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To estimate multiple-input multiple-output (MIMO) channels, invariablestep-size normalized least mean square (ISSNLMS) algorithm was applied toadaptive channel estimation (ACE). Since the MIMO channel is often described bysparse channel model due to broadband signal transmission, such sparsity can beexploited by adaptive sparse channel estimation (ASCE) methods using sparseISS-NLMS algorithms. It is well known that step-size is a critical parameterwhich controls three aspects: algorithm stability, estimation performance andcomputational cost. The previous approaches can exploit channel sparsity buttheir step-sizes are keeping invariant which unable balances well the threeaspects and easily cause either estimation performance loss or instability. Inthis paper, we propose two stable sparse variable step-size NLMS (VSS-NLMS)algorithms to improve the accuracy of MIMO channel estimators. First, ASCE forestimating MIMO channels is formulated in MIMO systems. Second, differentsparse penalties are introduced to VSS-NLMS algorithm for ASCE. In addition,difference between sparse ISS-NLMS algorithms and sparse VSS-NLMS ones areexplained. At last, to verify the effectiveness of the proposed algorithms forASCE, several selected simulation results are shown to prove that the proposedsparse VSS-NLMS algorithms can achieve better estimation performance than theconventional methods via mean square error (MSE) and bit error rate (BER)metrics.

Variable is Better Than Invariable: Stable Sparse VSS-NLMS Algorithms with Application to Estimating MIMO Channels