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 strengths. this work we consider a K-user asymmetric interference channel, where channel gains of links connected to Receiver k scaled with √{P αk }, k=1,2, ..., K, for 0 <; α 1 ≤ xmlns:xlink="http://www.w3.org/1999/xlink">2 ...≤ xmlns:xlink="http://www.w3.org/1999/xlink">K . For setting, show that optimal sum generalized degrees-of-freedom (GDoF) is characterized d xmlns:xlink="http://www.w3.org/1999/xlink">sum = Σ xmlns:xlink="http://www.w3.org/1999/xlink">k=1 xmlns:xlink="http://www.w3.org/1999/xlink">K xmlns:xlink="http://www.w3.org/1999/xlink">k + -α xmlns:xlink="http://www.w3.org/1999/xlink">K-1 /2 which matches existing result K/2 when ... 1. The achievability based on multi-layer alignment, alignment sub-schemes designed layers associated specific power levels, successive decoding applied at receivers. While converse symmetric case only requires bounding (DoF) selected two users, involves weighted GDoF J+2 corresponding weights (2 xmlns:xlink="http://www.w3.org/1999/xlink">J , 2 xmlns:xlink="http://www.w3.org/1999/xlink">J-1 xmlns:xlink="http://www.w3.org/1999/xlink">2 xmlns:xlink="http://www.w3.org/1999/xlink">1 ), geometric sequence common ratio 2, first J (1, 1) last ∈ {1,2, [log K/2]}.