On the Generalized Degrees of Freedom of the MIMO Interference Channel With Delayed CSIT

Abstract

The generalized degrees of freedom (GDoF) of the two-user multiple-input multiple-output interference channel is studied under the assumption of delayed channel state information at the transmitters. In particular, with $M$ antennas at each transmitter and $N$ antennas at each receiver, and in the non-trivial case when $M>N$ (with the case of $M\leq N$ not needing any CSIT), new lower and upper bounds on the symmetric GDoF are obtained that are parameterized by $\alpha $ , which links the interference-to-noise ratio (INR) and the signal-to-noise ratio (SNR) at each receiver via $\mathrm {INR}=\mathrm {SNR}^{{\alpha }}$ . A new upper bound for the symmetric GDoF is obtained by maximizing a bound on the weighted sum rate, which in turn is obtained from a combination of genie-aided side-information and an extremal inequality. The maximum weighted sum rate in the high SNR regime is shown to occur when the transmit covariance matrix at each transmitter is full rank. An achievability scheme is developed that is based on block-Markov encoding and backward decoding, and which incorporates channel statistics through interference quantization and digital multicasting. This symmetric GDoF lower bound is maximized separately for different ranges of ${\alpha }$ , by optimizing the transmit power levels in the achievability scheme separately in the very weak $[0\leq {\alpha }\leq ({1}/{2})]$ , weak $[({1}/{2}) , and strong $({\alpha }>1)$ interference regimes. The lower and upper bounds coincide when ${\alpha }\geq [({{r}+1})/({{r}+2})]$ , where ${r}=\min (2,{M}/{N})$ , thus characterizing the symmetric GDoF completely for strong interference and a range of values of weak interference. It is also shown that treating interference as noise is strictly sub-optimal from a GDoF perspective even when the interference is very weak.