A method and an apparatus for estimating likelihood values for signals of a sequence of signals transmitted from a transmitter through a channel to a receiver. The method employs a plurality of particles, each particle having a postulated transmitted signal history, and includes initializing a set of particles, evolving the set of particles over time to generate a succession of evolved sets of particles, tracing a plurality of paths through the succession of evolved sets of particles backwards in time, and determining a sequence of likelihood values for the transmitted sequence of signals using the paths. Communication systems in which a receiver receives signals from a transmitter with a plurality of transmit antennas, such as MIMO (Multiple-Input Multiple-Output) systems are able to use this method.