Joint Beamforming and Phase Shift Design for Hybrid-IRS-aided Directional Modulation Network

To make a good balance between performance, cost, and power consumption, a hybrid intelligent reflecting surface (IRS)-aided directional modulation (DM) network is investigated in this paper, where the hybrid IRS consists of passive and active reflecting elements. To maximize the achievable rate, two optimization algorithms, called maximum signal-to-noise ratio (SNR)-fractional programming (FP) (Max-SNR-FP) and maximum SNR-equal amplitude reflecting (EAR) (Max-SNR-EAR), are proposed to jointly design the beamforming vector and IRS phase shift matrix by alternately optimizing one and fixing another. The former employs the successive convex approximation and FP methods to solve the beamforming vector and hybrid IRS phase shift matrix, while the latter uses the maximum signal-to-leakage-noise ratio method and the criteria of phase alignment and EAR to design them. Simulation results show that the rates harvested by the proposed two methods are slightly lower than that of active IRS with higher power consumption, which are 35 percent higher than those of no IRS and random phase IRS, while passive IRS achieves only about 17 percent rate gain over the latter. Moreover, compared to Max-SNR-FP, the proposed Max-SNR-EAR method makes an obvious complexity reduction at the cost of a slight rate performance loss.