Can Continuous Aperture MIMO Achieve Much Better Performance than Discrete MIMO?

The concept of continuous-aperture multiple-input multiple-output (CAP-MIMO) technology has been proposed recently, which aims at achieving high spectrum density by deploying extremely dense antennas or even continuous antennas in a given aperture. The fundamental question of CAP-MIMO is whether it can achieve much better performance than the traditional discrete MIMO system. In this paper, to model the CAP-MIMO, we use self-adjoint operators to depict the structural characteristics of the continuous random electromagnetic fields from physical laws. Then, we propose a non-asymptotic performance comparison scheme between continuous and discrete MIMO systems based on the analysis of mutual information. We show the consistency of the proposed scheme by proving that the mutual information between discretized transceivers converges to that between continuous transceivers. Numerical analysis verifies the theoretical results, and suggests that the mutual information obtained from the discrete MIMO with widely adopted half-wavelength spaced antennas almost achieves the mutual information obtained from CAP-MIMO.