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

In this paper, a novel scheme using hybrid l(1)/l(2) 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 l(0) norm minimization problem, and then the proposed scheme is used to obtain the sparse solution. In the proposed scheme, a sequence of minimum weighted l(2) 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 l(1)/l(2) 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.