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.

The use of acoustical techniques in oceanography is well known. Traditional applications have concentrated on long range, low frequency propagation. Due a convergence of both technology and national interests, consideration of the possibilities for creating high frequency, real time, multi-dimensional imaging systems (2 and 3-D) has emerged. Unfortunately, due to a lack of experimental investigation, the propagation issues related to these frequencies are relatively unknown. The authors' group in underwater acoustic imaging applied to ocean exploration and oceanography has been taking high frequency acoustic pictures in the ocean for almost a decade. The first experiences were in using the traditional types of ocean going sonars such as side scans. More recently they have been developing a 3-dimensional multibeam imaging system for tracking small animals in the sea. As part of this effort they have been looking at both the spatial and temporal correlation scales for the propagation of high frequency sound.