Interference Alignment in a Poisson Field of MIMO Femtocells

The need for bandwidth and the incitation to reduce power consumption lead to the reduction of cell size in wireless networks. This allows reducing the distance between a user and the base station, thus increasing the capacity. A relatively inexpensive way of deploying small-cell networks is to use femtocells. However, the reduction in cell size causes problems for coordination and network deployment, especially due to the intra- and cross-tier interference. In this paper, we consider a two-tier multiple-input multiple-output (MIMO) network in the downlink, where a single macrocell base station with multiple transmit antennas coexists with multiple closed-access MIMO femtocells. With multiple receive antennas at both the macrocell and femtocell users, we propose an opportunistic interference alignment scheme to design the transmit and receive beamformers in order to mitigate intra- (or inter-) and cross-tier interference. Moreover, to reduce the number of macrocell and femtocell users coexisting in the same spectrum, we apply a random spectrum allocation on top of the opportunistic interference alignment. Using stochastic geometry, we analyze the proposed scheme in terms of the distribution of a received signal-to-interference-plus-noise ratio, spatial average capacity, network throughput, and energy efficiency. In the presence of imperfect channel state information, we further quantify the performance loss in spatial average capacity. Numerical results show the effectiveness of our proposed scheme in improving the performance of random MIMO femtocell networks.