Abstract The multiple signal classification (MUSIC) algorithm is a well-established method to evaluate the direction of arrival (DOA) of signals. However, the construction and eigen-decomposition of the sample covariance matrix (SCM) are computationally costly for MUSIC in hybrid multiple input multiple output (MIMO) systems, which limits the application and advancement of the algorithm. In this paper, we present a novel quantum method for MUSIC in hybrid MIMO systems. Our scheme makes the following three contributions. First, the quantum subroutine for constructing the approximate SCM is designed, along with the quantum circuit for the steering vector and a proposal for quantum singular vector transformation. Second, the variational density matrix eigensolver is proposed to determine the signal and noise subspaces utilizing the destructive swap test. As a proof of principle, we conduct two numerical experiments using a quantum simulator. Finally, the quantum labelling procedure is explored to determine the DOA. The proposed quantum method can potentially achieve exponential speedup on certain parameters and polynomial speedup on others under specific moderate circumstances, compared with their classical counterparts.
Abstract The multiple signal classification (MUSIC) algorithm is a well-established method to evaluate the direction of arrival (DOA) of signals. However, the construction and eigen-decomposition of the sample covariance matrix (SCM) are computationally costly for MUSIC in hybrid multiple input multiple output (MIMO) systems, which limits the application and advancement of the algorithm. In this paper, we present a novel quantum method for MUSIC in hybrid MIMO systems. Our scheme makes the following three contributions. First, the quantum subroutine for constructing the approximate SCM is designed, along with the quantum circuit for the steering vector and a proposal for quantum singular vector transformation. Second, the variational density matrix eigensolver is proposed to determine the signal and noise subspaces utilizing the destructive swap test. As a proof of principle, we conduct two numerical experiments using a quantum simulator. Finally, the quantum labelling procedure is explored to determine the DOA. The proposed quantum method can potentially achieve exponential speedup on certain parameters and polynomial speedup on others under specific moderate circumstances, compared with their classical counterparts.
The direction of arrival (DOA) estimation in array signal processing is an important research area. The effectiveness of the direction of arrival greatly determines the performance of multi-input multi-output (MIMO) antenna systems. The multiple signal classification (MUSIC) algorithm, which is the most canonical and widely used subspace-based method, has a moderate estimation performance of DOA. However, in hybrid massive MIMO systems, the received signals at the antennas are not sent to the receiver directly, and spatial covariance matrix, which is essential in MUSIC algorithm, is thus unavailable. Therefore, the spatial covariance matrix reconstruction is required for the application of MUSIC in hybrid massive MIMO systems. In this article, we present a quantum algorithm for MUSIC-based DOA estimation in hybrid massive MIMO systems. Compared with the best-known classical algorithm, our quantum algorithm can achieve an exponential speedup on some parameters and a polynomial speedup on others under some mild conditions. In our scheme, we first present the quantum subroutine for the beam sweeping based spatial covariance matrix reconstruction, where we implement a quantum singular vector transition process to avoid extending the steering vectors matrix into the Hermitian form. Second, a variational quantum density matrix eigensolver (VQDME) is proposed for obtaining signal and noise subspaces, where we design a novel objective function in the form of the trace of density matrices product. Finally, a quantum labeling operation is proposed for the direction of arrival estimation of the signal.
The direction of arrival (DOA) estimation in array signal processing is an important research area. The effectiveness of the direction of arrival greatly determines the performance of multi-input multi-output (MIMO) antennas. The multiple signal classification (MUSIC) algorithm, which is the most canonical and widely used subspace-based method for direction angle estimation, has a moderate estimation performance of DOA. In this article, we present a quantum algorithm for performing MUSIC. Compared with the best-known classical algorithm, quantum MUSIC can show a polynomial speedup. In our scheme, we first efficiently implement a non-Hermitian chain product subroutine for the matrix ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{R}}_{ss}\ensuremath{\in}{R}^{N\ifmmode\times\else\texttimes\fi{}N}$ with L snapshots, where the method is different from that of Cong and Duan [I. Cong and L. Duan, New J. Phys. 18, 073011 (2016)]. In this subroutine, we perform amplitude transduction [Y. R. Sanders, G. H. Low, A. Scherer, and D. W. Berry, Phys. Rev. Lett. 122, 020502 (2019)] by testing an inequality to neglect the calculation of the approximate arcsine function. Second, a quantum labeling operation based on the principal eigenvalues is proposed for preparing the coherent state of the principal eigenvectors. Finally, we generalize our results to some quantum algorithms with quantum principal component analysis subroutines and some existing quantum algorithms where the covariance matrices occur in the non-Hermitian chain product form.
