In this thesis, we study wireless multiuser communication systems in the regime of low spectral efficiencies, where users and the multiple access point are equipped with antenna arrays. Our first contribution is to develop a generic mathematical framework which captures tradeoffs between fundamental parameters of a low power multiuser system: spectral efficiency and energy per information bit, of each user. Using the framework that we developed we next consider variable data rate multiple access problem, in low power systems, where we remove the usual assumption of tight user coordination, and we allow users to select their own data rates and trans mit powers, without coordinating, and without negotiating with the access point. Here, every user has a set of low power codebooks, that we name the policy, which accommodates a range of small spectral efficiencies, but particular data rates of other users are assumed to be an unknown---compound parameter---at each mobile. In antenna-array transmission and reception, we demonstrate an elegant interpretation of users policies, where each policy is represented by partitioning spatial dimensions into blocks, and each block is dedicated to a different user. Finally, we address the paradigm of statistically correlated antenna arrays, where we derive the effective number of uncorrelated receive spatial dimensions, which we partition to represent users policies. As more correlated antennas are packed into a limited area we show that effective receive dimensionality converges to a finite limit which we evaluate for some simple geometries.