Performance of an ℓ1 Regularized Subspace-Based MIMO Channel Estimation With Random Sequences

Abstract

The conventional $\ell2$ multiburst (MB) channel estimation can achieve the Cramer-Rao bound asymptotically by using the subspace projection. However, the $\ell2\;\text{MB}$ technique suffers from the noise enhancement problem if the training sequences (TSs) are not ideally uncorrelated. We clarify that the problem is caused by an inaccurate noise whitening process. The $\ell1$ regularized MB channel estimation can, however, improve the problem by a channel impulse response length constraint. Asymptotic performance analysis shows that the $\ell1\;\text{MB}$ can improve channel estimation performance significantly over the $\ell2\;\text{MB}$ technique in a massive multiple-input multiple-output system when the TSs are not long enough and not ideally uncorrelated.