Interference alignment in the K-user MIMO interference channel with constant channel coefficients is considered. A novel constructive method for finding the interference alignment solution is proposed for the case where the number of transmit antennas equals the number of receive antennas (NT = NR = N ), the number of transmitter-receiver pairs equals K = N + 1, and all interference alignment multiplexing gains are one. The core of the method consists of solving an eigenvalue problem that incorporates the channel matrices of all interfering links. This procedure provides insight into the feasibility of signal vector spaces alignment schemes in finite dimensional MIMO interference channels.
Spatial interference alignment among a finite number of users is investigated as a technique to increase the probability of successful transmission in an interference limited clustered wireless ad hoc network. Using techniques from stochastic geometry, we build on the work of Ganti and Haenggi dealing with Poisson cluster processes with a fixed number of cluster points and provide a numerically integrable expression for the outage probability using an intra-cluster interference alignment strategy with multiplexing gain one. For a special network setting we derive a closed-form upper bound. We demonstrate significant performance gains compared to single-antenna systems without local cooperation.
Spatial interference alignment among a cluster of base stations is considered as a technique to mitigate inter-cell interference in the downlink of a large cellular network using OFDMA. We derive an expression for the mutual information achieved by clustered base station cooperation together with a zero-forcing receiver. Numerical performance results with throughput gains of up to 30% with respect to the noncooperating base stations case are demonstrated for users located in the central area of the cells. Those results provide insight into the applicability of interference alignment methods in upcoming cellular networks.
I. INTRODUCTIONInterference alignment was first considered in [1] as a coding technique for the two-user Multiple-Input MultipleOutput (MIMO) X channel, where it was shown to achieve multiplexing gains strictly higher than that of the embedded MIMO interference channel (IC), multiple-access channel (MAC), and broadcast channel (BC) taken separately. While requiring perfect channel knowledge, this coding technique is based only on linear precoding at the transmitters and zeroforcing at the receivers. The degrees of freedom region for the X channel was analyzed in [2] for an arbitrary number of antennas per user. This transmission technique was later generalized to the K-user interference channel [3], where it was shown to achieve almost surely a sum-rate multiplexing gain of K 2 per time, frequency and antenna dimension. In comparison, independent operation of K isolated point-topoint links would incur a sum-rate multiplexing gain of K per dimension. This indicates that interference alignment allows virtually interference-free communications at the cost of each user exploiting only half of the available degrees of freedom. Thanks to the alignment of all interfering signals in the same subspace from the point of view of all receivers simultaneously, interference can be removed simply through zero-forcing filtering.In [3], an explicit formulation of the precoding vectors achieving interference alignment is presented for singleantenna nodes with time-varying channels. In the multipleantenna case, no such closed-form solution is known, although achievability results on multiplexing gains are available. In [4], an inner bound and an outer bound on the total number of degrees of freedom for the MIMO case are presented. Achievability results on the total number of achievable degrees of freedom are also presented in [5]. An iterative algorithm was introduced in [6] to find numerically the precoding matrices
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