasing the efficiency as compared to CMA and LSCMA. A MATLAB testbed is proposed in this paper that uses MT-LSCMA based smart antenna system that adaptively updates the weights for source localization or DOA estimation of the LOS signal. Multipath interference (SOI or NLOS) signals are suppressed effectively. Performance is evaluated in terms of probability of resolution and root mean square error with the conventional MUltiple SIgnal Classification (MUSIC) algorithm as well as with recently proposed Modified-MUSIC (M-MUSIC)4, and Normalized Least Mean Square (NLMS)5 algorithms. Both M-MUSIC and NLMS have faster convergence rate with respect to their foundation methods of MUSIC and ——————— *Author for CorrespondenceE-mail: saurav.ece15@nitp.ac.inJ SCI IND RES VOL 79 DECEMBER 2020   1070LMS algorithms.6 While M-MUSIC uses block adaptation concepts, NLMS simply normalizes the adapted weight values. But NLMS, being non-blind adaptation method, requires a desired or training signal to develop the cost function. Industry level development can be achieved with the proposed MATLAB testbed.  The rest of the paper is organized as follows. Section-II deliberates on the materials and methods (data model of DOA estimation) by an MT-LSCMA based adaptive array or smart antenna system. A brief mathematical outline is also stated for MUSIC, M-MUSIC and NLMS DOA estimation methods. In section-III, results and discussions (simulation results) of MATLAB testbed is projected. Performance comparison based on probability of resolution and root mean square error areaccomplished here. The paper is concluded by section-IV with conclusion.  Materials and Methods  Data Model for DOA Estimation Basic notations used: 𝑁 represents the total number of elements of the smart antenna. 𝐷 signifies the number of narrowband signals, including the LOS (SOI) and NLOS (SNOI) that impinges on the array, while 𝑛 indicates the iteration number. Bold letter symbols depict matrices or vector quantities. All other notations would be made familiar as and when essential. In Fig. 1 a uniform linear array (ULA) of a smart antenna consisting of 𝑁similar and isotropic antenna elements, placed along the 𝑦 − axis with element spacing as 𝜆 2 is depicted. RF signal generated by a source in the far field region, directly falls on the array with a DOA of 𝜃 , with constant amplitude. Multipath uncorrelated interference signals of the same source impinge on the array from various directions, 𝜃 ,𝜃 , ……… 𝜃  etc. It is assumed that the signals travel through an AWGN, frequency selective channel that is homogenous and isotropic. Considering narrowband signal source, we can write the array input signal vector at the k  snapshot as: 𝑥(k) = 𝐴𝐵𝑆 (k) + 𝑛(k)     … (1) where 𝑥(k) = [𝑥 , …… . 𝑥 ]  is the received signal vector of the order of 𝑁 × 1. 𝐴 = 𝐴(𝜃) =[𝑎(𝜃 )	𝑎(𝜃 )……𝑎(𝜃 )] is the 𝑁 × 𝐷	array manifold matrix whose columns are {𝑎(𝜃 )}, signifying the response of the array to a narrowband signal originating from a specific bearing. 𝐵 = 𝑑𝑖𝑎𝑔(𝛽) is the 𝐷 × 1 channel gain matrix with parameters 𝛽 = [𝛽 	𝛽 ……𝛽 ] , where 𝛽 ∈ ℝ is the amplitude of the 𝑖  signal. 𝑆 (𝑘) = [𝑠(𝑘)𝑖 (𝑘)…… 𝑖 (𝑘)]  is the 𝐷 × 1 source vector with an overall 𝐷 narrowband signals impinging on the array including the LOS source and its multipath components. It is assumed that 𝐷 ≤ 𝑁. 𝑛(k) is the AWGN vector with zero mean and variance as 𝜎  and 𝜃 = [𝜃 ……𝜃 ] is the DOA vector of the impinging signals. (. )  represents vector transpose operation. The CM array receives 𝑥(𝑘) and form blocks of data vector as 𝑋 = [𝑥(1)…… . 𝑥(𝑝)] where 𝑝is the number of data samples in each block. As an alternative of directly estimating the correlation matrix 𝑅 , it estimates 𝑆 (𝑘) of 𝑆 (𝑘) and source direction vector 𝑎  in a block iterative process and hence the angle of arrival 𝜃 . From Fig. 1, the output of the weight-and-sum beam former is given by: 𝑦(𝑘) = 𝑤 (𝑘)𝑋(𝑘)    … (2) where 𝑤(𝑘) = [𝑤 (𝑘)……𝑤 (𝑘)]  are the adaptive weights accustomed by MT-LSCM algorithm and (. )  is the Hermitian transpose. To determine the adaptive weights, the dynamic nonlinear least-square CM optimizes ‖𝑤∗𝑋 − 𝑆‖∗	 				𝑠. 