In this paper, through extrinsic information transfer (EXIT) band chart analysis, an adaptive iterative decoding approach (AIDA) is proposed to reduce the iterative decoding complexity and delay for finite-length differentially encoded Low-density parity-check (DE-LDPC) coded systems with multiple-symbol differential detection (MSDD). The proposed AIDA can adaptively adjust the observation window size (OWS) of the MSDD soft-input soft-output demodulator (SISOD) and the outer iteration number of the iterative decoder (consisting of the MSDD SISOD and the LDPC decoder) instead of setting fixed values for the two parameters of the considered systems. The performance of AIDA depends on its stopping criterion (SC) which is used to terminate the iterative decoding before reaching the maximum outer iteration number. Many SCs have been proposed; however, these approaches focus on turbo coded systems, and it has been proven that they do not well suit for LDPC coded systems. To solve this problem, a new SC called differential mutual information (DMI) criterion, which can track the convergence status of the iterative decoding, is proposed; it is based on tracking the difference of the output mutual information of the LDPC decoder between two consecutive outer iterations of the considered systems. AIDA using the DMI criterion can adaptively adjust the out iteration number and OWS according to the convergence situation of the iterative decoding. Simulation results show that compared with using the existing SCs, AIDA using the DMI criterion can further reduce the decoding complexity and delay, and its performance is not affected by a change in the LDPC code and transmission channel parameters.

In this paper, we propose a novel noncoherent maximum likelihood detection (NMLD) method for differential spatial multiplexing (SM) multiple-input multiple-output (MIMO) systems. Unlike the conventional maximum likelihood detection (MLD) method which needs the knowledge of channel state information (CSI) at the receiver, NMLD method has no need of CSI at either the transmitter or receiver. After repartitioning the observation block of multiple-symbol differential detection (MSDD) and following a decision feedback process, the decision metric of NMLD is derived by reforming that of MSDD. Since the maximum Doppler frequency and noise power are included in the derived decision metric, estimations of both maximum Doppler frequency and noise power are needed at the receiver for NMLD. A fast calculation algorithm (FCA) is applied to reduce the computational complexity of NMLD. The feasibility of the proposed NMLD is demonstrated by computer simulations in both slow and fast fading environments. Simulation results show that the proposed NMLD has good bit error rate (BER) performance, approaching that of the conventional coherent MLD with the extension of reference symbols interval. It is also proved that the BER performance is not sensitive to the estimation errors in maximum Doppler frequency and noise power.

In this paper, multiple-symbol differential detection (MSDD) is applied to the differential unitary space-time-frequency coding (DUSTFC) scheme over frequency selective fading multiple-input multiple-output (MIMO) channels. The motivation of applying MSDD is to compensate for the performance loss of conventional (two-symbol observation) differential detection comparing with coherent detection, by extending the observation interval and considering the fading autocorrelations. Since the differential coding of DUSTFC can be performed in time or frequency domain, both the time-domain and frequency-domain MSDD are investigated. After calculating the frequency-domain fading autocorrelation, the decision metrics of MSDD considering appropriate fading autocorrelations are derived in time and frequency domain respectively. Bit error rate (BER) performances of the two kinds of MSDD are analyzed by computer simulations. Simulation results demonstrate that a considerable performance gain can be got by applying MSDD in both cases, and the transmit diversity gain can also be enhanced by applying MSDD. So that it is proved that full advantage of transmit diversity with DUSTFC can be taken by applying MSDD.

A novel fast calculation algorithm (FCA) for calculating the decision metric of the multiple-symbol differential detection (MSDD) considering the autocorrelation of a received sequence is proposed. In correspondence to the star quadrature amplitude modulation (QAM), the M algorithm is adopted to MSDD over Rayleigh fading channels, in order to reduce the number of search paths. The computational complexity of the decision metric can be greatly reduced by the proposed FCA and the M algorithm. Through computer simulations, it is confirmed that the symbol error rate (SER) performance of the MSDD considering autocorrelation is closer to that of the ideal coherent detection as the length of an observed sequence becomes larger over Rayleigh fading channels.

We propose a novel adaptive multiple-symbol differential detection (MSDD) scheme that has excellent performance over frequency selective fading (FSF) channels. The adaptive MSDD scheme consists of an adaptive noncoherent least mean square channel estimator that can accomplish channel estimation without any decision delay and the MSDD. The M-algorithm is introduced into this detection scheme to reduce the complication of computation due to increasing observed sequence length in the MSDD. Because of the application of the adaptive channel estimator and the M-algorithm, this adaptive MSDD make it possible that channel estimation is accomplished for every symbol along M surviving paths without any decision delay. And the SER performance of this adaptive MSDD is not affected by phase fluctuation introduced by a channel because the MSDD and the noncoherent channel estimator are applied. The adaptive MSDD scheme is applied to typical constellation of 16APSK, the (4,12) QAM and the star QAM. The excellent tracking performance of this adaptive MSDD scheme over FSF channels is confirmed by computer simulations.