Joint Single-Shot AoD/AoA Estimation in mmW Systems and Analysis under Hardware Impairments

In millimeter-wave (mmW) networks, beam training enables the base station and user to estimate the dominant angle of departure (AoD) and angle of arrival (AoA) and align their directional beams. With conventional phased arrays, the training requires an exhaustive beam sweeping (EBS), which imposes a large overhead. Alternative array architectures, including digital and true-time-delay arrays, enable simultaneous probing of different angular directions using different frequency components of the signal, which can speed up the training. In this work, we propose a beam training procedure based on frequency-dependent angle probing that uses a single Orthogonal Frequency-Division Multiplexing (OFDM) symbol to jointly estimate the AoD and AoA. We describe the design of the required training codebooks and frequency-domain power-based algorithm. Further, assuming an error-free array at the base station, we analyze how practical hardware impairments in the user's array affect the receive beamforming gain and misalignment probability in beam training. The proposed beam training is evaluated in realistic mmW channels and compared with existing beam training approaches in terms of the misalignment probability, angle estimation accuracy, required overhead, and computational complexity. The results indicate that the proposed algorithm requires a single OFDM symbol and low complexity to achieve a performance comparable to that of the EBS with arrays based on phase shifters.