Extended regression-based deep neural network with multi-task learning for fast source detection by sensor array

In this paper, we consider the two main tasks in source detection by a sensor array, i.e., source number detection and DOA estimation. Most of conventional methodologies employ two different stages for the two tasks, respectively, and they are facing the issue of high computational complexity. In this paper, we propose a deep neural network (DNN) framework which considers the two tasks as two simple extended regression tasks and implement them simultaneously using multi-task learning, named the extended regression-based DNN (ER-DNN). By noticing the sources are generally a few in space, we design the ER-DNN with simple fully connected layers for computational efficiency. Moreover, we employ the prior knowledge that an array of M sensors identifies M-1 sources at most to design two specified label vectors each with a length of M-1. In particular, each of the label vectors has the first K elements equal to the DOAs of the K sources. The difference between the two label vectors is that the label vector for estimating the DOAs of sources has the last M-K-1 elements equal to an arbitrary value, while the label vector for detecting the number of sources has the last M-K-1 elements with a fixed value out of the range of view (FOV) of the array. Thus, in order to avoid the negative transfer usually encountered in multi-task learning, two relevant loss functions are designed using extended regression. Theoretical analysis shows the ER-DNN significantly reduces computational complexity. Simulation results confirm the superiority of the ER-DNN over the existing methods in terms of source detection. Importantly, the ER-DNN is more efficient than the classical methods and the other DNN-based methods. Real data collected by a circular array further confirms the generalization of the ER-DNN model trained with simulation data.