Near-Field Sparse Channel Representation and Estimation in 6G Wireless Communications

The employment of extremely large antenna arrays and high-frequency signaling makes future 6G wireless communications likely to operate in the near-field region. In this case, the spherical wave assumption which takes into account both the user angle and distance is more accurate than the conventional planar one that is only related to the user angle. Therefore, the conventional planar wave based far-field channel model as well as its associated estimation algorithms need to be reconsidered. Here we first propose a distance-parameterized angular-domain sparse model to represent the near-field channel. In this model, the user distance is included in the dictionary as an unknown parameter, so that the number of dictionary columns depends only on the angular space division. This is different from the existing polar-domain near-field channel model where the dictionary is constructed on an angle-distance two-dimensional (2D) space. Next, using this model, joint dictionary learning and sparse recovery based channel estimation methods are proposed for both line of sight (LoS) and multi-path settings. To further demonstrate the effectiveness of the suggested algorithms, recovery conditions and computational complexity are studied. Our analysis shows that with the decrease of distance estimation error in the dictionary, the support set of the angular-domain sparse vector can be exactly recovered under certain Restricted Isometry Property (RIP) based conditions. The high storage burden and dictionary coherence issues that arise in the polar-domain 2D representation are also well addressed. Finally, simulations in multi-user communication scenarios support the superiority of the proposed near-field channel sparse representation and estimation over the existing polar-domain method in channel estimation error.