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

Abstract

This paper analyzes the gains of opportunistic communication in multiuser interference channels. Consider a fully connected n-user Gaussian interference channel. At each time instance, only K≤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 the instantaneous channel realizations and if all channel gains are bounded away from zero and infinity, the seminal results on interference alignment establish that for any K arbitrary active pairs the total number of spatial degrees of freedom per orthogonal time and frequency domain is K/2. In dense networks (n → ∞), however, as the size of the network increases, 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 opportunistically and dynamically selecting the K active pairs at each time instance, the number of degrees of freedom can exceed K/2 and in fact can be made arbitrarily close to K. More specifically, for single-antenna transmitters and receivers, the network size scaling as n ∈ ω(SNR <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d⌈d-1⌉</sup> ) when power allocation is allowed and scaling as n ∈ ω(SNR <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d(K-1)</sup> ) without power allocation are sufficient conditions for achieving d ∈ [1, K] degrees of freedom. Moreover, for achieving these degrees of freedom the transmitters do not require the knowledge of the instantaneous channel realizations. Hence, invoking opportunistic communication in the context of interference channels leads to achieving higher degrees of freedom that are not achievable otherwise. We extend the results for multi-antenna Gaussian interference channels.