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PIERS Online

A Novel Linear Beamforming Algorithm

Shuangning Shi, Yong Shang, Qinglin Liang

Published Jan 1, 2007• 3 citations
Publisher

Abstract

Quantum Signal Processing (QSP) beamformer, which is based on Quantum Sig- nal Processing framework, is presented in this paper. This new beamformer can realize the same output gain and signal-to-interference-and-noise ratio (SINR) as conventional beamformers through adjusting impact factors without pre-estimating the covariance matrix of received sig- nals. Finally, the efiectiveness and feasibility of the new beamformer are verifled by simulation results. DOI: 10.2529/PIERS061007112619

DOI
10.2529/piers061007112619

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Quantum Signal Processing (QSP) beamformer, which is based on Quantum Sig- nal Processing framework, is presented in this paper. This new beamformer can realize the same output gain and signal-to-interference-and-noise ratio (SINR) as conventional beamformers through adjusting impact factors without pre-estimating the covariance matrix of received sig- nals. Finally, the efiectiveness and feasibility of the new beamformer are verifled by simulation results. DOI: 10.2529/PIERS061007112619
This work explores the application of a Quantum algorithm, namely Weighted Subspace-Search-Variational-Quantum-Eigensolver (SSVQE), a variant of the traditional VQE algorithm, to predict optimal as well as sub-optimal sparse array configurations for the problem of beamforming. The optimization formulation is designed to maximize the Signal-to-Interference-plus-Noise Ratio (SINR), which is then reformulated into Quadratic Unconstrained Binary Optimization (QUBO) representation to serve as the Hamiltonian for the weighted SSVQE algorithm. The results obtained are presented along with classically obtained SINR plots to facilitate a comparison of the sparse array configurations. Our findings indicate that the output from the quantum algorithm precisely match with the results obtained from the classical method.
Abstract This study investigates the application of quantum algorithms, specifically the Variational Quantum Eigensolver (VQE) and the Quantum Approximate Optimization Algorithm (QAOA), to design optimal sensor configurations for beamforming, enhancing signal quality and overall system performance. We propose two distinct optimization formulations: one aimed at maximising array gain while the other aimed at maximising signal‐to‐noise‐interference ratio (SINR). Our findings show that the outputs obtained from quantum algorithms are consistent with those derived from classical methods.
In this article we present a signal processing framework that we refer to as quantum signal processing (QSP) (Eldar 2001) that is aimed at developing new or modifying existing signal processing algorithms by borrowing from the principles of quantum mechanics and some of its interesting axioms and constraints. However, in contrast to such fields as quantum computing and quantum information theory, it does not inherently depend on the physics associated with quantum mechanics. Consequently, in developing the QSP framework we are free to impose quantum mechanical constraints that we find useful and to avoid those that are not. This framework provides a unifying conceptual structure for a variety of traditional processing techniques and a precise mathematical setting for developing generalizations and extensions of algorithms, leading to a potentially useful paradigm for signal processing with applications in areas including frame theory, quantization and sampling methods, detection, parameter estimation, covariance shaping, and multiuser wireless communication systems. We present a general overview of the key elements in quantum physics that provide the basis for the QSP framework and an indication of the key results that have so far been developed within this framework. In the remainder of the article, we elaborate on the various elements in this figure.
Quantum Signal Processing (QSP) emerges as a groundbreaking paradigm, exploiting the principles of quantum mechanics to revolutionize the analysis, manipulation, and interpretation of signals. This paper introduces a novel framework for QSP, delineating its theoretical foundations and potential to surpass classical signal processing capabilities. The research delves into the development of quantum algorithms that exhibit superior efficiency in the frequency domain analysis and the processing of temporally entangled signal structures. A pivotal aspect of this work is the introduction of quantum Fourier transforms as a mechanism to achieve exponential speed-ups in signal decomposition. Furthermore, the paper explores the implementation of quantum error correction techniques to enhance the robustness of signal processing in the presence of quantum noise and decoherence. The practicality of QSP is demonstrated through simulated quantum circuits, providing a blueprint for future quantum computing hardware applications. The implications of this research are profound, suggesting a transformative impact on fields ranging from secure communications to biomedical imaging. By harnessing the entanglement and superposition properties inherent to quantum systems, QSP is poised to redefine the limits of what is computationally feasible within information processing.
The Quantum Approximate Optimization Algorithm (QAOA) is a promising quantum algorithm for solving combinatorial optimization problems. In this work, we explore the Recursive QAOA (RQAOA) approach, which improves upon the standard QAOA by successively reducing the problem size, to optimize sensor configuration for beamforming with the objective of maximizing the Signal-to-Interference-plus-Noise Ratio (SINR). We present a series of experiments across various setups, including different numbers of sensors and a range of optimizers. Additionally, we compare the obtained SINR with the maximum achievable SINR to assess the efficiency of the algorithm.
In recent years, quantum technologies have developed as transformative enablers for upcoming generation secure wireless communication by incorporating quantum sensing, computation, and cryptographic techniques for secure reliable data transmission. However, traditional quantum receiver models like Rydberg Atomic Quantum Receivers (RAQR), remain controlled by static signal processing, unmodeled noise interference, and the absence of incorporated quantum-level security. Hence, this research proposes a Secure Quantum Signal Processing Receiver (SQSP-R) which is an adaptive and noise-resilient framework that combines Quantum Signal Processing (QSP) with phase-based quantum encryption. Initially experimental data is gathered using simulated wireless transmission scenarios under changing frequency bands (10−45\mathbf{1 0} \boldsymbol{-} \mathbf{4 5}10−45 GHz), laser detuning levels, and noise settings to estimate system robustness and accuracy. This method applies a reconfigurable SU (2) rotation-based QSP layer that permits dynamic filtering, interference suppression, and phase-controlled demodulation. After that, a quantum random key generator confirms intrinsic encryption during the signal transformation process. Furthermore, a quantum reliability model quantitatively estimates decoherence, optical noise, and environmental disturbances over a real-time feedback optimization mechanism. This incorporated method confirms that the consistent signal fidelity and improved operational adaptability. Experimental evaluation established that the proposed SQSP-R highly enhance the reconstruction performance, attaining a Root Mean Square Error (RMSE) of 0.45−0.95\mathbf{0.45}-\mathbf{0.95}0.45−0.95 compared to the existing RAQR model.