Available Degrees of Spatial Multiplexing of a Uniform Linear Array with Multiple Polarizations: a Holographic Perspective

The capabilities of multi-antenna technology have recently been significantly enhanced by the proliferation of extra large array architectures. The high dimensionality of these systems implies that communications take place in the nearfield regime, which poses some questions as to their effective perfomrance even under simple line of sight configurations. In order to study these limitations, a uniform linear array (ULA) is considered here, the elements of which are three infinitesimal dipoles transmitting different signals in the three spatial dimensions. The receiver consists of a single element with three orthogonal infinitesimal dipoles and full channel state information is assumed to be available at both ends. A capacity analysis is presented when the number of elements of the ULA increases without bound while the interelement distance converges to zero, so that the total aperture length is kept asymptotically fixed. In particular, the total number of available spatial eigenmodes is shown to depend crucially on the receiver position in space, and closed form expressions are provided for the different achievability regions. From the analysis it can be concluded that the use of three orthogonal polarizations at the transmitter guarantees the almost universal availability of two spatial streams, whereas the use of only two polarizations results in a more extensive region where maximum multiplexing gain is available.