Precise Channel Estimation Approach for a mmWave MIMO System

Abstract

Channel estimation is a formidable challenge in mmWave Multiple Input Multiple Output (MIMO) systems due to the large number of antennas. Therefore, compressed sensing (CS) techniques are used to exploit channel sparsity at mmWave frequencies to calculate fewer dominant paths in mmWave channels. However, conventional CS techniques require a higher training overhead for efficient recovery. In this paper, an efficient extended alternation direction method of multipliers (Ex-ADMM) is proposed for mmWave channel estimation. In the proposed scheme, a joint optimization problem is formulated to exploit low rank and channel sparsity individually in the antenna domain. Moreover, a relaxation factor is introduced which improves the proposed algorithm’s convergence. Simulation experiments illustrate that the proposed algorithm converges at lower Normalized Mean Squared Error (NMSE) with improved spectral efficiency. The proposed algorithm also ameliorates NMSE performance at low, mid and high Signal to Noise (SNR) ranges.

On the Performance of Efficient Channel Estimation Strategies for Hybrid Millimeter Wave MIMO System

“…After the initial transmission, the received signal matrix Y at the receiver’s end can be determined as: where, the received signal matrix is the combination of different received vectors, i.e., , alike Y the combining matrix W and precoding matrix F is also representing by the set of different combining and precoding vectors i.e., and , respectively. Here, is the set of transmitted vectors, A is the channel matrix and are independent and identically distributed (I.I.D) complex additive white gaussian noise (AWGN), with zero mean and [ 34 ]. For the simplicity of the system, let’s consider that the all pilot symbols are identically similar, therefore, one can assume that .…”

“…According to the geometric virtual (GV) model of mmWave MIMO system explained in [ 12 , 18 ], Equation (2) can be further elaborated as: where, denotes the total number of propagation paths, expressing the complex channel gain of the l-th path, and it can be obtained from the random complex Gaussian distributions, and . and are the array response vectors (ARV) at the transmitters and receivers, respectively [ 34 ] (see the references therein). and are the elevation and azimuth AoA and AoD angles at the transmitters and receivers, respectively [ 34 ] (see the references therein).…”

“… and are the array response vectors (ARV) at the transmitters and receivers, respectively [ 34 ] (see the references therein). and are the elevation and azimuth AoA and AoD angles at the transmitters and receivers, respectively [ 34 ] (see the references therein). The elevation and azimuth AoA and AoD angles can be produced by uniform Laplacian distributions, allocated within the range of 0 and 2 …”

“…ADMM is used for the narrowband and wideband channel estimation of mmWave MIMO system by exploiting the sparsity and low rank properties of channel were jointly exploited for efficient CSI estimation in [ 16 , 33 ]. An extended version of ADMM (Ex-ADMM) with a Fortin and Glowinski’s constant (i.e., the relaxation parameter) is also used for the narrowband channel estimation of mmWave MIMO systems in [ 34 ]. A symmetric version of ADMM (S-ADMM) came into the research domain very recently [ 35 , 36 ].…”

“…In this paper, the overrelaxed version of relaxation parameter have been considered for simulation and experiments. To explain the superiority of the proposed scheme, various different popular start-of-art schemes namely, OMP [ 13 ] Vector Message Approximation Passing (VAMP) [ 37 ], Ex-ADMM [ 34 ], ADMM [ 33 ], Block Orthogonal Matching Pursuit (BOMP) [ 38 ], Generalized Approximate Message Passing with Gaussian Mixture (GAMP-GM) [ 39 , 40 ] and Singular Value Thresholding (SVT) [ 41 ] have been considered for the comparison. Furthermore, the eminence of the proposed scheme is explained in terms of normalized mean squared error (NMSE), achievable spectral efficiency (ASE), convergence, effect on the number of scatterers and the number of possible paths.…”