Waveform synthesis for diversity-based transmit beampattern design

Transmit beampattern design is a critically important task in many fields including defense and homeland security as well as biomedical applications. Flexible transmit beampattern designs can be achieved by exploiting the waveform diversity offered by an array of sensors that transmit probing signals chosen at will. Unlike a standard phased-array, which transmits scaled versions of a single waveform, a waveform diversity-based system offers the flexibility of choosing how the different probing signals are correlated with one another. Recently proposed techniques for waveform diversity-based transmit beampattern design have focused on the optimization of the covariance matrix R of the waveforms, as optimizing a performance metric directly with respect to the waveform matrix is a more complicated operation. Given an R, obtained in a previous optimization stage or simply pre-specified, the problem becomes that of determining a signal waveform matrix X whose covariance matrix is equal or close to R, and which also satisfies some practically motivated constraints (such as constant-modulus or low peak-to-average-power ratio constraints). We propose a cyclic optimization algorithm for the synthesis of such an X, which (approximately) realizes a given optimal covariance matrix R under various practical constraints. A numerical example is presented to demonstrate the effectiveness of the proposed algorithm.