Second-Order Statistics-Based Semi-Blind Techniques for Channel Estimation in Millimeter-Wave MIMO Analog and Hybrid Beamforming

Semi-blind (SB) channel estimation is conceived for millimeter wave (mmWave) analog-beamforming (AB) and hybrid-beamforming (HB)-based multiple-input multiple-output (MIMO) systems, which also exploits the data symbols for improving the estimation accuracy. A novel aspect of the proposed framework is that it directly estimates the analog beamformer/ combiner weights without necessitating the estimation of the entire mmWave MIMO channel matrix. By involving powerful matrix perturbation theoretic techniques, a closed-form expression is derived for the mean-squared-error (MSE) of the mmWave-AB-SB algorithm. As a further novelty, our mmWave-HB-SB technique relies on the decomposition of the channel matrix as the product of a decorrelating and a unitary matrix. Subsequently, the former is estimated purely relying on the unknown data symbols, whereas the latter is estimated exclusively from the training vectors. A lower bound on the MSE of the proposed mmWave-HB-SB technique is derived using the constrained Cramer-Rao lower bound (CRLB) framework. Furthermore, the performance gain of our mmWave-HB-SB technique over the conventional purely training-based scheme is also quantified analytically. Our simulation results demonstrate the superiority of the techniques advocated over the existing solutions and also verify the accuracy of our analytical findings.