DoF Analysis for Extended Coprime Arrays in Near-field Communications

In this paper, we consider a sparse array enabled near-field communication system and characterize its spatial multiplexing gain. To this end, a closed-form effective degree of freedom (EDoF) is first obtained for the sparse uniform linear array (S-ULA) and then extended to the extended coprime array (ECA). Based on the closed-form EDoF, we show that the EDoF only depends on the main-lobe of a defined effective beam pattern based on a sampling function. Specifically, given the same number of antennas and array sparsity, a narrower main-lobe generally leads to a larger EDoF. Based on this, we further show that the EDoF for the ECA is larger than that of the S-ULA and dense ULA (D-ULA), due to narrower main-lobe of the effective beam pattern. Furthermore, we characterize the channel capacity of the ECA systems based on the obtained EDoF analysis. Finally, numerical results validate the accuracy of the obtained EDoF and channel capacity.