The conventional l2 multi-burst (MB) channel estimation can achieve the Cramér-Rao bound asymptotically by using the subspace projection. However, the l2 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 l1 regularized MB channel estimation can, however, improve the problem by a channel impulse response length constraint. Asymptotic performance analysis shows that the l1 MB can improve channel estimation performance significantly over the l2 MB technique in a massive multiple-input multiple-output system when the TSs are not long enough and not ideally uncorrelated.
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