Detection of linear modulations in the presence of strong phase and frequency instabilities

Noncoherent sequence detection algorithms, previously proposed by the authors, have a performance which approaches that of coherent detectors and are robust to phase and frequency instabilities. These schemes exhibit a negligible performance loss in the presence of a frequency offset, provided this offset does not exceed an order of 1% of the signaling frequency. For higher values, the performance rapidly degrades. In this paper, detection schemes are proposed, characterized by high robustness to frequency offsets and capable of tolerating offset values up to 10% of the signaling frequency. More generally, these detection schemes are very robust to rapidly varying phase and frequency instabilities. The general case of coded linear modulations is addressed, with explicit reference to M-ary phase shift keying and quadrature amplitude modulation.     

On Pilot-Symbol-Assisted Carrier Synchronization for DVB-S2 Systems

We consider the problem of carrier synchronization in future 2nd-generation satellite digital video broadcasting (DVB-S2) receivers. In this scenario, this task is made harder by the complexity constraints, related to the use of consumer-grade equipment. Making use of the distributed pilot symbols of the DVB-S2 standard, low-complexity techniques for fine frequency estimation and for detection in the presence of a strong phase noise, typical of consumer-grade equipment, will be proposed. The performance of the described algorithms will be analysed in detail through computer simulations.     

Algorithms for iterative decoding in the presence of strong phase noise

We present two new iterative decoding algorithms for channels affected by strong phase noise and compare them with the best existing algorithms proposed in the literature. The proposed algorithms are obtained as an application of the sum-product algorithm to the factor graph representing the joint a posteriori probability mass function of the information bits given the channel output. In order to overcome the problems due to the presence in the factor graph of continuous random variables, we apply the method of canonical distributions . Several choices of canonical distributions have been considered in the literature. Well-known approaches consist of discretizing continuous variables or treating them as jointly Gaussian, thus obtaining a Kalman estimator. Our first new approach, based on the Fourier series expansion of the phase probability density function, yields better complexity/performance tradeoff with respect to the usual discretized-phase method. Our second new approach, based on the Tikhonov canonical distribution, yields near-optimal performance at very low complexity and is shown to be much more robust than the Kalman method to the placement of pilot symbols in the coded frame. We present numerical results for binary LDPC codes and LDPC-coded modulation, with particular reference to some phase-noise models and coded-modulation formats standardized in the next-generation satellite Digital Video Broadcasting (DVB-S2). These results show that our algorithms achieve near-coherent performance at very low complexity without requiring any change to the existing DVB-S2 standard.     

Linear predictive receivers for fading channels

The authors discuss maximum likelihood sequence detection (MLSD) based on prediction techniques for linearly modulated digital signals transmitted over fading channels. Efficient implementations of the sequence detector are investigated and a general formulation for computing the prediction coefficients is derived. Furthermore, the equivalence of different existing prediction-based receivers is shown     

On the cramer-rao bound for carrier frequency estimation in the presence of phase noise

We consider the carrier frequency offset estimation in a digital burst-mode satellite transmission affected by phase noise. The corresponding Cramer-Rao lower bound is analyzed for linear modulations under a Wiener phase noise model and in the hypothesis of knowledge of the transmitted data. Even if we resort to a Monte Carlo average, from a computational point of view the evaluation of the Cramer-Rao bound is very hard. We introduce a simple but very accurate approximation that allows to carry out this task in a very easy way. As it will be shown, the presence of the phase noise produces a remarkable performance degradation of. the frequency estimation accuracy. In addition, we provide asymptotic expressions of the Cramer-Rao bound, from which the effect of the phase noise and the dependence on the system parameters of the frequency offset estimation accuracy clearly result. Finally, as a by-product of our derivations and approximations, we derive a couple of estimators specifically tailored for the phase noise channel that will be compared with the classical Rife and Boorstyn algorithm, gaining in this way some important hints on the estimators to be used in this scenario     

Simplified Soft-Output Detection of CPM Signals Over Coherent and Phase Noise Channels

