Redefining Polar Boundaries for Near-Field Channel Estimation for Ultra-Massive MIMO Antenna Array

Ultra massive multiple-input-multiple-output (UM-MIMO) technology has emerged as a promising candidate for 6G networks, offering ultra-high spectral efficiency in wireless systems. The transition to large antenna arrays specially at high-frequency bands is fundamentally transforming wireless communication from the traditional far-field to the near-field realm. This transition poses a distinct challenge in channel estimation due to the associated pilot overhead from large antenna arrays and the absence of angular sparsity in near-field spherical wavefronts. However, polar-domain sparsity remains achievable, advocating the use of polar codebooks over traditional angle-based ones. Nevertheless, the size of the polar codebook presents a significant challenge, necessitating sampling of distance and angle points across the entire near-field. In this work, we investigate the near-field channel estimation techniques while identifying the boundaries of polar domain sparsity with minimal pilot overhead. We propose a novel polar codebook, which leverages our findings from sparsity analysis and exploits the beam-focusing properties of the near-field. Unlike existing work, the proposed polar codebook design is agnostic to user range information and has considerably reduced dimensions. Capitalizing on this new polar codebook, we introduce the beam focused simultaneous orthogonal matching pursuit (BF-SOMP) algorithm for efficient near-field channel estimation. To further improve the channel estimation accuracy, we then present a refinement procedure that iterates over off-grid angle and range samples to enhance the estimation accuracy. Simulation results demonstrate that the proposed polar codebook based algorithms outperform contemporary methods in terms of improved normalized mean square error (NMSE) and reduced computational complexity. When compared to existing channel estimation methods, the proposed algorithms achieve an NMSE improvement of 6 − 7 dB at low and high SNR values with 32 pilots, while utilizing a codebook nearly half the size of existing ones.