MLP solutions for approximating the Average Likekihood Ratio detector in radar applications

Multilayer perceptron (MLP) based detectors are proposed for detecting Gaussian signals with unknown correlation coefficient (rho_s) in additive white Gaussian noise. After proving the low robustness of the likelihood ratio (LR) based detector with respect to rho_s, the average likelihood ratio(ALR) based detector assuming a uniform distribution of rho_s in [0,1] is formulated. Due to the complexity of the involved integral, two NN based solutions are proposed. MLPs trained with target one-lag correlation coefficient (rho_s) varying uniformly in [0,1] outperform the LR-based detector for a fixed rho_s, when targets with rho_s varying uniformly in [0, 1] are considered for simulation. Two MLPs with 17 hidden neurons each are trained with rho_s varying uniformly in [0,b] and [b,1], respectively. Different values of b are studied: 0.25, 0.5 and 0.75. These three detectors outperform the single MLP, and the best results are obtained with b = 0.5 and 0.75. Finally, results show that the number of hidden units of the MLP trained with high values of rho_s can be reduced to 8, without reducing the detection capabilities.