Uniform Quantization for Multi-Antenna Amplify–Quantize–Forward Relay

In this paper, we investigate a multi-antenna amplify–quantize–forward (AQF) relay system, where a half-duplex relay quantizes both the real and imaginary components of amplified received signals, storing them in memory before forwarding them to a destination. Our focus lies on uniform quantization at the relay in the multiple-input multiple-output (MIMO) AQF relay channel. We start with theoretical analyses to determine quantization step sizes by deriving the power and mean square error of the quantized signals as functions of these step sizes. Subsequently, we introduce neural network-based deep learning methods to mitigate computational complexity. Specifically, we present supervised learning (SL) and unsupervised learning (USL) methodologies, with the latter employing a novel loss function designed to avoid the need for extensive training data collection. Furthermore, we propose a USL method with Monte Carlo (USL-MC), leveraging an approximated loss function to address the heightened complexity observed in multi-antenna systems. Given the challenge of finding optimal step sizes for the MIMO AQF relay, comparing outcomes across different determination algorithms proves to be a significant obstacle. To address this, we evaluate error performance at the destination for the entire AQF relay communication system by introducing a linear detection method with significantly reduced complexity in the MIMO AQF relay channel. The numerical results demonstrate that the quantization step sizes determined through deep learning methods exhibit excellent performance with small computational burden during implementation, particularly when compared to the theoretical approach. Notably, the USL-MC method stands out for its significantly reduced complexity, both in practical implementation and training, rendering half-duplex AQF relays viable for practical resource-constrained systems.