Improved Iterative Inverse Matrix Approximation Algorithm for Zero Forcing Precoding in Large Antenna Arrays

Abstract

Precoding algorithms are used in massive multiple-input multiple-output (mMIMO) communication systems to ensure effective signal transmission. The zero-forcing (ZF) is one of the most common linear precoding algorithms used in MIMO and mMIMO systems. ZF precoding is complex to implement because it requires direct matrix inversion of the gram matrix. Iterative algorithms have been proposed for approximating matrix inversions. However, iterative algorithms require initial conditions and pre-computations to converge to the optimal transmitted signal vector. This paper proposes a new improved iterative algorithm that guarantees convergence under any circumstances without dependency on any optimized initial parameter or condition. The proposed algorithm is based on a three-step iterative and iterative generalized inverse matrix approximation algorithm. The proposed algorithm was verified using a new correlated channel model that included mutual coupling effects and gain and phase variances caused by radio frequency elements at a base station (BS). The computational complexity of the proposed algorithm was then computed. This study analyzes and compares the bit error rate (BER) performance of the proposed algorithm with that of prominent existing algorithms. Moreover, the sum-rate performance of the proposed algorithm was analyzed. Simulations were performed under both correlated and uncorrelated channel conditions, for comparison and analysis. The simulation results demonstrate that the proposed algorithm outperforms the compared algorithms in terms of the convergence and convergence rates.INDEX TERMS Adaptive antenna system, approximate matrix inversion, iterative algorithms, massive MIMO, ZF precoding.

A Mutual Coupling-Based Full Self-Online Calibration Method for Antenna Arrays in Uplink

“…Direct inversion of matrices is unfavorable for hardware since direct inversion involves a division operator, which often leads to inaccurate results [4]. Therefore, many inverse matrix approximation methods have been proposed in the literature that degrades the inverse matrix operation to matrix multiplications and matrix sums.…”

“…The most prominent inverse matrix approximation methods can be listed as Newton iteration method (NI), Chebyshev iteration method (CI) and successive over relaxation-based approximate matrix inversion method [38]. However, all of these methods require initial conditions and a Toeplitz or a symmetrical precondition matrix to guarantee the convergence [4].…”

“…In absence of reciprocity of mutual coupling between neighboring antennas, (𝐶 𝑚𝑘 ≠ 𝐶 𝑘𝑚 ), the convergence of these inverse matrix approximation methods is not guaranteed. Therefore, we adopted the inverse matrix approximation method in [4], which is globally convergent without needing any initial Toeplitz or symmetric matrix and preconditions. Then the error compensation matrix in the desired pointing direction, 𝐌 ̃𝑒 −1 ϵ ℂ 𝑀×𝑀 , can be approximated as:…”

“…Large-scale phased array antennas are considered to play fundamental role in the fifth-generation (5G) [1], [2] and future sixth-generation (6G) wireless communication systems [3], [4]. The new generation 5G and 6G wireless systems are expected to be used in many civil, commercial, and military areas such as massive multiple-input multiple-output (mMIMO) [5], [6], autonomous driving [7], satellite systems [3], internet of things (IoT) [4], anti-jamming, and antispoofing [8]. With the latest developments in phased array antenna technology, beamforming is intended to be one of the key techniques for the next generation wireless systems [1], [2], [9].…”

“…In addition, it is suitable for offline, on-site and on-line calibration. 4) A generalized iterative inverse matrix approximation method [4] is adopted to improve the accuracy of estimation of the error compensation matrix in hardware. 5) The isolation problem related to the non-directional couplers mentioned in [13], is tackled by employing RF circulators for each antenna branch.…”