Low-Cost Beamforming and DOA Estimation Based on One-Bit Reconfigurable Intelligent Surface

This letter provides new insights into the minimum mean square error (MMSE)-based frequency-invariant beam former with the uniform circular array (FIB-UCA). By exploiting the symmetry of the UCA, we derive an explicit form of the white noise gain (WNG), the directivity factor (DF) and the MSE, and also derive the corresponding approximate expressions at low frequencies. We then investigate the impact of the look direction on the performance of the MMSE-based FIB-UCA. Interestingly, we further prove that fora UCA with the fixed aperture, the MMSE-based FIB with 2 N microphones achieves a similar WNG as that with 4 N microphones at low frequencies if the Nth-order beampattern is steered to microphone angles. We also derive a unified explicit form of weighting vector and reveal that the MMSE-based FIB-UCA reduces to the Jacobi-Anger expansion-based differential beam former with the UCA at low frequencies.