Efficient Hybrid Amplitude-Phase Quantization for Multi-Antenna Relay System

TL;DR

This work tackles memory bottlenecks in MIMO quantize-forward (QF) relay systems by introducing Hybrid Amplitude-Phase Quantization (H-APQ), which preserves the phase information handling of U-PQ while adopting Ordered Amplitude Quantization (O-AQ) to efficiently encode amplitudes. The relay memory burden is reduced by mapping amplitudes to a small set of ordered levels, with a tunable group size m that trades off memory against performance; analytical expressions for the amplitude quantization levels and bit count are provided. The authors evaluate H-APQ in an autoencoder-based end-to-end MIMO QF relay setup over Rayleigh fading, showing that moderate values of m (e.g., m=2) yield substantial memory savings while maintaining BER close to U-APQ, and that evenly spaced levels ($a_k = k\Delta$) perform well. The results indicate that H-APQ offers a practical, scalable solution for memory-constrained QF relays without sacrificing end-to-end reliability, making it suitable for large-scale MIMO deployments.

Abstract

This letter explores relay quantization in multi-antenna quantize-forward (QF) relay systems. Existing methods, such as uniform phase quantization (U-PQ) and uniform amplitude-phase quantization (U-APQ), suffer from performance saturation and high memory demands. To overcome these limitations, we propose hybrid amplitude-phase quantization (H-APQ), which adaptively quantizes received signal amplitudes based on their relative magnitudes while applying uniform quantization to individual phases. H-APQ significantly reduces memory consumption at the relay while maintaining strong overall performance, offering an efficient solution for multiple-input multiple-output (MIMO) QF relay systems.

Figures (6)

• Figure 1: An autoencoder-based QF relay system.
• Figure 2: Quantization algorithms at the relay.
• Figure 3: Ordered amplitude quantization $\mathbf{Q}^{\text{ O-AQ}} (\cdot)$.
• Figure 4: Number of quantization bits for various quantization methods at the relay.
• Figure 5: BER comparison for various quantization algorithms in the autoencoder-based MIMO QF relay systems with $M=4$, where H-APQ applies $a_k= k\Delta$.