Degrees of Freedom for Distributed MIMO Communications

Multiple input multiple output (MIMO) systems have assumed great importance in recent times because of their remarkably higher capacity compared to single input single output (SISO) systems. One of the most celebrated results in this context is that the capacity of a point-to-point MIMO system withM inputs andN outputs increases linearly as min(M;N) at high SNR. For power and bandwidth limited wireless systems this opens up another dimension “space” that can be exploited in a similar way as time and frequency. Similar to time division and frequency division multiplexing, MIMO systems present the possibility of multiplexing signals in space. For example, using the singular value decomposition of a MIMO channel, one can generate parallel channels in space similar to the multiple channels created by dividing time or frequency into orthogonal slots. Inspite of the theoretical duality of time, frequency, and space, the contextual constraints of a communication system create important differences that determine whether the degrees of freedom that exist in each of these dimensions are available or not. In particular, the availability of the spatial degrees of freedom depends upon two factors: cooperation within inputs and outputs, and channel knowledge. Previous work has shown that in the absence of channel knowledge the spatial degrees of freedom are lost [1, 2]. In this paper we will focus on communication scenarios with constrained cooperation between inputs and outputs. The traditional view of MIMO systems is that of a point-to-point multiple antenna system with multiple inputs representing the collocated antennas at the transmitter and the multiple outputs representing the collocated antennas at the receiver. In this paper we take a generalized view of MIMO systems where the inputs and outputs are distributed across users. The distributed MIMO model captures most multiuser communication scenarios. While multiuser communications have always been interesting topic, there has been a recent surge of interest in this area because of the growing popularity and applications of ad-hoc and sensor networks. What makes the generalized MIMO systems especially challenging is that unlike the point-to-point case, joint processing is not possible at the inputs or the outputs controlled by different users. The available spatial degrees of freedom are affected by the inability to jointly process the signals at the distributed inputs and outputs. In this paper our goal is to quantify the loss in the available degrees of freedom under the cooperation constraints imposed by various multiuser communication scenarios.