An Efficient Spatial Covariance Matrix Reconstruction Algorithm in the Hybrid Analog-Digital Structure

The use of the emerging hybrid analog-digital structure for future millimeter-wave communications has attracted much attention. Although this structure can reduce the power consumption considerably, the spatial covariance matrix (SCM), as the core of subspace-based direction of arrival (DOA) estimation algorithms, cannot be obtained directly. The beam sweeping algorithm (BSA) was proposed for SCM reconstruction from compressed measurements. However, the BSA is computationally intensive owing to the high-dimensional matrix-to-matrix multiplication and matrix inversion. To address this issue, a BSA algorithm with high accuracy and low computational-cost using the submatrix multiplication (BSASM) is proposed in this paper. By appropriately adjusting the weight, which consists of a switch and a phase shifter, connected to each antenna, the SCM can be accurately reconstructed with low-dimensional matrix-to-vector multiplication and 2-dimensional matrix inversion, thus reducing the computational-cost significantly. After SCM reconstruction, various DOA estimation algorithms can be exploited to obtain the DOA information. Simulation experiments are conducted to verify the performance of the proposed algorithm. The results indicate that using a substantially lower computational-cost, BSASM can reconstruct SCM more accurately than BSA.