Closed-form Solution to Directly Design FACE Waveforms for Beampatterns Using Planar Array

In multiple-input multiple-output radar systems, it is usually desirable to steer transmitted power in the region-of-interest. To do this, conventional methods optimize the waveform covariance matrix, R, for the desired beampattern, which is then used to generate actual transmitted waveforms. Both steps require constrained optimization, therefore, use iterative algorithms. The main challenges encountered in the existing approaches are the computational complexity and the design of waveforms to use in practice. In this paper, we provide a closed-form solution to design covariance matrix for the given beampattern using the planar array, which is then used to derive a novel closed-form algorithm to directly design the finite-alphabet constant-envelope (FACE) waveforms. The proposed algorithm exploits the two-dimensional fast-Fourier-transform. The performance of our proposed algorithm is compared with existing methods that are based on semi-definite quadratic programming with the advantage of a considerably reduced complexity.