Interference Alignment under Training and Feedback Constraints

We consider the \emph{effective} degrees of freedom (DoF) achieved by interference alignment when channel state information (CSI) is acquired by training and feedback. For a flat block-fading $K\times K$ interference channel with power $P$ per transmitter and $M$ antennas per node, we show that interference alignment achieves higher DoF than orthogonal transmission (e.g., TDMA) only if the channel coherence time is large and the capacity of feedback link is at least as $\Theta(\log P)$. Under this condition, to maximize the effective DoF, each receiver needs to feed back CSI via $(M^2- 1)\log P$ bits per coherence interval; smaller growth rate of feedback bits will decrease the effective DoF. We also show that in the presence of training and feedback cost, $K=3$ achieves the optimal DoF for a broad range of channel characteristics; with larger number of user pairs, the DoF falls short of its optimum and beyond a certain point becomes a decreasing function of $K$.