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Channel estimation is a formidable challenge in mmWave Multiple Input Multiple Output (MIMO) systems due to the large number of antennas. Therefore, compressed sensing (CS) techniques are used to exploit channel sparsity at mmWave frequencies to calculate fewer dominant paths in mmWave channels. However, conventional CS techniques require a higher training overhead for efficient recovery. In this paper, an efficient extended alternation direction method of multipliers (Ex-ADMM) is proposed for mmWave channel estimation. In the proposed scheme, a joint optimization problem is formulated to exploit low rank and channel sparsity individually in the antenna domain. Moreover, a relaxation factor is introduced which improves the proposed algorithm’s convergence. Simulation experiments illustrate that the proposed algorithm converges at lower Normalized Mean Squared Error (NMSE) with improved spectral efficiency. The proposed algorithm also ameliorates NMSE performance at low, mid and high Signal to Noise (SNR) ranges.

Precise Channel Estimation Approach for a mmWave MIMO System