MIMO with 1-bit Pre/Post-Coding Resolution: A Quantum Annealing Approach

TL;DR

A new preprocessing technique, which preserves the quadratic QUBO matrix from the detrimental effects of the Hamiltonian noise through nonlinear companding, is proposed, which significantly improves the quality of the D-WAVE solutions as well as the occurrence probability of the optimal solution.

Abstract

In this paper, we study the problem of digital pre/post-coding design in multiple-input multiple-output (MIMO) systems with 1-bit resolution per complex dimension. The optimal solution that maximizes the received signal-to-noise ratio relies on an NP-hard combinatorial problem that requires exhaustive searching with exponential complexity. By using the principles of alternating optimization and quantum annealing (QA), an iterative QA-based algorithm is proposed that achieves near-optimal performance with polynomial complexity. The algorithm is associated with a rigorous mathematical framework that casts the pre/post-coding vector design to appropriate real-valued quadratic unconstrained binary optimization (QUBO) problems. Experimental results in a state-of-the-art D-WAVE QA device validate the efficiency of the proposed algorithm. To further improve the efficiency of the D-WAVE quantum device, a new pre-processing technique which preserves the quadratic QUBO matrix from the detrimental effects of the Hamiltonian noise through non-linear companding, is proposed. The proposed pre-processing technique significantly improves the quality of the D-WAVE solutions as well as the occurrence probability of the optimal solution.

Figures (9)

• Figure 1: $N_R\times N_T$ MIMO channel with $1$-bit pre/post-coding vectors.
• Figure 2: $\mu$-law compander characteristic function; $\mu=255$ is considered in our experimental studies (commercial PCM).
• Figure 3: QUBO pre-processing technique to combat Hamiltonian/ICE noise.
• Figure 4: [top] D-WAVE performance for conventional QUBO (without pre-processing), [bottom] D-WAVE performance for companded QUBO (with pre-processing); QUBO problem of dimension $24$, ES benchmark (dashed line).
• Figure 5: [D-WAVE] Average SNR performance versus transmit power $P$ for different MIMO configurations; Algorithm \ref{['alg1']}/D-WAVE results (markers), ES benchmark (dashed line), RQ-M algorithm KRI3 (dashdotted line).