Finite alphabet constant-envelope waveform design for MIMO radar

The design of waveforms with specified auto- and cross-correlation properties has a number of applications in multiple-input multiple-output (MIMO) radar beampattern design. In this work, two algorithms are proposed to generate finite alphabet constant-envelope (CE) waveforms with required cross-correlation properties. The first-algorithm proposes a closed-form solution to find the finite alphabet CE waveforms to realize the given covariance matrix. Here, Gaussian random-variables (RV's) are mapped onto binary-phase shift keying (BPSK) and quadrature-phase shift keying (QPSK) symbols using nonlinear functions, and the cross-correlation relationship between the Gaussian RV's and BPSK/QPSK RV's is established. This cross-correlation relationship is exploited to convert the problem of finding the BPSK/QPSK waveforms to realize the covariance matrix, corresponding to the given beampattern, into finding the Gaussian RV's to realize another covariance matrix that can be easily found. In the second-algorithm, by exploiting the results of first-algorithm, a generalized algorithm to generate BPSK waveforms to approximate the given beampattern is proposed. Simulation results show that proposed finite alphabet CE waveforms outperform the existing algorithms to approximate the desired beampattern.