We investigate the optimality and power allocation algorithm of beam domain transmission for single-cell massive multiple-input multiple-output (MIMO) systems with a multiantenna passive eavesdropper. Focusing on the secure massive MIMO downlink transmission with only statistical channel state information of legitimate users and the eavesdropper at base station, we introduce a lower bound on the achievable ergodic secrecy sum-rate, from which we derive the condition for eigenvectors of the optimal input covariance matrices. The result shows that beam domain transmission can achieve optimal performance in terms of secrecy sum-rate lower bound maximization. For the case of single-antenna legitimate users, we prove that it is optimal to allocate no power to the beams where the beam gains of the eavesdropper are stronger than those of legitimate users in order to maximize the secrecy sum-rate lower bound. Then, motivated by the concave-convex procedure and the large dimension random matrix theory, we develop an efficient iterative and convergent algorithm to optimize power allocation in the beam domain. Numerical simulations demonstrate the tightness of the secrecy sum-rate lower bound and the near-optimal performance of the proposed iterative algorithm.Index Terms-Beam domain, massive MIMO, physical layer security, statistical channel state information (CSI), power allocation.

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The potential benefits of massive multiple-input multiple-output (MIMO) make it possible to achieve high-quality underwater acoustic (UWA) communications. Nevertheless, due to the wideband nature of UWA channels, existing massive MIMO techniques for radio frequency cannot be directly applied to UWA communications. This paper investigates a UWA massive MIMO system in the shallow-water environment, deploying large array apertures at both the transmitter and the receiver. We propose a beam-based UWA massive MIMO channel model and analyze its properties. Based on this model, we reveal that the transmit design for rate maximization can be performed in a dimensionreduced space related to the channel taps. Then, we prove that the beam-domain transmission is optimal to maximize the rate when with unlimited numbers of transducers. Furthermore, if the number of hydrophones also tends to infinity, the optimal power allocation can be obtained just by the water-filling algorithm and the corresponding rate positively correlates with the number of channel taps for the high signal-to-noise-ratio regime. Moreover, we devise a low-complexity algorithm to optimize the input covariance matrix for general cases. Simulation results illustrate the significant performance of the proposed algorithm and the high throughput achieved by massive MIMO.

The average multicast rate (AMR) is analyzed in a multicast channel utilizing analog beamforming with finitealphabet inputs, considering statistical channel state information (CSI). New expressions for the AMR are derived for noncooperative and cooperative multicasting scenarios. Asymptotic analyses are conducted in the high signal-to-noise ratio regime to derive the array gain and diversity order. It is proved that the analog beamformer influences the AMR through its array gain, leading to the proposal of efficient beamforming algorithms aimed at maximizing the array gain to enhance the AMR.