Hybrid pre-coding based on minimum SMSE considering insertion loss in mmWave communications

Hybrid pre-coding design is a promising research direction in large antenna array millimeter wave (mmWave) systems. The insertion loss is an inherent and significant feature of hybrid pre-coding, resulting in lower energy efficiency and inferior bit error rate (BER) performance. This paper takes the minimum sum-mean-square-error (Min-SMSE) considering the insertion loss as the optimization objective function, which aims at increasing the sum-rate and improving the BER performance. Then a hybrid pre-coding is designed based on this criterion with an adaptive overlapped subarray (OSA) architecture. It is proved that the optimization problem is non-convex. Thus, we decompose the optimization problem into two sub-optimum ones. One is to design the digital pre-coding based on the Min-SMSE criterion under the equivalent channel condition. The other one is to design the analog pre-coding based on the simplified Min-SMSE with the insertion loss objective function. Theoretical analyses of the proposed scheme are conducted, including the upper bound of the average BER, the lower bound of the average sum-rate, and the computational complexity. Simulation results show that our proposed scheme outperforms three representative hybrid pre-coding schemes with different architectures in both BER and sum-rate, when the numbers of the phase shifters and combiners are relatively small