Convolutional Neural Networks for Direction of Arrival Estimation Compared to Classical Estimators and Bounds

Recently, there has been a proliferation of applied machine learning (ML) research, including the use of convolutional neural networks (CNNs) for direction of arrival (DoA) estimation. With the increasing amount of research in this area, it is important to balance the performance and computational costs of CNNs with classical methods of DoA estimation such as Multiple Signal Classification (MUSIC). We outline the performance of both methods of DoA estimation for single-source and two-source cases for multiple array conditions. The results are also compared to the Cramer-Rao lower bound (CRLB) and conventional beamforming. For each source case, CNNs were trained for a perfect uniform line array (ULA) and tested against data from a perfect ULA, perturbed ULAs, ULAs with missing sensors, and ULAs with muffled sensors. We show that for the single-source case, the CNNs do not offer any performance improvement relative to MUSIC at low signal-to-noise ratio (SNR). For the two-source cases, the CNNs perform better than MUSIC but only at low SNR. For the remaining array cases, the CNNs outperform MUSIC. These results indicate that the performance improvements from CNNs are highest for situations where there is signal model to data mismatch (imperfect information). This work also illustrates that the CNN estimators developed in this work exceed the CRLB and are biased estimators caused by the lack of unbiased constraint in the loss function during training of the CNNs.