App equalization for non-ideal channel knowledge

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We study the problem of a-posteriori probability (APP) detection for data transmission over an inter-symbol interference (ISI) channel when the (possibly time-varying) channel impulse response (CIR) is not known precisely. Standard detection (or equalizatian) algorithms assume perfect knowledge of the CIR, even when it is only estimated by another entity, the channel estimator. We rederive the APP detection algorithm while modelling the errors made by the estimator as additive Gaussian noise and iden- tify conditions for which the resulting APP rules are simple to implement. Many practical communication systems encounter the problem of data transmission over an IS1 channel whose possibly time-varying CIR is not known to the receiver. A standard solution for this problem is to use separate entities for the basic tasks estimation (of the CIR and other channel parameters) and equalization or detection (retrieve the transmitted data), which opposes optimal (but typically highly complex) techniques performing the two tasks jointly. We discuss in this work the impact of non-ideal knowledge of the CIR on the common symbol- based APP equalization algorithm (l, 21. In our system setup, the estimation task is not treated jointly with equalization but merely the statistics of the estimation er- ror are incorporated. A detailed derivation of the result- ing APP rule and that of linear equalization techniques is presented in (3), which includes possible applications such as a framework for suboptimal joint estimation and equalization within iterative equalization and decoding (2). Here, we investigate when the APP rule stated in (3) is simple to implement using a trellis.