Quantum Annealing Algorithms for PAPR Minimisation in Wireless Networks

Abstract: In this thesis, we devise a scheme to run PAPR minimisation with 3GPP EVM requirement as constraint on the D-Wave Systems’ quantum annealer. The PAPR minimisation is a problem central to optimising the costs and performance of wireless networks becoming increasingly difficult for larger OFDM-MIMO systems, while the EVM constraint needs to be satisfied to reach an industry standard performance. The PAPR is a non-convex, complex-valued function featuring the l∞-norm, which to our knowledge has not been implemented on quantum annealers prior to this work. The EVM constraint is a linear system which has been previously implemented and solved on quantum annealers, but not in conjunction with the PAPR objective function. Our scheme rewrites the l∞-norm as a linear program and uses binary approximation to represent the real and imaginary parts of the complex-valued optimisation variables separately. It converts the binary problem into a QUBO form, which is mapped onto the graph of the physical qubits of the D-Wave annealer. The scheme introduces additional model parameters which are first optimised using a classical simulated annealing algorithm, and later amended for the quantum annealer. The performance of the l∞-norm and EVM minimisation is first assessed separately, on both quantum and simulated annealing, showing QA can perform competitively to SA. Finally, a 2×2 MIMO system is run on the quantum and simulated annealer, where SA finds a marginally better solution but the QA remains competitive. Lastly, the QA and SA sampling times are compared for several instances of the 2 × 2 MIMO problem, showing a possible time advantage on th QA.