Geometric construction of pulse pairs with small cross-correlation for dual transmitter synthetic aperture imaging

We introduce a method for the synthesis of pulse pairs that satisfy simultaneously the time-bandwidth condition and the maximum cross-correlation condition for all lags. Pulse pairs with such properties are essential to synthetic aperture imaging - including both SAS and SAR - when multiple transmitters are employed. Formulating the problem in a finite dimensional Euclidean space setting, we identify the geometric properties of the feasible set that arises from the maximum cross-correlation condition. We then develop an iterative algorithm that modifies the feasible set such that additional unit energy constraints on the signal pair are also satisfied. We illustrate the effectiveness of the method with several examples, where the cross-correlation function shows significant improvements over both the PN sequences, and pulses obtained by a previously reported method.