Near-Field Communication (NFC) System Capacity and Effective Degrees of Freedom (EDoF)

To augment our exposition, we represent the ordered positive singular values of matrix H as σ1 ≥ ... ≥ σDoF. Miller [4] demonstrated by employing prolate spheroidal wave functions that for small values of n, the σn values fall off slowly until they reach a critical threshold, beyond which they decay rapidly. This critical threshold is termed as the 'effective degree of freedom (EDoF)', denoted as EDoF1. Moreover, this phenomenon becomes more prominent as the number of transceiving antennas increases. These findings indicate that although harnessing more antennas can lead to an increased number of independent sub-channels, only the dominant EDoF1 ones can be effectively utilized for supporting reliable communications. Furthermore, for a large number of antennas, Miller [4] concludes that the upper limit of EDoF1 is proportional to the product of transmitter and receiver areas and it is inversely proportional to the link distance. These findings are derived using the uniform spherical wave (USW) model described in [1, Eqn. (35)]. The USW model is applicable in the nearfield region, where the communication distance exceeds the uniform-power distance, exhibiting uniform channel gains and non-linear phase-shifts. However, it is important to note that as the link distance becomes comparable to the transceiver sizes (i.e., NFC within the uniform-power distance), the accuracy of the USW model and the EDoF derived in [4] diminishes. To address this, Dardari introduced a more general formula for EDoF1 based on 2D sampling theory arguments for the non-uniform spherical wave (NUSW) model of [5]. Although this formula may present tractability challenges, again, it reveals that the upper limit of EDoF1 is proportional to the product of the transmitter and receiver areas, while it is inversely proportional to the link distance. These improvements enhance our understanding of EDoF in NFC systems. In summary, the conclusions drawn from [4] and [5] suggest that the number of dominant communication modes and channel capacity can be enhanced in two primary means: increasing the aperture size and reducing the communication distance. Remarkably, these strategies align with the commonly employed techniques for supporting NFC, emphasizing the superior spatial EDoF capabilities of NFC systems.