This paper considers the coded OFDM system and instead of discarding the cyclic prefix (CP) at the receiver, we utilize the CP observation for joint detection, decoding and channel estimation. In particular, detection and decoding are performed iteratively between an equalizer and a soft-input soft-output (SISO) decoder based on the turbo principle, and the expectation-maximization (EM) algorithm is employed in the equalizer for joint detection and channel estimation via message passing. Models for the CP observation, non-CP observation and the time correlation of the time-varying channel are presented in Forney-style factor graphs (FFGs), and a scheduling scheme is proposed to pass messages between the graphs. Simulation results show that with unknown channel impulse response (CIR), the performance of the proposed algorithm approaches the case where CIR is perfectly known and through proper exploitation of the CP, the proposed algorithm outperforms the conventional algorithm (i.e. CP is discarded) with known CIR, as well as the alternative algorithm in the literature (where CP is exploited) with unknown CIR.

This paper investigates the MMSE-based frequency domain equalization (FDE) algorithms in turbo equalization systems. As opposed to the conventional FDE systems where the cyclic prefix (CP) is discarded at the receiver, we take advantage of the redundancy and make use of all the observed signals for equalization purpose. First, we interpret the conventional frequency domain equalizer as a Forney-style factor graph (FFG), and accordingly an equalization algorithm is derived based on the Gaussian message passing (GMP) technique. Second, the normally discarded CP part is presented similarly using an FFG, and an algorithm that integrates both of the FFGs is proposed. As a result, two extrinsic messages about the data symbols are obtained rather than one, and they are merged together based on a symbol-wise combination. Third, with approximations made on two covariance matrices, the complexity of the proposed equalization algorithm is maintained at the same order as that of the conventional FDE algorithm, i.e. O(Nlog2N) per block per iteration. Simulations results verify that, a gain of around 0.7dB is achieved compared with the conventional algorithm at 1/4 CP ratio, for both 16QAM and 64QAM system with Gray mapping over AWGN or ISI channels.

In OFDM systems, cyclic prefix (CP) insertion and removal enables the use of a set of computationally efficient single-tap equalizers at the receiver. Due to the extra transmission time and energy, the CP causes a loss in both spectrum efficiency and power efficiency. On the other hand, as a repetition of part of the data, the CP brings extra information and can be exploited for detection. Therefore, instead of discarding the CP observation as in the conventional OFDM system, we utilize all the received signals in a soft-input soft-output equalizer of a turbo equalization OFDM system. First, the models for both the CP part and the non-CP part of observation are presented in a Forney-style factor graph (FFG). Then based on the computation rules of the FFG and the Gaussian message passing (GMP) technique, we develop an equalization algorithm. With proper approximation, the complexity of the proposed algorithm is reduced to \changedmathcal O(2RNlog2N+4RGlog2G+2RG) per data block for R iterations, where N is the length of the data block and G is equal to P+L-1 with P the length of the CP and L the maximum delay spread of the channel. To justify the performance improvement, SNR analysis is provided. Simulation results show that the proposed approach achieves a significant gain over the conventional approach and the turbo equalization system converges within two iterations.