Design of Sparse FIR Decision Feedback Equalizers in MIMO Systems Using Hybrid l ₁/ l ₂ Norm Minimization and the OMP Algorithm

Lihong Yu; Jiaxiang Zhao; Wei Xu; Haiyuan Liu

doi:10.3390/s18061860

Design of Sparse FIR Decision Feedback Equalizers in MIMO Systems Using Hybrid l ₁/ l ₂ Norm Minimization and the OMP Algorithm

Sensors (Basel). 2018 Jun 6;18(6):1860. doi: 10.3390/s18061860.

Authors

Lihong Yu¹, Jiaxiang Zhao², Wei Xu³, Haiyuan Liu⁴

Affiliations

¹ College of Computer and Control Engineering, Nankai University, Tianjin 300350, China. yulihongfly@mail.nankai.edu.cn.
² Tianjin Key Laboratory of Optoelectronic Sensor and Sensing Network Technology, College of Electronic Information and Optical Engineering, Nankai University, Tianjin 300350, China. zhaojx@nankai.edu.cn.
³ College of Electronic and Information Engineering, Tianjin Polytechnic University, Tianjin 300387, China. doctorxw@126.com.
⁴ Tianjin Key Laboratory of Optoelectronic Sensor and Sensing Network Technology, College of Electronic Information and Optical Engineering, Nankai University, Tianjin 300350, China. liuhaiyuan@nankai.edu.cn.

Abstract

In this paper, a novel scheme using hybrid l₁/l₂ norm minimization and the orthogonal matching pursuit (OMP) algorithm is proposed to design the sparse finite impulse response (FIR) decision feedback equalizers (DFE) in multiple input multiple output (MIMO) systems. To reduce the number of nonzero taps for the FIR DFE while ensuring its design accuracy, the problem of designing a sparse FIR DFE is transformed into an l₀ norm minimization problem, and then the proposed scheme is used to obtain the sparse solution. In the proposed scheme, a sequence of minimum weighted l₂ norm problems is solved using the OMP algorithm. The nonzero taps positions can be corrected with the different weights in the diagonal weighting matrix which is computed through the hybrid l₁/l₂ norm minimization. The simulation results verify that the sparse FIR MIMO DFEs designed by the proposed scheme get a significant reduction in the number of nonzero taps with a small performance loss compared to the non-sparse optimum DFE under the minimum mean square error (MMSE) criterion. In addition, the proposed scheme provides better design accuracy than the OMP algorithm with the same sparsity level.

Keywords: decision feedback equalization (DFE); hybrid l1/l2 norm minimization; multiple input multiple output (MIMO); orthogonal matching pursuit (OMP); sparse representation.