Abstract
This communication proposes a new relaxation variable based cost function for the problem of frequency invariant (FI) beampattern synthesis. Two constraints in the spatial and frequency domains are imposed on the optimization problem. The objective of sparsifying the relaxation variable is exploited in constructing the constraint in the spatial domain, and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> -spatial response variation (SRV) is introduced in the frequency domain constraint to reduce frequency variance. These constraints enable a desirable trade-off between beamwidth and FI properties while achieving accurate spatial-frequency response control. Since the resulting optimization problem is sparse and non-convex, it is then proposed to be solved by exploiting the reweighted- <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> norm in this paper. The remarked feature of the new approach is the improved target detection and anti-interference performance in radar and communication systems without waveform distortion. Simulation results validate the effectiveness of the proposed method.
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