Single antenna interference alignment for finite relay networks

We consider a K-user interference channel where sources communicate with destinations via only one layer of relays (i.e. no direct links) and show that the interference alignment for all user pairs can be achieved using a finite number of relays. Here we assume a quasi-static channel and all nodes are equipped with a single antenna. We employ two strategies: coding at the edge and coding in the middle, in which relays play different roles. In the coding at the edge strategy, relays generate equivalent channels and we use leakage minimization and asymptotic design schemes to construct precoding matrices for all users. We unveil a novel feature of relays: generating channel randomness. In the coding in the middle strategy, relays construct time-extended gain matrices, so we propose a novel and more effective relay coding design based on a rank minimization algorithm. Both strategies successfully implement interference alignment and approach high degrees of freedom per user.