On the Degrees of Freedom and Eigenfunctions of Line-of-Sight Holographic MIMO Communications

We consider a line-of-sight communication link between two holographic surfaces (HoloSs). We provide a closed-form expression for the number of effective degrees of freedom (eDoF), i.e., the number of orthogonal communication modes that can be established between the HoloSs. The framework can be applied to general network deployments beyond the widely studied paraxial setting. This is obtained by utilizing a quartic approximation for the wavefront of the electromagnetic waves, and by proving that the number of eDoF corresponds to an instance of Landau's eigenvalue problem applied to a bandlimited kernel determined by the quartic approximation of the wavefront. The proposed approach overcomes the limitations of the widely utilized parabolic approximation for the wavefront, which provides inaccurate estimates in non-paraxial deployments. We specialize the framework to typical network deployments, and provide analytical expressions for the optimal, according to Kolmogorov's $N$-width criterion, basis functions (communication waveforms) for optimal data encoding and decoding. With the aid of numerical analysis, we validate the accuracy of the closed-form expressions for the number of eDoF and waveforms.

A Bayesian Compressive Sensing Approach to Robust Near-Field Antenna Characterization

A novel probabilistic sparsity-promoting method for robust near-field (NF) antenna characterization is proposed. It leverages on the measurements-by-design (MebD) paradigm and it exploits some a-priori information on the antenna under test (AUT) to generate an over-complete representation basis. Accordingly, the problem at hand is reformulated in a compressive sensing (CS) framework as the retrieval of a maximally-sparse distribution (with respect to the overcomplete basis) from a reduced set of measured data and then it is solved by means of a Bayesian strategy. Representative numerical results are presented to, also comparatively, assess the effectiveness of the proposed approach in reducing the "burden/cost" of the acquisition process as well as to mitigate (possible) truncation errors when dealing with space-constrained probing systems.