Convex optimization applied to transmit beampattern synthesis and signal waveform design for MIMO radar

This paper deals with designing the signal waveforms transmitted via multiple-input multiple-output (MIMO) radar antennas to approximate a given transmit beampattern, and also to minimize the cross-correlation of different echoes. In this paper, we consider a non-uniform but fixed elemental power constraint instead of the uniform elemental power one while still maintaining the same total transmit power. With the relaxed constraint and for a given power gain, we first construct a set of transmit beams or signal waveform vectors with globally optimal peak sidelobe levels. Next, we combine these beams or the corresponding vectors according to some ratios to synthesize a desired transmit beampattern or its corresponding probing signal matrix. Convex optimization is applied to get these vectors and their ratios. Numerical comparison shows that our synthesized transmit beampattern has lower peak sidelobe levels and also has lower cross- correlation peak sidelobe levels due to relaxing the uniform elemental power constraint. Additionally, the probing signal transmitted by each antenna element has a constant modulus because of the fixed elemental power constraint.