Single-Carrier Delay Alignment Modulation for Multi-IRS Aided Communication

Delay alignment modulation (DAM) is a promising technology to achieve inter-symbol interference (ISI)-free single-carrier communication, by leveraging <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">delay compensation</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">path-based beamforming</i> , rather than the conventional channel equalization or multi-carrier transmission. In particular, when there exist a few strong time-dispersive channel paths, DAM is able to effectively align different propagation delays and achieve their constructive superposition, thus especially appealing for intelligent reflecting surfaces (IRSs)-aided communications with controllable multi-paths. In this paper, we apply single-carrier DAM to multi-IRS aided communication and study its design and achievable performance. We first provide an asymptotic analysis showing that when the number of base station (BS) antennas is much larger than the number of IRSs, an ISI-free channel can be established from the BS to the user with appropriate delay pre-compensation and the simple path-based maximal-ratio transmission (MRT) beamforming. We then consider the general system setup and study the problem of joint path-based beamforming design at the BS and phase shifts design at the IRSs for DAM transmission, by considering the three classical beamforming techniques on a per-path basis, namely the low-complexity path-based MRT beamforming to maximize the desired signal power, the path-based zero-forcing (ZF) beamforming for ISI-free DAM communication, and the optimal path-based minimum mean-square error (MMSE) beamforming to maximize the signal-to-interference-plus-noise ratio (SINR). As a comparison, orthogonal frequency-division multiplexing (OFDM)-based multi-IRS aided communication is considered for benchmarking. Simulation results are provided which demonstrate the significant performance gain of DAM over OFDM, in terms of spectral efficiency and bit error rate (BER), as well as its lower peak-to-average-power ratio (PAPR).