Co-Design of Waveform Correlation Matrix and Antenna Positions for MIMO Radar Transmit Beampattern Formation

Reconfigurable Linear Antenna Arrays for Beam-Pattern Matching in Collocated MIMO Radars

“…Extending the ideas behind sparse receive array methodologies to that of sparse MIMO array design with new terminologies such as array optimization, antenna placement, antenna selection, etc. has been done in studies such as [24], [27]- [32].…”

“…In the recent studies [30]- [32], the problem of joint design of waveform covariance matrix and antenna position vector (a binary vector that indicates the position of active and inactive antennas in the array with one and zero values, respectively) has been investigated. Solving this problem has two goals: a) to select a specific number of antennas N from a set of candidate antennas M which are initially configured in a ULA array (the number of candidate antennas is larger than the selecting antennas, i.e., M > N ); and b) to design the waveform covariance matrix which matches the transmit beam-pattern to the desired one, using the reconfigured array.…”

“…Also in [31] an iterative greedy local binary search approach based on dynamic programming and evolutionary algorithms is devised to handle the position vector optimization. In [32], for the joint design problem, authors considered two optimization criteria, i.e., the MSE for beam-pattern matching as well as a defined criterion for controlling mainlobe ripple and sidelobe levels. In both formulations, first, the couple between the covariance matrix and the position vector is eliminated, and then a successive convex approximation (SCA) algorithm is proposed to solve the resultant problems.…”

“…Despite the high computational complexity of the proposed methods in [30]- [32] due to the cyclic and iterative methods for optimizing position vector utilized in these works, none of them guarantee the optimality of the results. The reason is in one hand, the problem of joint design of covariance matrix and antenna position vector is not convex and can have several local minimums, and on the other hand, all of these methods have a random parameter in their process which results in falling in these local minimums rather than necessarily reach the global optimum point.…”

“…The reason is in one hand, the problem of joint design of covariance matrix and antenna position vector is not convex and can have several local minimums, and on the other hand, all of these methods have a random parameter in their process which results in falling in these local minimums rather than necessarily reach the global optimum point. Hence in practice, several optimization runs are usually carried out and then the minimal objective value is chosen [32]. Also in some cases, the optimization process will not converge at all because of the inaccurate choice of optimization parameters.…”