Frequency-Invariant Beampattern Synthesis for Wideband MIMO Radar Under Nulling and PAPR Control

Abstract

This article investigates the problem of frequency-invariant (FI) beamforming of wideband multiple-input multiple-output (MIMO) radars and presents two design criteria to synthesize wideband FI beampatterns under peak-to-average power ratio (PAPR) and nulling constraints. Precisely, the two criteria are to apply the least-squares and absolute errors, respectively, to approximate a desired transmit beampattern. Both criteria result in nonconvex constrained optimization problems. For the former, the solution is derived via reformulating the initial problem into a quadratic form, which can be solved by alternating direction method of multipliers (ADMM). For the latter, the design problem is formulated into an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${l_{1}}$</tex-math></inline-formula> -norm real-valued form, which is solved iteratively by using a nested ADMM (N-ADMM) algorithm. Moreover, both the convergence and computational complexities of these two algorithms are discussed. Numerical simulations show that the obtained beampatterns by the proposed algorithms can well approximate the given beampattern under the required constraints.