Degrees of Freedom of Certain Interference Alignment Schemes with Distributed CSIT

In this work, we consider the use of interference alignment (IA) in a MIMO interference channel (IC) under the assumption that each transmitter (TX) has access to channel state information (CSI) that generally differs from that available to other TXs. This setting is referred to as distributed CSIT. In a setting where CSI accuracy is controlled by a set of power exponents, we show that in the static 3-user MIMO square IC, the number of degrees-of-freedom (DoF) that can be achieved with distributed CSIT is at least equal to the DoF achieved with the worst accuracy taken across the TXs and across the interfering links. We conjecture further that this represents exactly the DoF achieved. This result is in strong contrast with the centralized CSIT configuration usually studied (where all the TXs share the same, possibly imperfect, channel estimate) for which it was shown that the DoF achieved at receiver (RX) i is solely limited by the quality of its own feedback. This shows the critical impact of CSI discrepancies between the TXs, and highlights the price paid by distributed precoding.Comment: This is an extended version of a conference submission which will be presented at the IEEE conference SPAWC, Darmstadt, June 201

Large System Analysis of Linear Precoding in Correlated MISO Broadcast Channels under Limited Feedback

In this paper, we study the sum rate performance of zero-forcing (ZF) and regularized ZF (RZF) precoding in large MISO broadcast systems under the assumptions of imperfect channel state information at the transmitter and per-user channel transmit correlation. Our analysis assumes that the number of transmit antennas $M$ and the number of single-antenna users $K$ are large while their ratio remains bounded. We derive deterministic approximations of the empirical signal-to-interference plus noise ratio (SINR) at the receivers, which are tight as $M,K\to\infty$. In the course of this derivation, the per-user channel correlation model requires the development of a novel deterministic equivalent of the empirical Stieltjes transform of large dimensional random matrices with generalized variance profile. The deterministic SINR approximations enable us to solve various practical optimization problems. Under sum rate maximization, we derive (i) for RZF the optimal regularization parameter, (ii) for ZF the optimal number of users, (iii) for ZF and RZF the optimal power allocation scheme and (iv) the optimal amount of feedback in large FDD/TDD multi-user systems. Numerical simulations suggest that the deterministic approximations are accurate even for small $M,K$.Comment: submitted to IEEE Transactions on Information Theor