MIMO waveforms design with good correlation properties under bound constraints

We develop a new fast and efficient algorithm for designing multiple-input multiple-output (MIMO) waveforms with low auto- and cross-correlation sidelobes. Unlike the existing methods that consider unimodular signals, we design both signal amplitudes and phases to minimize the weighted integrated sidelobe level (WISL) of signals. Bound constraints on signal amplitudes are forced into the optimization to balance the transmitter efficiency and the degrees of optimization freedom, which also can provide a feasible set that facilitates efficient optimization. The amplitude-bounded signals design problem is formulated as a quartic optimization problem with bound constraints and equality (constant energy) constraints. We propose a novel algorithm based on the limited-memory Broyden-Fletcher-Goldfarb-Shanno with bound constraints (L-BFGS-B) method to solve the resultant problem. An algorithmic enhancement via nonlinear conjugate gradient (NCG) method is also developed to improve the proposed method. In addition, we derive the gradients of the cost function with respect to (w.r.t.) the signal amplitudes and phases and calculate them with the help of fast Fourier transformation (FFT), which makes the proposed method very computationally efficient. Numerical simulations illustrate that the proposed algorithm outperforms the state-of-the-art methods in both optimization performance and computational efficiency.