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.

Low Complexity Optimization for Line-of-Sight RIS-Aided Holographic Communications

The synergy of metasurface-based holographic surfaces (HoloS) and reconfigurable intelligent surfaces (RIS) is considered a key aspect for future communication networks. However, the optimization of dynamic metasurfaces requires the use of numerical algorithms, for example, based on the singular value decomposition (SVD) and gradient descent methods, which are usually computationally intensive, especially when the number of elements is large. In this paper, we analyze low complexity designs for RIS-aided HoloS communication systems, in which the configurations of the HoloS transmitter and the RIS are given in a closed-form expression. We consider implementations based on diagonal and non-diagonal RISs. Over line-of-sight channels, we show that the proposed schemes provide performance that is close to that offered by complex numerical methods.

On the Degrees of Freedom of RIS-Aided Holographic MIMO Systems

In this paper, we study surface-based communication systems based on different levels of channel state information for system optimization. We analyze the system performance in terms of rate and degrees of freedom (DoF). We show that the deployment of a reconfigurable intelligent surface (RIS) results in increasing the number of DoF, by extending the near-field region. Over Rician fading channels, we show that an RIS can be efficiently optimized only based on the positions of the transmitting and receiving surfaces, while providing good performance if the Rician fading factor is not too small.