Achievable Rate Region and Path-Based Beamforming for Multi-User Single-Carrier Delay Alignment Modulation

Delay alignment modulation (DAM) is a novel wideband transmission technique for millimeter wave (mmWave) massive multiple-input multiple-output (MIMO) systems, which exploits the high spatial resolution and multi-path sparsity to mitigate inter-symbol interference (ISI), without the need of channel equalization or multi-carrier transmission. In particular, DAM leverages the delay pre-compensation and path-based beamforming to effectively align the multi-path components, thus achieving the constructive multi-path combination for eliminating the ISI while preserving the multi-path power gain. Different from the existing works only considering single-user DAM, this paper investigates the DAM technique for multi-user mmWave massive MIMO communication. First, we consider the asymptotic regime when the number of antennas $M_{t}$ at base station (BS) is sufficiently large. It is shown that by employing the simple delay pre-compensation and per-path-based maximal ratio transmission (MRT) beamforming, the single-carrier DAM is able to perfectly eliminate both ISI and inter-user interference (IUI). Next, we consider the general scenario with $M_{t}$ being finite. In this scenario, we characterize the achievable rate region of the multi-user DAM system by finding its Pareto boundary. Specifically, we formulate a rate-profile-constrained sum rate maximization problem by optimizing the per-path-based beamforming, which is optimally solved via the second-order cone programming (SOCP). Furthermore, we present three low-complexity per-path-based beamforming strategies based on the MRT, zero-forcing (ZF), and regularized zero-forcing (RZF) principles, respectively, and study their correspondingly achievable sum rates. Finally, we provide simulation results to demonstrate the performance of our proposed strategies as compared to two benchmark schemes based on the strongest-path-based beamforming and the prevalent orthogonal frequency division multiplexing (OFDM), respectively. It is shown that DAM achieves higher spectral efficiency and/or lower peak-to-average-ratio (PAPR), for systems with high spatial resolution and multi-path diversity.