On the impact of low-rank interference on distributed multi-agent optimization

In this paper, we study the impact of low-rank interference on the problem of optimizing a sum of convex objective functions corresponding to multiple agents. We prove that the impact of interference can mathematically be regarded as additional constraints to original unconstrained optimization. The proposed analysis uses the notion of interference alignment where the agent transmissions are aligned in either the null space or range space of interference. We consider two cases: (i) when the interference is uniquely determined by the transmitter; and, (ii) when the interference is only determined by the receiver. The former requires the null space of the interference while the latter requires the range space. Experiments on distributed source localization demonstrate good performance of our interference cancellation strategy.