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. 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, 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. 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 number of numerical examples are presented to demonstrate the effectiveness of the proposed algorithm.