Joint Optimization of Transmit Waveforms Design and Antenna Positions Selection Based on MIMO Ambiguity Function

MIMO ambiguity function integrates the effects of transmit waveforms and array geometry and characterizes the resolution properties of radar systems in the range, Doppler, and spatial domains. This paper considers the joint design of transmit waveforms and transmit array antenna positions based on optimization of the MIMO ambiguity function. Two design issues are considered here, one is to find orthogonal waveform set and transmit array geometry to obtain the highest resolution and low sidelobes, and the other is to match a desired transmit beampattern while reducing range sidelobes. Since sparse arrays provide larger array apertures and more degrees of optimization freedom than the uniform arrays with the same number of antennas, we consider the sparse array design by selecting a given number of antenna positions from a set of possible grid points with equal spacing. The joint optimization of transmitted waveforms and antenna positions has many advantages, but it also leads to Boolean-nonconvex problems that are difficult to solve. Therefore, we propose a multi-step method based on the nonlinear conjugate gradient (NCG) method and the limited-memory Broyden-Fletcher-Goldfarb-Shanno with bound constraints (L-BFGS-B) algorithm to solve the design problems. Simulation results demonstrate the proposed method can obtain the transmit waveforms and array configuration with the desired performance and is superior to the existing methods.