L_p minimisation in sparse array beamforming using semidefinite relaxation

ABSTRACT

The paper considers the design of sparse arrays in the interference active environment to minimise the system complexity and achieve reduced hardware cost. For this, we propose a sparse array design methodology to attain maximum signal-to-interference plus noise ratio (MaxSINR) in the presence of interfering signals. We formulate the optimisation problem as a real-valued quadratically constrained quadratic program (QCQP) with the non-convex ${\ell }_p$ norm to promote sparsity, which is iteratively controlled in the proposed approach. We employ the semidefinite relaxation (SDR) technique and the principle of the majorization-minimisation (MM) algorithm to solve the non-convex QCQP problem. The efficacy of the proposed algorithm is demonstrated through the simulation results. The sparse array obtained through the proposed method performs well when compared with the reweighted ${\mathrm{\ell }}_1$ algorithm.

KEYWORDS:

• Adaptive beamforming
• sparse array
• Signal-to-interference-plus-noise ratio (SINR)
• SDR
• ${\mathrm{\ell }}_p$-minimisation
• MM algorithm
• QCQP
• reweighted ${\mathrm{\ell }}_1$-norm

Disclosure statement

No potential conflict of interest was reported by the author(s).