Multi-layer Interference Alignment and GDoF of the K-User Asymmetric Interference Channel

In wireless networks, link strengths are often affected by some topological factors such as propagation path loss, shadowing and inter-cell interference. Thus, different users in the network might experience different link strengths. In this work we consider a K-user asymmetric interference channel, where the channel gains of the links connected to Receiver k are scaled with P^{\alpha_k /2}}, k=1,2,...,K, for 0< \alpha_1 \leq \alpha_2 \leq \cdots \leq \alpha_K \leq 1. For this setting, we show that the optimal sum generalized degrees-of-freedom (GDoF) is characterized as dsum = (\sum_{k=1}^K \alpha_k + \alpha_K -\alpha_{K-1})/2, which matches the existing result dsum= K/2 when \alpha_1 = \alpha_2 = ... = \alpha_K =1. The achievability is based on multi-layer interference alignment, where different interference alignment sub-schemes are designed in different layers associated with specific power levels, and successive decoding is applied at the receivers. While the converse for the symmetric case only requires bounding the sum degrees-of-freedom (DoF) for selected two users, the converse for this asymmetric case involves bounding the weighted sum GDoF for selected J+2 users, with corresponding weights (2^{J}, 2^{J-1}, ... , 2^{2}, 2^{1}), a geometric sequence with common ratio 2, for the first J users and with corresponding weights (1, 1) for the last two users, for J \in {1,2, ... , \lceil\log (K/2)\rceil }