The article analyses methods for determining the direction of arrival (DOA) of radio signals, particularly the MUSIC and ESPRIT algorithms. It is shown that the complexity of traditional approaches grows cubically with the number of antennas, which complicates their application in large-scale systems. The use of quantum algorithms for solving systems of linear equations and computing eigenvalues is proposed, allowing for a significant reduction in computational costs. The study examines the processing of complex matrices and presents a comparison table between classical and quantum versions of the algorithm in terms of computational complexity and structure.
This paper introduces a pioneering method in the realm of signal processing for Massive Multiple-Input Multiple-Output (MIMO) systems, leveraging the synergistic potential of hybrid quantum-classical computing paradigms. The escalating demand for high data rate communications necessitates the advancement of MIMO technologies. However, the computational complexity associated with signal processing in such systems, especially in scenarios involving large array sizes, presents a significant challenge. This study proposes an innovative framework that integrates quantum computing algorithms with traditional classical methods to address this challenge. The quantum algorithms are specifically designed to expedite matrix operations and optimization tasks that are central to MIMO signal processing, such as channel estimation and precoding. A comparative analysis with purely classical approaches demonstrates a substantial improvement in computational efficiency and latency reduction, while maintaining, and in certain aspects enhancing, the accuracy of signal detection and system throughput. Furthermore, this hybrid approach offers scalability and adaptability to varying channel conditions and system configurations, a crucial feature for next-generation wireless communication systems. The theoretical foundation is complemented by simulation results, showcasing the feasibility and effectiveness of this approach in practical scenarios. This research not only paves the way for advanced signal processing techniques in Massive MIMO systems but also opens new horizons in the application of quantum computing in telecommunications.
Quantum wireless sensing using Rydberg atomic receivers enables high-sensitivity signal acquisition direction-of-arrival (DoA) estimation. However, it suffers from a fundamental limitation, where only the magnitude of the received signal is observable. The recently proposed Quantum-MUSIC algorithm addresses this problem by recovering phase information through alternating minimization and subsequently applying the MUSIC algorithm for DoA estimation. However, the existing approach relies on an ℓ2-norm phase retrieval step, making it highly sensitive to outlier measurements produced by hardware faults, sensor saturation, or adversarial interference. In this letter, we propose a \emph{Robust Quantum-MUSIC} (RobQMUSIC) framework that replaces the ℓ2-norm with an ℓ1-norm formulation. The resulting weighted phase-retrieval problem is solved efficiently via an Iteratively Reweighted Least Squares (IRLS) scheme embedded within the alternating minimization loop, requiring no increase in structural complexity relative to the baseline algorithm. Simulation results demonstrate that RobQMUSIC achieves near-identical DoA estimation accuracy to Quantum-MUSIC under ideal conditions, while maintaining robust performance over a wide range of outlier contamination levels at which Quantum-MUSIC fails entirely.
Near-field wavefront curvature enables joint angle-range localization, but exploiting it entails repeated covariance-eigenspace tests over a two-dimensional spherical manifold. We propose a quantum subspace-projection algorithm (Q-SPARSE) for super-resolution estimation of parameters in the near field, employing spectral signature similar to MUSIC. Q-SPARSE prepares each spherical steering hypothesis as a quantum state, applies quantum phase estimation (QPE) to covariance-generated evolution, and converts the resolved spectral mass into a localization spectrum. The proposed method does not need the full classical preparation of the eigenstates, which is a major bottleneck of the QPE algorithm, the main subroutine in quantum variants of MUSIC algorithms. Under an ideal signal-noise partition, its score equals the classical signal-subspace overlap exactly and thus preserves the maximizer of normalized near-field MUSIC. For a finite q number of qubit phase registers, we derive the score from the complete QPE kernel, and propose a nearest-bin selection scheme with soft-thresholding based on Marchenko-Pastur-calibrated logistic weighting decision criteria. Numerical results on IBM's QISKIT software platform are demonstrated for near-field array processing.