Degrees of Freedom of the Interference Channel with a Cognitive Helper

Abstract

In this letter, we characterize the degrees of freedom (DoF) of the K≥ 3 user Gaussian interference network with a cognitive helper where each node is equipped with a single antenna. Specifically, the users send independent messages to their corresponding receiver through their own antenna and via the help of the cognitive helper. For this network, we show that the sum DoF value is upper bounded by (K+1)/ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> when K is odd and K <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> / <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2(K+1)</sub> when K is even, respectively. While the new DoF upper bounds are simply derived based on the fact that cooperation among users does not decrease the capacity region, we provide a new achievable scheme to obtain a total of (K+1)/ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> DoF for any K≥ 3. Thus, we establish that the exact sum DoF value of the network is given as <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(K+1)</sup> /2, whenever K is odd. The new achievable scheme is based on interference neutralization and asymptotic interference alignment.