False-Alarm-Controllable Radar Target Detection by Differentiable Neyman Pearson Criterion for Neural Network

Compared with the classical constant false alarm ratio (CFAR) detector, the neural network (NN)-based detector has data-driven representation learning ability, which can improve the detection performance of weak targets in a nonhomogeneous environment. Under the extreme sample imbalance scenario (ESIS) for marine radar, it is difficult to control the probability of false alarm (PFA) by a variable threshold for the network output by adopting the cross-entropy (CE) loss function. The Neyman Pearson (NP) criterion is used to find the optimal detector under the constraint of PFA in radar detection and may be used as a loss function for NN to realize false-alarm-controllable detection. However, it is nondifferentiable and cannot be used directly for NN. Therefore, first, we theoretically deduce two differentiable-NP loss functions for NNs under the ESIS to realize the NP criterion approximately. Second, we theoretically analyze the differentiable-NP loss under the ESIS from the gradient perspective. Third, based on the differentiable-NP loss, we achieve the false-alarm-controllable detection under the ESIS by utilizing a lightweight U-Net segmentation network. Fourth, to improve the PFA control capability of the segmentation network, we adopt a smaller fixed-size label for each target to reduce the influence of target random size, and we dynamically adjust the regular loss term to diminish the deviation caused by the nondifferentiable operation. The experimental results show that the proposed method can accurately control PFA and get a better detection performance compared with other methods in the measurement data from marine navigation radar.