Cramér-Rao Bounds for Holographic Positioning

Multiple antennas arrays play a key role in wireless networks for communications but also for localization and sensing applications. The use of large antenna arrays at high carrier frequencies (in the mmWave range) pushes towards a propagation regime in which the wavefront is no longer plane but spherical. This allows to infer the position and orientation of a transmitting source from the received signal without the need of using multiple anchor nodes, located in known positions. To understand the fundamental limits of large antenna arrays for localization, this paper combines wave propagation theory with estimation theory, and computes the Cram\'er-Rao Bound (CRB) for the estimation of the source position on the basis of the three Cartesian components of the electric field, observed over a rectangular surface area. The problem is referred to as holographic positioning and is formulated by taking into account the radiation angular pattern of the transmitting source, which is typically ignored in standard signal processing models. We assume that the source is a Hertzian dipole, and address the holographic positioning problem in both cases, that is, with and without a priori knowledge of its orientation. To simplify the analysis and gain further insights, we also consider the case in which the dipole is located on the line perpendicular to the surface center. Numerical and asymptotic results are given to quantify the CRBs, and to quantify the effect of various system parameters on the ultimate estimation accuracy. It turns out that surfaces of practical size may guarantee a centimeter-level accuracy in the mmWave bands.

Wavenumber-Division Multiplexing in Line-of-Sight Holographic MIMO Communications

The ultimate performance of any wireless communication system is limited by electromagnetic principles and mechanisms. Motivated by this, we start from the first principles of wave propagation and consider a multiple-input multiple-output (MIMO) representation of a communication system between two spatially-continuous volumes of arbitrary shape and position. This is the concept of holographic MIMO communications. The analysis takes into account the electromagnetic noise field, generated by external sources, and the constraint on the physical radiated power. The electromagnetic MIMO model is particularized for a system with parallel linear sources and receivers in line-of-sight conditions. Inspired by orthogonal-frequency division-multiplexing, we assume that the spatially-continuous transmit currents and received fields are represented using the Fourier basis functions. In doing so, a wavenumber-division multiplexing (WDM) scheme is obtained whose properties are studied with the conventional tools of linear systems theory. Particularly, the interplay among the different system parameters (e.g., transmission range, wavelength, and sizes of source and receiver) in terms of number of communication modes and level of interference is studied. Due to the non-finite support of the electromagnetic channel, we prove that the interference-free condition can only be achieved when the receiver size grows to infinity. The spectral efficiency of WDM is evaluated via the singular-value decomposition architecture with water-filling and compared to that of a simplified architecture, which uses linear processing at the receiver and suboptimal power allocation.