Bayesian estimation of discrete signals with local dependencies.

Overview & Synopsis

The aim of this thesis is to study the problem of data detection in wireless communication system, for both case of perfect and imperfect channel state information at the receiver. As well known, the complexity of MLSE being exponential in the channel memory and in the symbol alphabet cardinality is quickly unmanageable and forces to resort to sub-optimal approaches. Therefore, first we propose a new iterative equalizer when the channel is unknown at the transmitter and perfectly known at the receiver. This receiver is based on continuation approach, and exploits the idea of approaching an original optimization cost function by a sequence of more tractable functions and thus reduce the receiver's computational complexity. Second, in order to data detection under linear dynamic channel, when the channel is unknown at the receiver, the receiver must be able to perform joint equalization and channel estimation. In this way, we formulate a combined state-space model representation of the communication system. By this representation, we can use the Kalman filter as the best estimator for the channel parameters. The aim in this section is to motivate rigorously the introduction of the Kalman filter in the estimation of Markov sequences through Gaussian dynamical channels. By this we interpret and make clearer the underlying approximations in the heuristic approaches. Finally, if we consider more general approach for non linear dynamic channel, we can not use the Kalman filter as the best estimator. Here, we use switching state-space model (SSSM) as non linear state-space model. This model combines the hidden Markov model (HMM) and linear state-space model (LSSM). In order to channel estimation and data detection, the expectation and maximization (EM) procedure is used as the natural approach. In this way extended Kalman filter (EKF) and particle filters are avoided.