Capacity Lower Bound for Double-Sided Correlated Extremely Large-Scale Array Systems

To explore the impact of spatial non-stationarity on the performance of extra-large scale multiple-input multiple-output (XL-MIMO) communication systems, this letter proposes a new double-sided correlated channel model based on the visibility region (VR). Based on the proposed model, the corresponding downlink ergodic capacity is investigated. We find that when the VR size remains constant, the ergodic capacity decreases as the number of transmit antennas increases. Due to the closed-form expressions for ergodic capacity being related to Laguerre polynomials, which requires numerical integration for evaluation, the closed-form lower bounds on ergodic capacity are investigated. In XL-MIMO systems, the number of transmit antennas is significantly greater than the rank of the XL-MIMO channel, and we use the theorem of principal minor determinant expansion and Binet-Cauchy theorem to obtain the closed-form lower bound on the ergodic capacity. Compared to the Monte-Carlo simulation results, the proposed lower bound is tight and suitable for application in XL-MIMO communication systems.