Sparsity-enhanced linear time-invariant MIMO system identification

This paper addresses the problem of linear time-invariant multi-input-multi-output (MIMO) system identification. Specifically, we focus on identifying the finite impulse responses (FIRs) of a MIMO system. Observing that the FIRs are often approximately sparse, namely containing many near-zero elements, this paper proposes to use the ℓ₁ regularized least squares (ℓ₁-LS) method as the estimator. Comparing to the traditional identification methods, such as least squares, the ℓ₁-LS method exploits the sparse nature of the FIRs, hence brings three advantages: (1) better estimation of the time-delays, (2) better estimation of the effective lengths of the FIRs, and (3) lower requirement of input-output data. Simulation results validate the efficacy of the proposed sparsity-enhanced identification approach.