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Description

We introduce a method for the synthesis of pulse pairs that satisfy a given time-bandwidth condition, and have small cross-correlations for all lags. Pulse pairs with such properties are essential to synthetic aperture imaging---which includes both SAS and SAR---when multiple transmitters are employed. We formulate the problem in a finite dimensional Euclidean space and identify the geometric properties of the feasible set that arises from the small cross-correlation conditions. An iterative algorithm is developed that modifies the feasible set such that additional unit energy constraints on the signal pair are simultaneously satisfied. We illustrate the effectiveness of the method with examples; the cross-correlation function of the pulses that we obtain shows significant improvements over that of pseudo-noise sequences, and of pulses obtained by a previously reported method.