Connection between ML estimation of output labels of SIMO channels and clustering algorithms

We investigate the connection between maximum likelihood (ML) estimation of output labels of a single input multiple output (SIMO) vector channel and clustering algorithms. We demonstrate that suppressing the system dynamics as captured by the state transition diagram of the vector Markov source, the approximations of the ML estimator of the noiseless channel outputs, leads to various forms of clustering algorithms and we propose modifications of the LBG algorithm for their solution. It is shown that more complex forms of LBG type algorithm result by using more refined approximations in the expression of the ML estimator of the noiseless channel output vectors. The development is based on the polyphase decomposition of the output sequences of the SIMO channel. Such a decomposition allows for an easy description of the system dynamics as transitions between phases. Subsequently this information, in addition to the embedded algebraic structure of the outputs inherited from the input, allows the development an efficient clustering algorithm that can be used for the estimation of the noiseless channel output labels and the construction of the state transition diagram of the underlying vector Markov source. After such labelling, standard Viterbi decoding can be used for data detection.