In this work, we consider the problem of optimization of the training sequence length when a Maximum a posteriori (MAP) detector is used. We consider a transmission over a Single Input Single Output (SISO) frequency selective channel and a transmission over a Multiple-Input Multiple-Output (MIMO) flat fading channel. We study the case where a non-iterative receiver is used and the case where a turbo-detector composed of a MAP detector a MAP decoder is used. The optimal length of the training sequence is found by maximizing an effective Signal-to-Noise Ratio (SNR) taking into account the data throughput loss due to the use of pilot symbols. We then consider an Orthogonal Frequency Division Multiplexing (OFDM). We consider the case where the Frequency Division Duplexing (FDD) mode is used. We jointly optimize the power allocation and the feedback. We also propose low complexity bit loading algorithms with limited feedback for an OFDM system. We emphasize that there are two methods to return the bit allocation from the receiver to the transmitter and precise which method minimizes the number of feedback bits.
