On the Low-Complexity, Hardware-Friendly Tridiagonal Matrix Inversion for Correlated Massive MIMO Systems

Massive multiple-input multiple-output (M-MIMO) is a substantial pillar in fifth generation (5G) mobile communication systems. Although the maximum likelihood (ML) detector attains the optimum performance, it has an exponential complexity. Linear detectors are one of the substitutions and they are comparatively simple to implement. Unfortunately, they sustain a considerable performance loss in high loaded systems. They also include a matrix inversion which is not hardware-friendly. In addition, if the channel matrix is singular or nearly singular, the system will be classified as an ill-conditioned and hence, the signal cannot be equalized. To defeat the inherent noise enhancement, iterative matrix inversion methods are used in the detectors’ design where approximate matrix inversion is replacing the exact computation. In this paper, we study a linear detector based on iterative matrix inversion methods in realistic radio channels called QUAsi Deterministic RadIo channel GenerAtor (QuaDRiGa) package. Numerical results illustrate that the conjugate-gradient (CG) method is numerically robust and obtains the best performance with lowest number of multiplications. In the QuaDRiGA environment, iterative methods crave large n to obtain a pleasurable performance. This paper also shows that when the ratio between the user antennas and base station (BS) antennas ( β ) is close to 1, iterative matrix inversion methods are not attaining a good detector’s performance.

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“…It takes the benefit of iterative structure to progressively enhance the computing precision of the matrix inversion [ 52 ]. The Gram matrix

decomposed into

, where D is the main diagonal entries and E is the non-diagonal elements [ 53 , 54 ]. The Gram matrix inversion can be approximated as

which converges to

is fulfilled.…”

Section: Matrix Inversion Methodsmentioning

confidence: 99%

A Low Complexity Near-Optimal Iterative Linear Detector for Massive MIMO in Realistic Radio Channels of 5G Communication Systems

Albreem

Alsharif

Kim

2020

Entropy

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“…To perform the algorithm, we initially set x to 0, and solve (4) to obtain the initial Y. With updated Y, we solve (5) to update x. The proposed algorithm is summarized in Algorithm 1.…”

Section: B Solving the Subproblem (5)mentioning

confidence: 99%

“…While for a large N t , such as 128, the proposed algorithm shows superior computational reduction by a factor of 1 6 as compared to MMSE. Note, although our algorithm requires more computations than MMSE for small N t , it does not exhibit any matrix inversion or matrix multiplications, which is more advantageous in terms of hardware implementations [5]. In this letter we propose an iterative low complexity algorithm based on Alternating Minimization.…”

Section: Computational Complexity Analysismentioning

confidence: 99%

“…This is far from the theoretical limit that leads to the orthogonality mentioned above [4]. Therefore, the linear detectors still need to perform a matrix inversion for the signal detection of the uplink massive MIMO system, which entails extensive computational complexity [5]. Neumann series expansion, Cholesky decomposition, and successive over-relaxation techniques are proposed in the literature to reduce the complexity of the matrix inversion process in the MMSE detector [6] [7].…”

Section: Introductionmentioning

confidence: 99%

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A Low-Complexity Detection Algorithm for Uplink Massive MIMO Systems Based on Alternating Minimization

Elgabli

Elghariani

Aggarwal

et al. 2019

IEEE Wireless Commun. Lett.

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In this paper, we propose an algorithm based on the Alternating Minimization technique to solve the uplink massive MIMO detection problem. The proposed algorithm is specifically designed to avoid any matrix inversion and any computations of the Gram matrix at the receiver. The algorithm provides a lower complexity compared to the conventional MMSE detection technique, especially when the total number of user equipment (UE) antennas (across all users) is close to the number of base station (BS) antennas. The idea is that the algorithm reformulates the maximum likelihood (ML) detection problem as a sum of convex functions based on decomposing the received vector into multiple vectors. Each vector represents the contribution of one of the transmitted symbols in the received vector. Alternating Minimization is used to solve the new formulated problem in an iterative manner with a closed form solution update in every iteration. Simulation results demonstrate the efficacy of the proposed algorithm in the uplink massive MIMO setting for both coded and uncoded cases.

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“…Although, recent publications of matrix inversion architectures and complex arithmetic operations are in the current state-of-the-art literature, many of these works have been focused in the design of LUT, CORDICs, or iterative techniques [18][19][20]. Other approaches have considered parallel hardware implementations.…”

Section: Introductionmentioning

confidence: 99%

FPGA-Based Hardware Matrix Inversion Architecture Using Hybrid Piecewise Polynomial Approximation Systolic Cells

et al. 2020

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The hardware of the matrix inversion architecture using QR decomposition with Givens Rotations (GR) and a back substitution (BS) block is required for many signal processing algorithms. However, the hardware of the GR algorithm requires the implementation of complex operations, such as the reciprocal square root (RSR), which is typically implemented using LookUp Table (LUT) and COordinate Rotation DIgital Computer (CORDICs), among others, conveying to either high-area consumption or low throughput. This paper introduces an Field-Programmable Gate Array (FPGA)-based full matrix inversion architecture using hybrid piecewise polynomial approximation systolic cells. In the design, a hybrid segmentation technique was incorporated for the implementation of piecewise polynomial systolic cells. This hybrid approach is composed by an external and internal segmentation, where the first is nonuniform and the second is uniform, fitting the curve shape of the complex functions achieving a better signal-quantization-to noise-ratio; furthermore, it improves the time performance and area resources. Experimental results reveal a well-balanced improvement in the design achieving high throughput and, hence, less resource utilization in comparison to state-of-the-art FPGA-based architectures. In our study, the proposed design achieves 7.51 Mega-Matrices per second for performing 4 × 4 matrix operations with a latency of 12 clock cycles; meanwhile, the hardware design requires only 1474 slice registers, 1458 LUTs in an FPGA Virtex-5 XC5VLX220T, and 1474 slice registers and 1378 LUTs when a FPGA Virtex-6 XC6VLX240T is used.

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On the Low-Complexity, Hardware-Friendly Tridiagonal Matrix Inversion for Correlated Massive MIMO Systems

Cited by 32 publications

References 43 publications

A Low Complexity Near-Optimal Iterative Linear Detector for Massive MIMO in Realistic Radio Channels of 5G Communication Systems

A Low Complexity Near-Optimal Iterative Linear Detector for Massive MIMO in Realistic Radio Channels of 5G Communication Systems

A Low-Complexity Detection Algorithm for Uplink Massive MIMO Systems Based on Alternating Minimization

FPGA-Based Hardware Matrix Inversion Architecture Using Hybrid Piecewise Polynomial Approximation Systolic Cells

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