The finite-state Markov channel (FSMC) is a discrete time-varying channel whose variation is determined by a finite-state Markov process. These channels have memory due to the Markov channel variation. We obtain the FSMC capacity as a function of the conditional channel state probability. We also show that for i.i.d. channel inputs, this conditional probability converges weakly, and the channel's mutual information is then a closed-form continuous function of the input distribution. We next consider coding for FSMCs. In general, the complexity of maximum-likelihood decoding grows exponentially with the channel memory length. Therefore, in practice, interleaving and memoryless channel codes are used. This technique results in some performance loss relative to the inherent capacity of channels with memory. We propose a maximum-likelihood decision-feedback decoder with complexity that is independent of the channel memory. We calculate the capacity and cutoff rate of our technique, and show that it preserves the capacity of certain FSMCs. We also compare the performance of the decision-feedback decoder with that of interleaving and memoryless channel coding on a fading channel with 4PSK modulation.

Capacity, mutual information, and coding for finite-state Markov channels

Two open-loop algorithms are developed for estimating jointly frequency offset and symbol timing of a linearly modulated waveform transmitted through a frequency-flat fading channel. The methods exploit the received signal's second-order cyclostationarity and, with respect to existing solutions: (1) they take into account the presence of time-selective fading effects; (2) they do not need training data; (3) they do not rely on the Gaussian assumption of the complex equivalent low-pass channel process; and (4) they are tolerant to additive stationary noise of any color or distribution. Performance analysis of the proposed methods using Monte Carlo simulations, unifications, and comparisons with existing approaches are also reported.

https://www.dtc.umn.edu/s/resources/comoff~1.pdf

Frequency offset and symbol timing recovery in flat-fading channels: a cyclostationary approach

In this paper, decision-feedback differential detection (DF-DD) of M-ary differential phase-shift keying (MDPSK) signals, which has been introduced previously for the additive white Gaussian noise (AWGN) channel by Leib et al. (1988) and Edbauer (1992), is extended to flat Rayleigh fading channels. The corresponding DF-DD metric is derived from the multiple-symbol detection (MSD) metric and for genie-aided DF-DD, an exact expression for the bit-error rate (BER) of QDPSK (M=4) is calculated. Furthermore, the dependence of BER on the power spectrum of the fading process is investigated for feedback filters of infinite order. It is shown that in this case, for ideally bandlimited fading processes, the error floor of conventional differential detection (DD) can be removed entirely. Simulation results confirm that both MSD and DF-DD with feedback filters of finite order can reduce the error floor of conventional DD significantly. DF-DD thereby causes considerably less computational load.

Decision-feedback differential detection of MDPSK for flat Rayleigh fading channels

The problem of maximum likelihood (ML) detection for uncoded and coded M-PSK signals on Rayleigh fading channels is investigated. It is shown that, if the received signal is sampled at baud-rate, a ML receiver employing per-survivor processing can be implemented. The error rate performance of this receiver is evaluated by means of computer simulations and its limitations are discussed. In addition, it is shown that, on a fast fading channel, the error floor in the BER curve can be appreciably lowered if more than one received signal sample per symbol interval is processed by the receiver algorithm, Finally, a sub-optimum two-stage receiver structure for interleaved coded PSK systems is proposed. Its error rate performance is assessed for simple trellis-coded modulation schemes and compared to that provided by other receiver structures.

Maximum likelihood decoding of uncoded and coded PSK signal sequences transmitted over Rayleigh flat-fading channels

Novel coherent detectors for DQPSK and /spl pi//4-DQPSK on Rayleigh fading channels are presented. The detectors are based on decision feedback and minimum mean-square error (MMSE) channel estimation. The proposed detectors may be used in both single carrier and multicarrier systems. Analytical results in the form of expressions for channel estimation error variance and bit error probability, both with and without diversity, are derived. The MMSE-based detector has a significantly lower irreducible bit error probability floor compared to a conventional differential detector. For most practical applications, the error floor of the MMSE-based detector is negligible. Simulated results are presented to verify the analysis and justify the approximations made.

Decision-directed coherent detection in multicarrier systems on Rayleigh fading channels

The paper develops a receiver structure for random Gaussian signals in additive noise based on the classic maximum likelihood (M-L), estimator-correlator derivation of Kailath [1960], and applies it to differential phase shift keying (DPSK) on the correlated Rayleigh-fading channel. It is shown to lower the error floor found in the performance of conventional DPSK receivers by orders of magnitude. In addition, the maximum-likelihood procedure is shown to make uncorrelated symbol decisions. The performance of both conventional and optimal receivers, which require knowledge of the channel statistics, is examined analytically. A recursive, channel-adaptive version of the optimal receiver, utilizing decision feedback to estimate the channel statistics, is developed. Its simulated performance shows no penalty compared to theoretical calculations which require explicit knowledge of the channel statistics. >

Wayne C. Dam

Papers

An adaptive maximum likelihood receiver for correlated Rayleigh-fading channels

An adaptive maximum likelihood receiver for correlated Rayleigh fading channels