Abstract: In this paper we study the effective degree of freedom (EDoF) for extremely large-scale multiple-input multiple-output (XL-MIMO) systems. We consider two XL-MIMO hardware designs, uniform planar array (UPA) based and continuous aperture (CAP) based XL-MIMO, as well as two representative near-field channel models: scalar Green function based and dyadic Green function with triple polarization based models. First, for UPA-based XL-MIMO with a discrete array aperture, we evaluate the EDoF performance by applying discrete channel matrices generated by the scalar or dyadic Green channel model. Then, for CAP-based XL-MIMO, a tailored EDoF performance evaluation framework for a two-dimensional (2D) CAP plane based system is constructed by leveraging asymptotic analysis and extending the analysis approaches for a one-dimensional (1D) CAP line segment based system. This framework incorporates the triple-polarized auto-correlation kernel function, which can efficiently capture the impact of multiple polarization on the EDoF performance. Numerical results show that, with an increase in the number of antennas, the UPA-based XL-MIMO system can achieve an EDoF performance close to the EDoF performance for the CAP plane based XL-MIMO system. Moreover, the EDoF performance can be enhanced by the multiple polarization in channels and increased physical size of the transceiver.

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