  As Extremely Large-Scale Multiple-Input-Multiple-Output (XL-MIMO) technology
advances and carrier frequency rises, the near-field effects in communication
are intensifying. A concise and accurate near-field XL-MIMO channel model
serves as the cornerstone for investigating the near-field effects. However,
existing wave-number domain XL-MIMO channel models under near-field conditions
require non-closed-form oscillatory integrals for computation, making it
difficult to analyze the channel characteristics in closed-form. To obtain a
more succinct channel model, this paper introduces a closed-form approximate
expression based on the principle of stationary phase. It was subsequently
shown that when the scatterer distance is larger than the array aperture, the
closed-form model can be further simplified as a trapezoidal spectrum. We
validate the accuracy of the proposed approximation through simulations of
power angular spectrum similarity. The results indicate that the proposed
approximation can accurately approximate the near-field wave-number domain
channel within the effective Rayleigh distance.
