1. A demodulator for a base station receiver in a cellular communication system, said demodulator comprising: means for receiving and filtering transmitted diversity signals; a plurality of digital signal processors for executing in real time a demodulating procedure employing a multi-state maximum likelihood sequence estimator (MLSE) Process and being executable repeatedly to demodulate successive data groups in each of successive slots in a data frame; said MLSE Process having multiple calculation components including branch metric, path metric, traceback and channel estimate components that are executed in a predetermined order in each symbol to demodulate data in each data group and that are partitioned among said processors in a predetermined manner; means for data linking said processors to enable output data from predetermined components to be applied as input data to other predetermined components for time ordered calculations in accordance with the demodulation procedure; at least a first of said processors having at least one of the filtered diversity signals applied as an input thereto and having means for executing a branch metric component to make branch metric calculations therefor; and at least an output one of said processors generating a demodulated output for subsequent decoding.