Sparse Channel Estimation for Pixel Antennas: Addressing the Pilot Rank Deficiency

Composed of multiple interconnected pixels controlled by on/off RF switches, the pixel antenna can generate reconfigurable radiation patterns that can be further exploited to construct diverse pilot sequences for effective channel estimation. However, such pilot sequences inherently have rank deficiency, making it difficult to effectively and efficiently acquire the full channel state information (CSI) across all available radiation patterns. To tackle this difficulty, we consider a sparse environment with a limited number of propagation paths for a pixel antenna system, where a user equipped with a pixel antenna transmits only a limited number of pilots to recover the CSI under all radiation patterns. The proposed algorithm exploits the limited number of propagation paths that are invariant with the pixel antenna patterns, and then formulates the full channel estimation as a sparse recovery problem in the angular domain solved by Generalized Approximate Message Passing (GAMP). Moreover, to mitigate the rank deficiency of pilot sequences, we additionally incorporate a Multipath Matching Pursuit (MMP) algorithm for robust initialization. The overall proposed scheme, termed MMP-GAMP, achieves higher estimation accuracy than other algorithm baselines, while requiring lower pilot overhead.