Improved Convergence Speed of a DCD-Based Algorithm for Sparse Solutions

Zhi Quan,Shuhua Lv

doi:10.3390/a13060136

Abstract

To solve a system of equations that needs few updates, such as sparse systems, the leading dichotomous coordinate descent (DCD) algorithm is better than the cyclic DCD algorithm because of its fast speed of convergence. In the case of sparse systems requiring a large number of updates, the cyclic DCD algorithm converges faster and has a lower error level than the leading DCD algorithm. However, the leading DCD algorithm has a faster convergence speed in the initial updates. In this paper, we propose a combination of leading and cyclic DCD iterations, the leading-cyclic DCD algorithm, to improve the convergence speed of the cyclic DCD algorithm. The proposed algorithm involves two steps. First, by properly selecting the number of updates of the solution vector used in the leading DCD algorithm, a solution is obtained from the leading DCD algorithm. Second, taking the output of the leading DCD algorithm as the initial values, an improved soft output is generated by the cyclic DCD algorithm with a large number of iterations. Numerical results demonstrate that when the solution sparsity γ is in the interval [ 1 / 8 , 6 / 8 ] , the proposed leading-cyclic DCD algorithm outperforms both the existing cyclic and leading DCD algorithms for all iterations.

Highlights

With the development of information technology, the number of participated devices and data transmission rate have substantially increased in recent years
By properly selecting the number of updates of the solution vector used in the leading dichotomous coordinate descent (DCD) algorithm, a solution is obtained from the leading DCD algorithm
The results show that the proposed leading-cyclic DCD algorithm improves the convergence speed of the cyclic DCD algorithm and lowers the steady-state level

Summary

Introduction

With the development of information technology, the number of participated devices and data transmission rate have substantially increased in recent years. Solving the problems in a wide range of signal processing applications is equivalent to getting the solution of a linear least squares (LS) problem [1]. These applications include adaptive antenna array applications [2], multi-user detection [3], multiple-input multiple-output (MIMO) detection [4], echo cancellation [5], equalization [6], and system identification [1,7,8,9]. If the channel information is known, zero forcing (ZF) algorithm and minimum mean-square error (MMSE) algorithm are popular to be used in these applications. They are simple to implement but require the operation of matrix inversion. When the system size is large, the complexity of the matrix inversion is prohibitively high

Results

Discussion

Conclusion