Maximum-likelihood detection in the presence of interference

We study maximum-likelihood (ML) sequence estimation in interference through a direct derivation of the likelihood function, and using the expectation-maximization (EM) algorithm. It is seen that, irrespective of the interference statistics, the likelihood function is composed of two parts: the first, which has the same form as for a purely additive white Gaussian noise (AWGN) channel, operates only on the signal component in the null-space of the interference; the second part depends on the statistics of the interference and operates on the signal part which is in the space of interference.