A Novel Method based on Sequential Unconstrained Programming for Transmit Beamforming in Colocated MIMO Radars

The design of the waveform covariance matrix for beampattern matching in colocated multiple-input multiple-output (MIMO) radars represents a challenging problem because of its large number of variables and the presence of multiple constraints. The solutions available in the technical literature are computationally intensive and usually rely on iterative procedures that minimize a constrained mean square error (MSE). In this manuscript, a new computationally efficient method for beampattern matching design is proposed. This method, called sequential weight-shift unconstrained programming (SWSUP), allows to compute the covariance matrix of the probing signals achieving a desired beampattern at the transmit side of a colocated MIMO radar. Its derivation is based on the idea of reformulating the beampattern matching problem in an unconstrained form that can be tackled by breaking it into two subproblems. The first subproblem admits a closed-form solution, whose accuracy, in terms of MSE, is comparable to provided by other known methods. The solution of the second subproblem, instead, is evaluated through an iterative procedure and allows to achieve further improvement. Our numerical results evidence that the SWSUP method achieves precise beampattern matching with a substantially lower computational effort and computing time with respect to various existing alternatives.