Channel Diversity needed for Vector Space Interference Alignment
Abstract
We consider vector space interference alignment strategies over the $K$user interference channel and derive an upper bound on the achievable degrees of freedom as a function of the channel diversity $L$, where the channel diversity is modeled by $L$ realvalued parallel channels with coefficients drawn from a nondegenerate joint distribution. The seminal work of Cadambe and Jafar shows that when $L$ is unbounded, vector space interference alignment can achieve $1/2$ degrees of freedom per user independent of the number of users $K$. However wireless channels have limited diversity in practice, dictated by their coherence time and bandwidth, and an important question is the number of degrees of freedom achievable at finite $L$. When $K=3$ and if $L$ is finite, Bresler et al show that the number of degrees of freedom achievable with vector space interference alignment is bounded away from $1/2$, and the gap decreases inversely proportional to $L$. In this paper, we show that when $K\geq4$, the gap is significantly larger. In particular, the gap to the optimal $1/2$ degrees of freedom per user can decrease at most like $1/\sqrt{L}$, and when $L$ is smaller than the order of $2^{(K2)(K3)}$, it decays at most like $1/\sqrt[4]{L}$.
 Publication:

arXiv eprints
 Pub Date:
 February 2014
 arXiv:
 arXiv:1402.5326
 Bibcode:
 2014arXiv1402.5326L
 Keywords:

 Computer Science  Information Theory
 EPrint:
 22 pages, 4 figures. Presented in part at the IEEE International Symposium on Information Theory, Honolulu, USA, June 2014. Published in IEEE Transactions on Information Theory (Volume: 62, Issue: 4, April 2016)