Performance of QUBO-Formulated MIMO Detection Under Hardware Precision Constraints

TL;DR

This paper analyzes how finite-precision hardware affects QUBO-based MIMO detection, proposing quantization schemes and guidelines to preserve detection accuracy with fewer bits.

Contribution

It introduces novel homogeneous and heterogeneous quantization schemes and derives conditions to maintain optimal detection performance under hardware precision constraints.

Findings

Heterogeneous quantization achieves baseline error rates with fewer bits.

Derived sufficient conditions for quantization precision to preserve optimal solutions.

Numerical experiments confirm effectiveness across various MIMO configurations.

Abstract

The evolution of multiple-input, multiple-output (MIMO) systems requires the efficient detection algorithms to overcome the exponential computational complexity of optimal maximum likelihood detection. Reformulating MIMO detection as a quadratic unconstrained binary optimization (QUBO) problem enables the use of highly parallel, physics-inspired, hardware-accelerated solvers and non-von Neumann architectures. However, embedding continuous-valued QUBO coefficients into hardware introduces quantization noise due to finite precision, which can severely degrade detection accuracy. This paper presents a rigorous analysis of the performance impact of finite-precision, hardware-accelerated QUBO solvers in MIMO detection. We analytically derive the probability distribution functions of the QUBO matrix entries and introduce novel homogeneous and heterogeneous quantization schemes based on either instantaneous channel state information or its statistical features. We further derive a sufficient condition on the precision required to maintain the optimal solution after quantization. Extensive numerical experiments, across various MIMO system sizes and modulation orders (up to 256-QAM), show that heterogeneous quantization matches the full-precision baseline bit error rate using significantly fewer bits than homogeneous approaches. We provide hardware-aware guidelines for selecting the optimal quantization strategy.