Joint Beamforming Optimization for RIS Enhanced mmWave Communications with Spatial Modulation

This paper investigates the reconfigurable intelligent surface (RIS) enhanced millimeter wave (mmWave) communications with spatial modulation (SM). To enhance the bit error ratio (BER) performance, we formulate a joint reflecting coefficients of RIS and the hybrid precoder design problem based on the maximum of minimum Euclidean distance criterion. Unfortunately, the resulting max-min optimization problem turns out to be intractable due to the unit-modulus constraints and intricately coupled variables. However, based on the alternating optimization technique, we show that this problem could be successfully tackled by jointly using the alternating direction method of multipliers (ADMM) and element-wise block coordinate descent (EBCD) algorithms. Numerical results demonstrate that the proposed method achieves a fast convergence rate, and can provide a substantial BER improvement even with 1-bit resolution RIS compared with existing benchmark schemes.