Optimal waveform design for generalized likelihood ratio and adaptive matched filter detectors using a diversely polarized antenna

In this paper, we address the performance optimization of adaptive detectors in Gaussian noise with unknown covariance matrix, based on a diversely polarized antenna (DPA). First, a general signal model is presented, where the system response is related to the characteristics of its transmitted pulses. Two adaptive detectors, i.e., generalized likelihood ratio and adaptive matched filter, are then adopted, and their expressions for the probabilities of false alarm and detection are provided. In particular, a waveform design algorithm to enhance the detection performance of both the detectors is proposed. Finally, simulation results illustrate the performance gain obtained with the proposed waveform design algorithm, i.e., by optimally selecting the polarization of the transmitted pulses of the DPA.

► We use two detectors: generalized likelihood ratio test and adaptive matched filter.
► General expressions for probabilities of false alarm and detection are obtained.
► We prove the detection probability is a monotonically increasing function of a parameter.
► In a diversely polarized antenna, this parameter is relevant to the transmit polarization.
► We enhance the detection probability by optimally selecting the transmit polarization.