On Doppler tolerance of Costas-coded stepped-frequency signal and its application to wideband orthogonal detection for multiple sound sources

We consider the problem of reducing the computation complexity in wideband matched filter, which is arose from the calculation of the time compressed replicas. To solve this problem, the Doppler tolerance of Costas waveform is derived by calculating the correlation loss of the time-compressed echo and the frequency translated version of the transmitted signal first. Then a narrowband approximation method for wideband detection is proposed to partition the anticipated target Doppler range into several segments. As a result, the generation of replicas is much simpler than the conventional wideband ones and the wideband matched filter processing is more efficient. At last, we extend this method to the application to wideband echo detection in the context of multiple sources and targets. Based on the Costas Doppler tolerance and its orthogonality, a wideband orthogonal detector is designed to increase the detection efficiency. Simulation results prove the validity of the Doppler tolerance calculation and its effectiveness in wideband orthogonal detection.