Design of an intelligent reflecting surface aided mmWave massive MIMO using X-precoding

In this paper, we consider an intelligent reflecting surface (IRS) aided millimeter wave (mmWave) massive multiple-input multiple-output (MIMO) system using hybrid beamforming/combining. To enhance error performance, we adopt X-code (or X-precoder), a low-complexity precoding technique for traditional MIMO channels, to encode information symbols. We first derive an upper bound on word error rate (WER), based on which we design jointly IRS phase shifts and X-code (or X-precoder) to minimize WER. Specifically, we propose two algorithms for IRS design exploiting alternating optimization and gradient ascent optimization methods. Then we devise X-code and X-precoder, respectively, by minimizing average WER over all channel realizations and WER for each channel realization. We also provide their diversity analysis. Further, we present the procedure of decoupling fully digital beamformer/combiner at transceiver into the optimal hybrid one. Finally, simulation results show that both IRS optimization algorithms have similar WERs whereas gradient ascent approach has a lower computational complexity. Simulations demonstrate that the designed X-code (or X-precoder) provides a significant performance gain.