Damped Jacobi Methods Based on Two Different Matrices for Signal Detection in Massive MIMO Uplink

Abstract

For massive multiple-input multiple-output (m-MIMO) uplink, the performances of the linear minimum mean-square error (MMSE) detector are considered near optimal, and they occupy benchmark place for most linear iterative detectors. However, the MMSE algorithm is known by its load computational complexity due to the implication of large-scale matrix inversions, and in other hand, iterative methods are often preferred in signal detection because of its low complexity. In this paper, we propose a New Damped Jacobi (NDJ) detector in order to improve the performance of the classical Jacobi linear algorithm. Starting from the classical Jacobi technique to our new proposal, we go through the development of two variants; one uses a damping factor and the other uses a stair-matrix. However, the NDJ incorporates a damping factor in its construction and basing also on stair matrix instead of diagonal matrix. The performances in terms of convergence and low complexity of each Jacobi variant studied in this paper are analyzed. Finally, some simulation examples are given to illustrate the advantages of the new proposed algorithm.

Initialization of an Iterative Low-Complexity Method for Signal Precoding in MM-Wave Massive MIMO Systems

“…Probably, among all the iterative linear methods, the Jacobi method is the simplest one to avoid the direct calculation of matrix inversion [15]. In fact, the Jacobi method solves a diagonally dominant linear system At=b.…”

MMSE Signal Detection for MIMO Systems based on Ordinary Differential Equation

“…It is possible to construct novel algorithms for MMSE estimation by adopting the perspective of numerical methods, which is different from conventional discrete-time algorithms such as [21]. In other words, we can also obtain benefits on digital-domain signal processing through the expression as an ODE.…”

“…In this section, we evaluate the estimation performance of the discrete-time MMSE estimation algorithms obtained using numerical methods. The performance is compared with that of a conventional MMSE estimation algorithm [21] based on the Jacobi [36] and successive over-relaxation (SOR) methods [37]. We call the method in this paper the Jacobi SOR algorithm.…”

“…Construction of a solution method considering numerical stability and flexible selection of the step size of the solution method enables the development of high-performance algorithms. Conventional detection algorithms such as [20] and [21] have no mention of the above viewpoints. The theoretical analysis of the continuous-time detection method is also useful in discrete-time algorithms.…”

Proposta de um Algoritmo para Redução dos Cálculos da Inversa da Matriz de Filtragem para Detecção Linear de Sinais em Sistemas Uplink MIMO Massivo

“…No entanto, à medida que o número de arranjos de antenas aumenta, a complexidade computacional da inversão da matriz de filtragem do algoritmo MMSE torna-se alta para implementac ¸ão em hardware. Na literatura, vários algoritmos têm sido propostos para detecc ¸ão do sinal em sistemas uplink MIMO massivo, aproximando a inversa da matriz do canal por meio de métodos iterativos com o objetivo de reduzir a complexidade computacional [Wu et al 2013, Gao et al 2014, Dai et al 2015, Wu et al 2016, Qin et al 2016, Tang et al 2016, Lee 2017, Shahabuddin et al 2017, Jiang et al 2018, Lee 2019, Jin et al 2019, Yakhelef and Saidi 2020, Naceur 2021.…”