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arXiv:2402.07643 · IEEE Wireless Communications Letters

A Lattice-Reduction Aided Vector Perturbation Precoder Relying on Quantum Annealing

Samuel Winter, Yangyishi Zhang, Gan Zheng, Lajos Hanzo

Published Feb 14, 2024• 3 citations
arXivHTMLPDF

Abstract

Quantum annealing (QA) is proposed for vector perturbation precoding (VPP) in multiple input multiple output (MIMO) communications systems. The mathematical framework of VPP is presented, outlining the problem formulation and the benefits of lattice reduction algorithms. Lattice reduction aided quantum vector perturbation (LRAQVP) is designed by harnessing physical quantum hardware, and the optimization of hardware parameters is discussed. We observe a 5dB gain over lattice reduction zero forcing precoding (LRZFP), which behaves similarly to a quantum annealing algorithm operating without a lattice reduction stage. The proposed algorithm is also shown to approach the performance of a sphere encoder, which exhibits an exponentially escalating complexity.

DOI
10.1109/lwc.2024.3365874

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Quantum annealing (QA) is proposed for vector perturbation precoding (VPP) in multiple input multiple output (MIMO) communications systems. The mathematical framework of VPP is presented, outlining the problem formulation and the benefits of lattice reduction algorithms. Lattice reduction aided quantum vector perturbation (LRAQVP) is designed by harnessing physical quantum hardware, and the optimization of hardware parameters is discussed. We observe a 5dB gain over lattice reduction zero forcing precoding (LRZFP), which behaves similarly to a quantum annealing algorithm operating without a lattice reduction stage. The proposed algorithm is also shown to approach the performance of a sphere encoder, which exhibits an exponentially escalating complexity.
In a multi-user system with multiple antennas at the base station, precoding techniques in the downlink broadcast channel allow users to detect their respective data in a non-cooperative manner. Vector Perturbation Precoding (VPP) is a non-linear variant of transmit-side channel inversion that perturbs user data to achieve full diversity order. While promising, finding an optimal perturbation in VPP is known to be an NP-hard problem, demanding heavy computational support at the base station and limiting the feasibility of the approach to small MIMO systems. This work proposes a radically different processing architecture for the downlink VPP problem, one based on Quantum Annealing (QA), to enable the applicability of VPP to large MIMO systems. Our design reduces VPP to a quadratic polynomial form amenable to QA, then refines the problem coefficients to mitigate the adverse effects of QA hardware noise. We evaluate our proposed QA based VPP (QAVP) technique on a real Quantum Annealing device over a variety of design and machine parameter settings. With existing hardware, QAVP can achieve a BER of 10−4with 100µs compute time, for a 6 × 6 MIMO system using 64 QAM modulation at 32 dB SNR.
In this article, we study the problem of digital pre/postcoding design in multiple-input multiple-output (MIMO) systems with 1-b 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/postcoding 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 preprocessing technique, which preserves the quadratic QUBO matrix from the detrimental effects of the Hamiltonian noise through nonlinear companding, is proposed. The proposed preprocessing technique significantly improves the quality of the D-WAVE solutions as well as the occurrence probability of the optimal solution.
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.
In this letter, we study the analogue pre/post-coding vector design for a point-to-point multiple-input multiple-output (MIMO) system with 1-bit phase shifters. Specifically, we focus on the signal-to-noise ratio (SNR) maximization problem which corresponds to a combinatorial NP-hard due to the binary phase resolution. Two classical computation heuristics are proposed i.e., i) an 1-bit real-valued approximation of the optimal digital designs, and ii) an alternating optimization where a Rayleigh quotient problem is solved at each iteration. An iterative quantum annealing (QA)-based heuristic is also investigated, which outperforms classical counterparts and achieves near-optimal performance while ensuring polynomial time complexity. Experimental results in a real-world D-WAVE QA device validate the efficiency of the proposed QA approach.
The rapid advancement of quantum computing provides unprecedented opportunities for the optimization of multiple-input, multiple-output (MIMO) systems. This paper investigates the efficacy of harnessing quantum algorithms, particularly the Quantum Approximate Optimization Algorithm (QAOA) and Grover's algorithm, for the optimization of MIMO systems. The paper establishes a theoretical framework that maps MIMO optimization problems onto quantum circuits, ensuring a reduction in computational complexity compared to classical algorithms. The proposed methodology is validated through a series of numerical simulations. Notable improvements are observed in both convergence speed and the quality of the optimized solutions. Furthermore, the synergy of quantum computing and MIMO presents new frontiers for reducing interference, enhancing throughput, and ensuring robustness against environmental uncertainties. These results affirm the potential of integrating quantum computing techniques in MIMO system optimization, heralding a transformative era for wireless communication paradigms.
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