𝑡											|𝑆 (𝑡)| = 1							𝑡 = 1,……𝑁 where ‖. ‖ is the vector 2−norm. The minimization is achieved by projecting 𝑤∗𝑋 into the set of constant modulus signals through dividing entry-wise by modulus by means of the projection operator 𝑟(𝑆) =( )| ( )| …… ( )| ( )| , where 𝑛 is the number of iterations. Finally, we can optimize over 𝑤and find the least square solution as 𝑤∗ = 𝑆𝑋ϯ, where ϯ denotes the Moore-Penrose pseudo inverse. Given an initial point 𝑤( ), the value of the weights updated by block iteration is given by:   Fig.1 — DOA estimation with LSCM array  GANGULY et al.: AN EFFICIENT SOURCE LOCALIZATION METHOD IN PRESENCE OF MULTIPATH   1071𝑆( ) = 𝑟(𝑆) 𝑤( )∗𝑋𝑤( ) = 𝑆( )𝑋ϯ      … (3) The weight updating calculation of MT-LSCMA  is given by Eq. (3). In a changing environment,  the data blocks are updated for each iteration, resulting in dynamic MT-LSCMA. The iterations continue until appropriate convergence is satisfied. Characteristically, this is somewhat similar to the Sample Matrix Inversion (SMI) algorithm.7,8  The summary of the proposed method is provided below in Table 1. For the conventional MUSIC algorithm, we use the array correlation matrix from equation (1) as 𝑅 =𝐴𝑅 𝐴 + 𝑅  where 𝑅  is the 𝐷 × 𝐷 source covariance matrix and 𝑅  is the 𝑁 × 𝑁 noise correlation matrix. MUSIC, being a subspace based method, performs eigenvalue decomposition of 𝑅  and estimates signal and noise subspace (𝐸  and 𝐸  respectively) from 𝑅 . Finally, the spectrum [𝑎(𝜃) 𝐸 𝐸 𝑎(𝜃)]  is calculated w.r.t  𝜃 to estimate 𝐷 number of peaks from the pseudospectrum.  In M-MUSIC algorithm, as proposed by Liu et al.4 a new array correlation matrix 𝑅  is formed from randomly chosen 𝑁  elements from 𝑁 for 𝑁 < 𝑁. Next, Nyström approximation is employed for estimation of noise subspace, 𝐸 . After this, the procedure continues in a similar approach as MUSIC in estimating DOA angle 𝜃.  The NLMS algorithm for DOA estimation, as proposed by Bakhshi and Shahtalebi5, uses a training or desired signal 𝑑 to minimize the mean square error (MSE) with the output of the array in an iterative, normalized updating. The DOA angle is estimated by optimizing   𝜃 = 𝑎𝑟𝑔𝑚𝑎𝑥𝜃 {‖𝑎(𝜃)| ‖},   where ‖𝑎(𝜃)| ‖ is the norm of the weight estimates and 𝑛 is the total number of iterations.  Results and Discussion  Simulation Results A MATLAB based testbed of smart antenna is designed where we inspect the performance of the proposed method and compare with the established schemes of source localization/DOA estimation, namely MUSIC, M-MUSIC and NLMS. The experiments are carried out in MATLAB R2018,  on a laptop based on Intel (R) Core (TM) i7-8656U CPU @ 4.6	𝐺𝐻𝑧 and 8 GB RAM. The system type is 64-bit operating system-Microsoft Windows 10 Home edition. A 3	𝐺𝐻𝑧 signal is generated in the far field of an 16 − element ULA based receiver, whose antenna element spacing is fixed at = 0.005	𝑚.	 This narrowband signal, having constant amplitude, is the LOS (or SOI) that impinges on the ULA at an angle of 35°. Three multipath interfering signals constituting NLOS (or SNOI) arrive at the ULA from ±50° and −30°. The number of snapshots is considered to be 𝑘 = 10. The block length of MT-LSCMA is assumed to be 𝑝 = 130. For M-MUSIC, 𝑁 = 8 and for NLMS, the step size is set at 𝜇 = 0.1. The DOAs are expected to be random variables with uniform distribution over (−90°90°). Considering AWGN, the SNR is varied between −15	𝑑𝐵	to 15	𝑑𝐵.  A plot of the variation of a normalized array factor (in	𝑑𝐵) with DOA of the proposed method at 𝑆𝑁𝑅 =0	𝑑𝐵 is given in Fig. 2. The vertical dotted line at 35°   Fig. 2 — Variation of normalized AF with DOA angles at SNR = 0	dB Table 1 — DOA estimation procedure of the proposed method 1. Receive k snapshots of 𝑥(k) 2. Form the block sets 𝑋 = [𝑥(1)…… 𝑥(p)] 3. Establish the weight update vectors of MT-LSCMA by using equation (3) and estimate the manifold matrix 𝐴 = [𝑎(𝜃 )…… 𝑎(𝜃 )] 4. 𝜃 = 𝑎𝑟𝑔𝑚𝑎𝑥 𝑎∗𝑎(𝜃)‖𝑎(𝜃)‖ For each column vector 𝑎(𝜃 ) of 𝐴, estimate 𝜃  from the peaks of the plot. The projection of 1D of each 𝑎  into the array steering matrix is given by: J SCI IND RES VOL 79 DECEMBER 2020   1072(angle of arrival) indicates the LOS source and the other vertical dotted lines specify the multipath interference signal directions. The interference locations are suppressed considerably while the direction of the LOS has high value of normalized AF (Fig. 2).  