A Coordinate Descent Framework for Beampattern Design and Waveform Synthesis in MIMO Radars

In this article, we consider the problem of transmit waveform design for collocated multiple-input multiple-output (MIMO) radar under a constant-envelope (CE) constraint by taking advantage of the coordinate descent (CD) method. In this article, two algorithms are proposed to generate the CE waveforms. In the first algorithm, unlike the two stage methods, we propose an algorithm for direct design of the transmit waveform in order to approximate a desired beampattern (BP). Since our optimization problem is nonconvex multivariate (samples of the transmit waveform matrix), therefore, the CD method is leveraged, which converts the multivariate minimization into a number of scalar minimizations by cyclically (iteratively) optimizing w.r.t. each of the variables (coordinates) assuming the others are fixed. In the second algorithm, by exploiting the results of the first-algorithm, an algorithm to generate a transmit waveform for approximation of a given covariance matrix (CM) is proposed. We take into account in each of the two cases both the finite-alphabet phase codes and the continuous phase codes. In the former, a discrete Fourier transform based procedure is proposed in order to reduce the calculations involved in the searching step over the phase alphabet set. In the latter, both accurate and approximate closed form solutions for the phase code are derived. The experimental results show that, in the first case (BP approximation), our methods can attain to the performance of the nonconstrained methods and in the second case (realizing a given CM), our method has gained higher performance compared with some recent counterparts.