Neural Network Based Optimization of Transmit Beamforming and RIS Coefficients Using Channel Covariances in MISO Downlink

TL;DR

The paper addresses downlink beamforming in RIS-enabled MISO systems when only slow-varying channel covariances are available. It introduces an unsupervised Beamforming Neural Network (BNN) for BS beams and a supervised RIS CNN for RIS phases, enabling near-instantaneous inference using covariance information. RIS CNN is trained on solutions from ADMM, while BNN is trained unsupervised to maximize approximate sum-rate, yielding higher performance than statistical ZF with water-filling under heavier loads and with significantly reduced computation time. This covariance-based, two-network framework enables scalable, low-latency optimization for RIS-assisted networks without relying on instantaneous CSI.

Abstract

We propose an unsupervised beamforming neural network (BNN) and a supervised reconfigurable intelligent surface (RIS) convolutional neural network (CNN) to optimize transmit beamforming and RIS coefficients of multi-input single-output (MISO) downlink with RIS assistance. To avoid frequent beam updates, the proposed BNN and RIS CNN are based on slow-changing channel covariances and are different from most other neural networks that utilize channel instances. Numerical simulations show that the proposed BNN with RIS CNN can achieve much higher sum rates than zeroforcing beamforming with waterfilling power allocation does, especially for systems with higher load, and reduces computation time.

Figures (7)

• Figure 1: A MISO downlink with a BS with $N_t$ antennas, $M$ direct-path UEs, and $K$ UEs with RIS assistance. Each UE has a single receive antenna.
• Figure 2: Approximate sum rates for BNN and ZF beamforming with random RIS coefficients and BNN with RIS CNN coefficients with $N_t = 16$, $N = 30$, $M=1$, $K=1$, $\rank(\bm{R}_{h_k})=1$, and $\rank(\bm{R}_{g_k})=1, \forall k$.
• Figure 3: Approximate sum rates for BNN with either random RIS or RIS CNN, and ZF beams with random RIS ($N_t = 16$, $N =30$, $K = 1$, $M =5$ or $9$, $\rank(\bm{R}_{h_k})=1$, and $\rank(\bm{R}_{g_k})=1, \forall k$).
• Figure 4: Approximate sum rates for BNN with either random RIS or RIS CNN, and ZF beams with random RIS ($N_t = 16$, $N =30$, either $M=5$ and $K = 5$ or $M =3$ or $K=3$, $\rank(\bm{R}_{h_k})=1$, and $\rank(\bm{R}_{g_k})=1, \forall k$).
• Figure 5: Approximate sum rates for BNN with either random RIS or RIS CNN, and ZF beams with random RIS ($M = 3$, $K =3$, either $N_t = 16$ and $N=60$ or $N_t=10$ and $N=30$, $\rank(\bm{R}_{h_k})=1$, and $\rank(\bm{R}_{g_k})=1, \forall k$).