Channel Estimation for Dense Array Systems via Ice-Filling

By deploying a large number of antennas with sub-half-wavelength spacing in a compact space, dense array systems (DASs) can fully unleash the multiplexing and diversity gains of limited apertures. To acquire these gains, accurate channel estimation is necessary but challenging due to the large antenna numbers. To overcome this obstacle, this paper reveals that a well-designed observation matrix, that exploits the high spatial correlation of DAS channels, is crucial for realizing near-optimal channel estimation. To materialize this vision, we propose to design the observation matrix by maximizing the mutual information between received pilots and channels. An ice-filling algorithm is proposed to solve the formulated problem. Its key idea is to properly assign the observation vectors with the eigenvectors of the channel covariance matrix in a greedy manner. Theoretical analysis reveals that the proposed algorithm is equivalently a quantized version of the water-filling principle, which guarantees its near-optimal channel estimation performance. Finally, numerical results confirm that our proposed designs outperform existing channel estimation methods significantly.