Optimal multicarrier phase-coded waveform design for detection of extended targets

We design a parametric multicarrier phase-coded (MCPC) waveform that achieves the optimal performance in detecting an extended target in the presence of signal-dependent interference. Traditional waveform design techniques provide only the optimal energy spectral density of the transmit waveform and suffer a performance loss in the synthesis process of the time-domain signal. Therefore, we opt for directly designing an MCPC waveform in terms of its time-frequency codes to obtain the optimal detection performance. First, we describe the modeling assumptions considering an extended target buried within the signal-dependent clutter with known power spectral density, and deduce the performance characteristics of the optimal detector. Then, considering an MCPC signal transmission, we express the detection characteristics in terms of phase-codes of the MCPC waveform and propose to optimally design the MCPC signal by maximizing the detection probability. Our numerical results demonstrate that the designed MCPC signal attains the optimal detection performance and requires a lesser computational time than the other parametric waveform design approach.