Signal set design with constrained amplitude spectrum and specified time-bandwidth product

A new method for designing signals with a given time-bandwidth product, such that all the signals in the set have a flat amplitude spectrum and have low cross-correlation function values is introduced. It is shown that these signals lie on a signal parameter space ellipse. For a given duration and bandwidth, it is possible to trade off the cardinality of the set for better cross-correlation properties between remaining members of the set. Proof that the cross-correlation between these signals is bounded from above by a factor proportional to the square-root of inverse distance between these signals along one of the axes of the ellipse is given. It is also shown that the cross-correlation between two signals that are furthest apart is bounded by the square-root of inverse time-bandwidth product of the signals in the set. An example design is then given and a comparison of this signal set to some well-known signal sets illustrates that it performs better when the metric is maximum cross-correlation value. The proposed signal set also has the advantage that it can be designed for any time-bandwidth product instead of discrete values