access icon free Minimum mean squares error beamforming with cyclic sub-vector optimisation

© The Institution of Engineering and Technology
Received 03/04/2019, Accepted 20/03/2020, Revised 22/02/2020, Published 24/03/2020

A cyclic sub-vector optimisation (CSVO) beamforming approach is investigated. With the proposed algorithm, an array beamforming vector is partitioned into a number of sub-vectors of small sizes, allowing reduced-dimension processing. Then multiple optimisation cycles are carried out by the block coordinate descent method, which leads to an optimal beamforming vector. The proposed scheme still needs to compute the matrix inversion, but the size of the matrix can be flexibly chosen and the computational complexity is manageable. The proof of the convergence and complexity analysis is given. The simulation results demonstrate the effectiveness and fine features of the proposed algorithm. Although the convergence rate of the CSVO is slightly slower, the CSVO has lower computational complexity than that of the diagonal loading conjugate gradient applied to normal equations algorithm. In comparison with other sub-vector approaches, the proposed algorithm gains a faster convergence rate and improved stability.

Inspec keywords: gradient methods; conjugate gradient methods; least mean squares methods; array signal processing; computational complexity; least squares approximations; convergence of numerical methods; optimisation; vectors; matrix inversion; iterative methods; mean square error methods

Other keywords: array beamforming vector; multiple optimisation cycles; reduced-dimension minimum mean squares error; complexity analysis; CSVO; normal equations algorithm; optimal beamforming vector; cyclic sub-vector optimisation beamforming approach; reduced-dimension processing; sub-vector approaches; convergence; matrix inversion

Subjects: Other topics in statistics; Optimisation techniques; Optimisation techniques; Interpolation and function approximation (numerical analysis); Interpolation and function approximation (numerical analysis); Radio links and equipment; Signal processing and detection

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