(n,K)-user Interference Channels: Degrees of Freedom

We analyze the gains of opportunistic communication in multiuser interference channels. Consider a fully connected $n$-user Gaussian interference channel. At each time instance only $K\leq n$ transmitters are allowed to be communicating with their respective receivers and the remaining $(n-K)$ transmitter-receiver pairs remain inactive. For finite $n$, if the transmitters can acquire channel state information (CSI) and if all channel gains are bounded away from zero and infinity, the seminal results on interference alignment establish that for any $K$ {\em arbitrary} active pairs the total number of spatial degrees of freedom per orthogonal time and frequency domain is $\frac{K}{2}$. Also it is noteworthy that without transmit-side CSI the interference channel becomes interference-limited and the degrees of freedom is 0. In {\em dense} networks ($n\rightarrow\infty$), however, as the size of the network increase, it becomes less likely to sustain the bounding conditions on the channel gains. By exploiting this fact, we show that when $n$ obeys certain scaling laws, by {\em opportunistically} and {\em dynamically} selecting the $K$ active pairs at each time instance, the number of degrees of freedom can exceed $\frac{K}{2}$ and in fact can be made arbitrarily close to $K$. More specifically when all transmitters and receivers are equipped with one antenna, then the network size scaling as $n\in\omega(\snr^{d(K-1)})$ is a {\em sufficient} condition for achieving $d\in[0,K]$ degrees of freedom. Moreover, achieving these degrees of freedom does not necessitate the transmitters to acquire channel state information. Hence, invoking opportunistic communication in the context of interference channels leads to achieving higher degrees of freedom that are not achievable otherwise.