Optimal signal/filter design for multi-target detection in colored noise

We consider the design of optimal transmit waveforms/receive-filters for detecting multiple unknown targets in a known interference environment. Specifically, we introduce constraints on the signal/filter cross correlation function, which is of fundamental importance in practice. The incorporation of these constraints leaves the problem analytically intractable, and numeric techniques must be employed. We show that unlike the solutions to the more relaxed formulations found in the literature, eigenfunction solutions are no longer applicable, and the Neyman-Pearson receiver is no longer the most appropriate choice for many scenarios.