The design of beamforming for downlink multi-user massive multi-input multi-output (MIMO) relies on accurate downlink channel state information (CSI) at the transmitter (CSIT). In fact, it is difficult for the base station (BS) to obtain perfect CSIT due to user mobility, latency/feedback delay (between downlink data transmission and CSI acquisition). Hence, robust beamforming under imperfect CSIT is needed. In this paper, considering multiple antennas at all nodes (base station and user terminals), we develop a multi-agent deep reinforcement learning (DRL) framework for massive MIMO under imperfect CSIT, where the transmit and receive beamforming are jointly designed to maximize the average information rate of all users. Leveraging this DRL-based framework, interference management is explored and three DRL-based schemes, namely the distributed-learning-distributed-processing scheme, partial-distributed-learning-distributed-processing, and central-learning-distributed-processing scheme, are proposed and analyzed. This paper \textrm{1)} highlights the fact that the DRL-based strategies outperform the random action-chosen strategy and the delay-sensitive strategy named as sample-and-hold (SAH) approach, and achieved over 90$\%$ of the information rate of two selected benchmarks with lower complexity: the zero-forcing channel-inversion (ZF-CI) with perfect CSIT and the Greedy Beam Selection strategy, \textrm{2)} demonstrates the inherent robustness of the proposed designs in the presence of user mobility.
In this paper, we study the waveform and passive beamforming design for intelligent reflecting surface (IRS)-aided wireless power transfer (WPT). Generalized multi-user and low complexity single-user algorithms are derived based on alternating optimization (AO) framework to maximize the weighted sum output DC current, subject to transmit power constraints and passive beamforming phases unit modulus constraints. The input signal waveform and IRS passive beamforming phase shifts are jointly designed as a function of users' individual frequency-selective channel state information (CSI). The energy harvester nonlinearity is explored and two IRS deployment schemes, namely frequency selective IRS (FS-IRS) and frequency flat IRS (FF-IRS), are modeled and analyzed. This paper highlights the fact that IRS can provide an extra passive beamforming gain on output DC power over conventional WPT designs and significantly influence the waveform design by leveraging the benefit of passive beamforming, frequency diversity and energy harvester nonlinearity. Even though FF-IRS exhibits lower output DC current than FS-IRS, it still achieves substantially increased DC power over conventional WPT designs. Performance evaluations confirm the significant benefits of a joint waveform and passive beamforming design accounting for the energy harvester nonlinearity to boost the performance of single-user and multi-user WPT system.