In a lattice-reduction-aided receiver based wireless communications system, soft estimates of transmitted bit values are determined from a received signal by applying lattice reduction to the channel estimate and equalising the received signal in accordance with the reduced basis channel, and determining probabilities of transmitted bits having particular values by generating a set of candidate vectors in the reduced basis based on nearest candidate vectors, determining a corresponding transmitted symbol vector for each candidate vector and, on the basis of the received signal determining the probability of each transmitted bit value having been transmitted.