ℓ1 LS and ℓ2 MMSE-Based Hybrid Channel Estimation for Intermittent Wireless Connections

Abstract

Broadband wireless channels observed at a receiver cannot fully exhibit dense nature in a low to moderate signal-to-noise ratio (SNR) regime, if the channels follow a typical propagation scenario such as Vehicular-A or Pedestrian-B. It is hence expected that $\ell1$ -regularized channel estimation methods can improve channel estimation performance in the broadband wireless channels. However, it is well-known that the $\ell2$ multiburst (MB) channel estimation achieves the Cramer–Rao bound (CRB) asymptotically. This is because the $\ell2$ MB technique formulated as a minimum-mean-square-error (MMSE) problem improves the mean squared error (MSE) performance by utilizing the subspace projection. Performance analysis shows that $\ell1$ -regularized channel estimation does not improve the MSE performance significantly over the $\ell2$ MB technique so far as the subspace channel model assumption is correct. We demonstrate, however, a receiver with $\ell1$ -regularized channel estimation can improve bit error rate (BER) performance if the assumption is not always correct. For this purpose, we focus on intermittent transmission (TX) scenario which is defined as a generalized TX sequence having arbitrary length interruption between two continuous TX bursts. A receiver with the $\ell2$ MB method suffers from BER deterioration in an intermittent TX scenario having abrupt channel changes. As a solution to the problem, we propose a new algorithm which is a hybrid of $\ell1$ -regularized least square (LS) and $\ell2$ MMSE channel estimation techniques. Simulation results show that the receiver with the proposed algorithm achieves a significant BER gain over that of the $\ell2$ MB technique in the intermittent TX scenario.