We consider continuous phase modulations (CPMs) in iteratively decoded serially concatenated schemes. Although the overall receiver complexity mainly depends on that of the CPM detector, almost all papers in the literature consider the optimal maximum a posteriori (MAP) symbol detection algorithm and only a few attempts have been made to design low-complexity suboptimal schemes. This problem is faced in this paper by first considering the case of an ideal coherent detection, then extending it to the more interesting case of a transmission over a typical satellite channel affected by phase noise. In both cases, we adopt a simplified representation of an M-ary CPM signal based on the principal pulses of its Laurent decomposition. Since it is not possible to derive the exact detection rule by means of a probabilistic reasoning, the framework of factor graphs (FGs) and the sum-product algorithm (SPA) is used. In the case of channels affected by phase noise, continuous random variables representing the phase samples are explicitly introduced in the FG. By pursuing the principal approach to manage continuous random variables in a FG, i.e., the canonical distribution approach, two algorithms are derived which do not require the presence of known (pilot) symbols, thanks to the intrinsic differential encoder embedded in the CPM modulator.     

Theoretical analysis and performance limits of noncoherent sequencedetection of coded PSK

A theoretical performance analysis of noncoherent sequence detection schemes previously proposed by the authors for combined detection and decoding of coded M-ary phase-shift keying (M-PSK) is presented. A method for the numerical evaluation of the pairwise error probability-for which no closed-form expressions exist-is described, the classical union bound is computed, and results are compared with computer simulations. An upper bound on this pairwise error probability is also presented. This upper bound may be effectively used for the definition of an equivalent distance, which may be useful in exhaustive searches for optimal codes. Using this bound, it is proven that, in the general coded case, the considered noncoherent decoding schemes perform as close as desired to an optimal coherent receiver when a phase memory parameter is sufficiently large. In the case of differentially encoded M-PSK, a simple expression of the asymptotic bit-error probability is derived, which is in agreement with simulations for high as well as low signal-to-noise ratio (SNR)     

On trellis-based truncated-memory detection

We propose a general framework for trellis-based detection over channels with infinite memory. A general truncation assumption enables the definition of a trellis diagram, which takes into account a considered portion of the channel memory and possible coding memory at the transmitter side. It is shown that trellis-based maximum a posteriori (MAP) symbol detection algorithms, in the form of forward-backward (FB) algorithms, can be derived on the basis of this memory-truncation assumption. A general approach to the design of truncated-memory (TM) FB algorithms is proposed, and two main classes of algorithms, characterized by coupled and decoupled recursions, respectively, are presented. The complexity of the derived TM-FB algorithms is analyzed in detail. Moreover, it is shown that MAP sequence detection algorithms, based on the Viterbi algorithm, follow easily from one of the proposed classes. Looking backward at this duality between MAP symbol detection algorithms and MAP sequence detection algorithms, it is shown that previous solutions for one case can be systematically extended to the other case. The generality of the proposed framework is shown by considering various examples of stochastic channels. New detection algorithms, as well as generalizations of solutions previously published in the literature, are embedded in the proposed framework. The obtained results do suggest that the performance of the proposed detection algorithms ultimately depends on the truncation depth, almost regardless of the specific detection strategy.     

Novel MSE adaptive control of optical PMD compensators

We describe a new effective technique for the adaptive adjustment of the control parameters of any structure of polarization-mode dispersion compensator, such as, e.g., those based on a cascade of polarization controllers and polarization-maintaining fibers. This technique is based on the mean square error between the photodetected signal and the decided symbol and allows us to obtain fast convergence and a lower outage probability with a very limited complexity.     

Maximum-likelihood sequence detection with closed-form metrics in OOK optical systems impaired by GVD and PMD

This paper thoroughly investigates the maximum-likelihood sequence detection (MLSD) receiver for the optical ON-OFF keying (OOK) channel in the presence of both polarization mode dispersion and group velocity dispersion (GVD). A reliable method is provided for computing the relevant performance for any possible value of the system parameters, with no constraint on the sampling rate. With one sample per bit time, a practically exact expression of the statistics of the received samples is found, and therefore the performance of a synchronous MLSD receiver is evaluated and compared with that of other electronic techniques such as combined feedforward and decision-feedback equalizers (FFE and DFE). It is also shown that the ultimate performance of electronic processing can be obtained by sampling the received signal at twice the bit rate. An approximate accurate closed-form expression of the receiver metrics is also identified, allowing for the implementation of a practically optimal MLSD receiver.