Information Theoretic Limits for Wireless Information Transfer Between Finite Spatial Regions

Abstract

Since the first multiple-input multiple-output (MIMO) experiments performed at Bell Laboratories in the late 1990’s, it was clear that wireless communication systems can achieve improved performances using multiple antennas simultaneously during transmission and reception. Theoretically, the capacity of MIMO systems scales linearly with the number of antennas in favorable propagation conditions. However, the capacity is significantly reduced when the antennas are collocated. A generalized paradigm for MIMO systems, spatially distributed MIMO systems, is proposed as a solution. Spatially distributed MIMO systems transmit information from a spatial region to another with each region occupying a large number of antennas. Hence, for a given constraint on the size of the spatial regions, evaluating the information theoretic performance limits for information transfer between regions has been a central topic of research in wireless communications. This thesis addresses this problem from a theoretical point of view. Our approach is to utilize the modal decomposition of the classical wave equation to represent the spatially distributed MIMO systems. This modal analysis is particularly useful as it advocates a shift of the “large wireless networks” research agenda from seeking “universal” performance limits to seeking a multi-parameter family of performance limits, where the key parameters, space, time and frequency are interrelated. However, traditional performance bounds on spatially distributed MIMO systems fail to depict the interrelation among space, time and frequency. Several outcomes resulting from this thesis are: i) estimation of an upper bound to degrees of freedom of broadband signals observed over finite spatial and temporal windows, ii) derivation of the amount of information that can be captured by a finite spatial region over a finite bandwidth, iii) a new framework to illustrate the relationship between Shannon’s capacity and the spatial channels, iv) a tractable model to determine the information capacity between spatial regions for narrowband transmissions. Hence, our proposed approach provides a generalized theoretical framework to characterize realistic MIMO and spatially distributed MIMO systems at different frequency bands in both narrowband and broadband conditions.