Cascaded Multi-Head Attention Transformer Framework for Direction of Arrival Estimation

Abstract

Deep neural networks have demonstrated significant potential in direction of arrival (DOA) estimation. However, some existing architectures, especially convolution-based ones, mainly emphasize local feature extraction and may not sufficiently capture long-range dependencies in array observations. To better model such nonlocal correlations, this paper presents a Cascaded Multi-Head Attention Transformer (CMA-Former) for grid-based DOA estimation. The sample covariance matrix is first converted into a compact token sequence using its upper-triangular off-diagonal entries. For each entry, the real part, the imaginary part, and the sine and cosine of its phase are stacked as input features, providing a periodic phase encoding that avoids the discontinuity inherent in raw phase values. A stack of customized Transformer encoders, each equipped with cascaded multi-head attention modules whose head count increases progressively, is then employed to capture sensor-pair correlations across multiple representation subspaces and scales. Finally, a classification token together with a classification head produces confidence scores over a predefined angular grid. Simulation results show that CMA-Former achieves an RMSE lower than or comparable to that of the deep-learning baselines considered. Moreover, it attains a higher estimation success rate for closely spaced sources, indicating an improved capability to resolve adjacent targets. At high SNR, the performance of all grid-based methods is bounded by the off-grid error floor imposed by the fixed angular grid. In addition, a hardware experiment using a cascaded mmWave radar platform further demonstrates the feasibility of applying CMA-Former to real radar measurements without retraining. The source code is publicly available at https://github.com/Syyyt/CMA-Former-official