Hybrid Channel Estimation with Quantized Phase Feedback for Over-the-Air Computation

To reduce the signaling overhead of over-the-air computation, a hybrid channel estimation scheme is proposed, where reciprocity-based and feedback-based channel estimation are combined. In particular, the impact of quantized phase-feedback is studied while the amplitude is assumed estimated exactly. The scheme enables selecting the estimation precision of amplitude and phase separately, depending on the importance of each. Two variants of the scheme are proposed: As shown through simulations and theory, the second variant with reciprocity-based estimation of the channel phase, and optimal quantization of phase feedback, can outperform the first variant estimating the phase by feedback only.