A new beamspace method, called convolutional beamspace (CBS), is proposed for direction-of-arrival (DOA) estimation based on passive arrays. The array output is processed by spatial filtering followed by uniform or nonuniform decimation (downsampling). It achieves all the same advantages as classical beamspace methods, including lower computational complexity, increased parallelism of subband processing, and smaller bias. Moreover, unlike classical beamspace, it allows root-MUSIC and ESPRIT to be performed directly for ULAs without additional preparation since the Vandermonde structure is preserved under the CBS transformation. It can also yield smaller estimation errors for correlated sources compared to element-space. Also, with difference coarray method, the nonuniform decimation scheme allows more accurate estimation of more sources.

Besides, the CBS method is extended to the 2-D mmWave MIMO case. A proper counterpart of CBS is designed at the transmitter: uniform expansion (upsampling) followed by spatial filtering. With this design, all the benefits of 1-D CBS like low complexity, good estimation performance, and Vandermonde structure preservation will be also obtained by 2-D CBS. CBS can be also realized by a hybrid analog and digital implementation. The proposed CBS precoder and combiner with any filter coefficients can be implemented in a hybrid way under the unit-magnitude constraints of phase shifters. The 2-D CBS method can be the foundation for further extension to higher-dimensional cases for reconfigurable-intelligent-surface-aided systems or autonomous vehicles.  

▶ P.-C. Chen and P. P. Vaidyanathan, "Convolutional beamspace for linear arrays," in IEEE Trans. Signal Process, vol. 68, pp. 5395–5410, 2020. (Link)
▶ P.-C. Chen and P. P. Vaidyanathan, "Hybrid convolutional beamspace for DOA estimation of millimeter wave sources," in Asilomar Conf. on Signal, Syst., Comput., 2023, pp. 86-90. (Link)
▶ P.-C. Chen and P. P. Vaidyanathan, "Channel estimation for mmWave using the convolutional beamspace approach," in IEEE Trans. Signal Process, 2024 (to appear).