Now we compare this method with MUSIC,  M-MUSIC and NLMS in terms of probability of resolution (𝑃 ) and root mean square error (RMSE) of the estimated DOA of the LOS signal. We define probability of resolution as follows8 𝑃 = 𝑃𝑟𝑜𝑏 𝜃 − 𝜃 ≤ , 𝑖 = 1……𝑚,  where Δ𝜃 = min	{|𝜃 − 𝜃 |, 1 ≤ 𝑖 ≤ 𝑖 ≤ 𝑚}.  The RMSE for 𝑄 number of Monte Carlo trials is given as below8 𝑅𝑀𝑆𝐸 = ∑ ∑ (𝜃 − 𝜃 ) , assuming 𝑄 = 1000 trials. The same experimental parameters of DOAs of the LOS and NLOS signals are fixed.  The variation of RMSE with SNR varied between ±15	𝑑𝐵 with steps of 1	𝑑𝐵 as shown in Fig. 3a.  The plot clearly depicts that the proposed method outperforms the other methods as SNR increases.  M-MUSIC and NLMS almost have the same performance over the total SNR range while MUSIC, like the proposed method has improved performance at higher SNR values. The variation of 𝑃  with SNR in the same range with steps is given in Fig. 3b. The proposed method shows slightly better resolution than MUSIC and NLMS as SNR increases, while the resolution ability of M-MUSIC in the same SNR range remains inferior.  Conclusions A MATLAB testbed is proposed in this paper for efficient DOA estimation or source localization of a smart antenna system in presence of interfering multipath signals. Multi-target LSCM algorithm   Fig. 3(a-b) — (a) Variation of RMSE of DOA estimation with SNR and (b) Variation of P  with SNR  GANGULY et al.: AN EFFICIENT SOURCE LOCALIZATION METHOD IN PRESENCE OF MULTIPATH   1073exploits the constant amplitude property of the line-of-sight signal in the multipath scenario and efficiently locate the source direction while suppressing the multipath signals received by the adaptive array of smart antenna. Simulation results in resolution and root mean square error versus SNR (dB) clearly shows that the proposed method performs better thanthe conventional MUSIC algorithm and newly developed M-MUSIC and NLMS algorithms at considerable SNR values. Lower computational complexity can be achieved as sub-space based decomposition can be avoided as in MUSIC and M-MUSIC. In addition, higher spectral efficiency can be accomplished as compared to NLMS as constant modulus based algorithm do not require training or desired signal to adapt the weights. Block adaptation correspondingly involves a lesser number of iterations to achieve global minima, making it a fast estimation process. The MATLAB based testbed can be extended for the development of industry level smart antenna system.  Acknowledgement The first author would like to acknowledge the Ministry of Electronics and Information Technology (Meity), Govt. of India for supporting and financial assistance during research work through Visvesvaraya Ph.D. scheme for Electronics and IT. (Unique Awardee Number: VISPHD-MEITY-1742)  References 1 Treichler J R and Agee B G, A new approach to multipath correction of constant modulus signals, IEEE Transactions on Acoustics, Speech and Signal Processing, ASSP-31(2) (1983) 459–472.  2 Agee B G, the least square CMA: A new technique for rapid correction of constant modulus signals, in International Conference on Acoustics, Speech and Signal Processing, Tokyo, 1986.  3 Ganguly S, Ghosh J and Kishore P K, Performance analysis of array signal processing algorithms for adaptive beamforming, in URSI Asia Pacific-Radio Science Conference, New Delhi, 2019.  4 Liu G, Chen H, Sun X and Qiu R C, Modified MUSIC algorithm for DOA estimation with Nyström approximation, IEEE Sensors Journal, 16(12) (2016) 4673–4674.  5 Bakhshi G and Shahtalebi K, Role of the NLMS algorithm in direction of arrival estimation for antenna arrays, IEEE Communications Letters, 22(4) (2018) 760–763.  6 Sharma A and Mathur S, Performance analysis of adaptive array signal processing algorithms, IETE Technical Review, 33(5) (2016) 472–491.  7 Saxena P and Kothari G A, Performance analysis of adaptive beamforming algorithms for smart antennas, in Proc IERI-2014 International Conference on Future Information Engineering, Beijing, 2014.  8 Gross F, Smart antennas, in Smart Antennas With MATLAB, 2nd edn (McGraw -Hill Education, New York) 2015   pp. 237–296.  

An Efficient Source Localization Method in Presence of Multipath using Smart Antenna System

http://nopr.niscair.res.in/bitstream/123456789/55732/1/JSIR%2079%2812%29%201069-1073.pdf

An Efficient Source Localization Method in Presence of Multipath using Smart Antenna System

Abstract

Similar works

Full text

Available Versions

NOPR