A Low Complexity Signal Detection Scheme Based on Improved Newton Iteration for Massive MIMO Systems

A Low Complexity Signal Detection Scheme Based on Improved Newton Iteration for Massive MIMO Systems

Abstract: Massive multiple-input multiple-output (MIMO) systems need to handle a large number of matrix inversion operations during the signal detection process. Several methods have been proposed to avoid exact matrix inversion in massive MIMO systems, which can be roughly divided into approximation methods and iterative methods. In this paper, we first introduce the relationship between the two types of signal detection methods. Then an improved Newton iteration method is proposed on the basis of the relationship. And by converting matrix-matrix product into matrix-vector product, the computational complexity is substantially reduced.

Finally, numerical simulations further verify that the proposed Newton method outperforms Neumann series expansion and the existing Newton method, and can approach the performance of MMSE method within a few iterations, regardless of whether the base station can obtain perfect channel state information or not.

Existing system: In this paper, we first analyze the relationship between different types of detection methods. The estimation results after k iterations in the iterative methods, when the

proposed initial estimate is selected, are equivalent to k-th order expansion in Neumann series. And the results of k iterations in Newton method can be seen as the results of 2k 1 iterations in the iterative method. On the basis of the proposed relationship, we propose an improved Newton iteration method for massive MIMO systems and optimize it. Finally, simulation results indicate that the proposed method outperforms the existing Newton iteration method, MMSE-PIC method and NSE in terms of bit error rate (BER) performance and computational complexity.

Proposed system: Recently, abundant works are devoted to addressing the complexity issue of signal detection in massive MIMO systems. Generally, iterative methods and approximation methods are two main types of these algorithms. The truncated Neumann Series expansion (NSE) is utilized to approximate the matrix inversion in the performance and computational complexity of which scale with the number of the selected series terms synchronously. In addition, points out that Newton iteration method has faster convergence rate than the Neumann series expansion.

The GMPID method considers Gaussian signal sources, and in each iteration the means and variances are transmitted between the nodes and its convergence is also analyzed. And gives a rigorous proof that iterative LMMSE can achieve the optimal sum-capacity of the multiuser MIMO systems for any system.

Advantages: In summary, the proposed algorithm can be used for massive MIMO systems with arbitrary configuration because of its dual advantages in performance and complexity. However, Neumann series approximation and Newton iteration method can only be utilized in systems with large ratio between BS and user antennas.

In, the MMSE-PIC algorithm with Neumann series expansion approximation is proposed for massive MIMO systems. Moreover, to avoid exact matrix inversion, the iteration detection methods, Jacobi, Richardson, successive over relaxation (SOR), Gauss-Seidel, etc., are also employed to approach the performance of the MMSE detection.

Disadvantages: In this paper, the relationship between different types of signal detection methods for massive MIMO systems is introduced, based on which we propose an improved Newton detection method to achieve the performance of MMSE method and optimize it.

Moreover, by adopting matrix-vector products, the computational complexity is reduced by an order of magnitude. Compared to NSE and the existing Newton method, the BER performance of the proposed Newton method is significantly enhanced while maintaining lower complexity.

Modules: Neumann series expansion : MASSIVE multiple-input multiple-output (MIMO) is a rising technology that promises remarkable improvements in terms of energy efficiency, power consumption and link reliability compared to conventional MIMO. It has been demonstrated that linear detection schemes, such as minimum mean square error (MMSE) method, can achieve near-optimal performance. However, a large number of matrix inversion operations are involved in linear detection algorithms.

Recently, abundant works are devoted to addressing the complexity issue of signal detection in massive MIMO systems. Generally, iterative methods and approximation methods are two main types of these algorithms. The truncated Neumann Series expansion (NSE) is utilized to approximate the matrix inversion in the performance and computational complexity of which scale with the number of the selected series terms synchronously. In addition, points out that Newton iteration method has faster convergence rate than the Neumann series expansion.

The GMPID methods consider Gaussian signal sources, and in each iteration the means and variances are transmitted between the nodes and its convergence are also analyzed.

Successive over relaxation : In, the MMSE-PIC algorithm with Neumann series expansion approximation is proposed for massive MIMO systems. Moreover, to avoid exact matrix inversion, the iteration detection methods, Jacobi, Richardson, successive over relaxation

(SOR), Gauss-Seidel, etc., are also employed to approach the performance of the MMSE detection. All algorithms are committed to making trade-offs between computational complexity and performance. In this paper, we first analyze the relationship between different types of detection methods. The estimation results after k iterations in the iterative methods, when the proposed initial estimate is selected, are equivalent to k-th order expansion in Neumann series. And the results of k iterations in Newton method can be seen as the results of 2k 1 iterations in the iterative method. On the basis of the proposed relationship, we propose an improved Newton iteration method for massive MIMO systems and optimize it.

Finally, simulation results indicate that the proposed method outperforms the existing Newton iteration method, MMSE-PIC method and NSE n terms of bit error rate (BER) performance and computational complexity.

MMSE method: Compared to, the performance of all algorithms in is remarkably improved due to the increase in the number of BS antennas. It can be seen from that the bit error rate of all algorithms decreases as the number of iterations (or the order of NSE) increases. And after 3 iterations, the performance of the proposed Newton iteration method can deliver that of MMSE method, while the NSE, the MMSEPIC and the existing Newton method are still far from MMSE method. And the proposed hybrid iteration method converges to MMSE with lower complexity after 4 iterations. The proposed methods outperform other methods in this system configuration, which means that the proposed method requires lower complexity or SNR for the same performance.