Alan Barbieri

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.

Time-frequency packing for linear modulations: spectral efficiency and practical detection schemes

We investigate the spectral efficiency, achievable by a low-complexity symbol-by-symbol receiver, when linear modulations based on the superposition of uniformly time- and frequency-shifted replicas of a base pulse are employed. Although orthogonal signaling with Gaussian inputs achieves capacity on the additive white Gaussian noise channel, we show that, when finite-order constellations are employed, by giving up the orthogonality condition (thus accepting interference among adjacent signals) we can considerably improve the performance, even when a symbol-by-symbol receiver is used. We also optimize the spacing between adjacent signals to maximize the achievable spectral efficiency. Moreover, we propose a more involved transmission scheme, consisting of the superposition of two independent signals with suitable power allocation and a two-stage receiver, showing that it allows a further increase of the spectral efficiency. Finally, we show that a more involved equalization algorithm, based on soft interference cancellation, allows to achieve an excellent bit-error-rate performance, even when error-correcting codes designed for the Gaussian-noise limited channel are employed, and thus does not require a complete redesign of the coding scheme.

On MAP symbol detection for ISI channels using the Ungerboeck observation model

In this letter, the well-known problem of a transmission over an additive white Gaussian noise channel affected by known intersymbol interference is considered. We show that the maximum a posteriori (MAP) symbol detection strategy, usually implemented by using the Forney observation model, can be equivalently implemented based on the samples at the output of a filter matched to the received pulse, i.e., based on the Ungerboeck observation model. Although interesting from a conceptual viewpoint, the derived algorithm has a practical relevance in turbo equalization schemes for partial response signalling, where the implementation of a whitening filter can be avoided.

Joint Iterative Detection and Decoding in the Presence of Phase Noise and Frequency Offset

We present a new algorithm for joint detection and decoding of iteratively decodable codes transmitted over channels affected by a time-varying phase noise (PN) and a constant frequency offset. The proposed algorithm is obtained as an application of the sum-product algorithm to the factor graph representing the joint a posteriori distribution of the information symbols and the channel parameters given the channel output. The resulting algorithm employs the soft-output information on the coded symbols provided by the decoder and performs forward-backward recursions, taking into account the joint probability distribution of phase and frequency offset. We present simulation results for high-order coded modulation schemes based on low-density parity-check codes and serially concatenated convolutional codes, showing that, despite its low complexity, the algorithm is able to cope with a strong PN and a significant uncompensated frequency offset, thus avoiding the use of complicated data-aided frequency-estimation schemes operating on a known preamble. The robustness of the algorithm in the presence of a time-varying frequency offset is also discussed

Spectrally-efficient continuous phase modulations

We investigate the spectral efficiency of continuous phase modulations (CPMs). To this end, we need an effective bandwidth definition for a CPM signal, whose power spectral density has in principle an infinite support. The definition we adopt is based on the spacing between adjacent carriers in a frequency division multiplexed CPM system. We consider the inter-channel interference, which depends on the channel spacing, and we evaluate the spectral efficiency achievable by a single-user receiver in the considered multi-channel scenario. We then optimize the channel spacing with the aim of maximizing the spectral efficiency, showing that impressive improvements with respect to the spectral efficiencies reported in the literature and obtained by heuristic approaches can be achieved.

OFDM versus Single-Carrier Transmission for 100 Gbps Optical Communication

We analyze the orthogonal frequency division multiplexing (OFDM) technique in long-haul next generation optical communication links and compare it with the well-established single-carrier (SC) data transmission using high-level modulation formats and coherent detection. The analysis of the two alternative solutions is carried out in the 100 Gbps scenario, which is commonly considered to be the next upgrade of existing optical links, with special emphasis on quaternary phase-shift keying (QPSK) modulations. The comparison between OFDM and SC takes into account the main linear and nonlinear impairments of the optical channel, e.g., group velocity dispersion (GVD), polarization mode dispersion (PMD), self-phase modulation (SPM), cross-phase modulation (XPM), and four-wave mixing (FWM), as well as the phase noise due to transmit and receive lasers, their relative frequency offset, other synchronization aspects, the overall complexity, the power and spectral efficiency, and the technological constraints.

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.

Reduced-Complexity BCJR Algorithm for Turbo Equalization

We propose novel techniques to reduce the complexity of the well-known Bahl–Cocke–Jelinek–Raviv (BCJR) algorithm when it is employed as a detection algorithm in turbo equalization schemes. In particular, by also considering an alternative formulation of the BCJR algorithm, which is more suitable than the original for deriving reduced-complexity techniques, we describe three reduced-complexity algorithms, each of them being particularly effective over one of the three different classes of channels (minimum-phase, maximum-phase, and mixed-phase channels) affected by intersymbol interference. The proposed algorithms do not explore all paths on the trellis describing the channel memory, but they work only on the most promising ones, which are chosen according to the maximum a posteriori criterion. Moreover, some optimization techniques for improving the effectiveness of the proposed solutions are described. Finally, we report the results of computer simulations showing the impressive performance of the proposed algorithms, and compare them with other solutions in the literature.

On the Information Rate and Repeat-Accumulate Code Design for Phase Noise Channels

We investigate the information rate of channels affected by phase noise, aiming at predicting the ultimate performance limits in this scenario. Moreover, a closed-form upper bound is also derived for phase shift keying (PSK) modulations. Finally, we consider the design of nonsystematic irregular repeat-accumulate (RA) codes for this channel trying to give new insights on the codes to be employed for such an application.

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.