Fast Block LMS Based Estimation of Angularly Sparse Channels for Hybrid Wideband Millimeter Wave MIMO Systems

Adaptive block-based least-mean squares (BLMS)-based techniques are conceived for channel estimation in single-carrier (SC) wideband millimeter wave (mmWave) hybrid MIMO systems. In this context, a frequency-domain channel estimation model is developed for SC wideband systems, followed by a novel fast BLMS (FBLMS) technique, which has a significantly lower computational complexity than the existing channel estimation schemes designed for mmWave hybrid MIMO systems. The proposed FBLMS technique is also robust, since it does not require any second-order statistical information, such as the cross-covariance vector and covariance matrix. Next a beamspace domain representation of the mmWave MIMO channel is obtained, followed by the development of the sparse-FBLMS (SFBLMS) scheme for the estimation of the wideband mmWave MIMO channel that additionally exploits the angular-sparsity for improved channel estimation performance. Analytical expressions are derived for the mean squared estimation error (MSEE) and mean squared observation error (MSOE) of both the proposed FBLMS and SFBLMS techniques. Furthermore, a systematic procedure is developed for determining the beneficial range of the values of the regularization parameter, which ensures a high channel estimation accuracy of the SFBLMS over FBLMS. A hybrid precoder and combiner design is also proposed for SC wideband systems by employing the channel estimates obtained using the above techniques. Simulation results are presented to illustrate the performance of the proposed BLMS-based schemes in comparison to the existing schemes, which closely match the theoretical results derived.