In this paper, we focus on orthogonal time frequency space (OTFS) modulated transmissions over doubly-selective channels. Specifically, we investigate the state-of-the-art techniques for effective detection in high-mobility scenarios and introduce innovative strategies aimed at achieving an optimal trade-off between complexity and performance. The proposed solutions are based on the Ungerboeck observation model and exploit the structure of the resulting channel matrix in the Doppler-delay domain. In particular, the first proposed method, denoted as HBCJRG, belongs to the family of message-passing algorithms, whose strength lies in a scheduling scheme that prioritizes the strongest interferers during the detection process. In contrast, the second proposed approach, denoted as ICG, is based on interference cancellation. Differently from the HBCJRGapproach, whose required computational load grows quadratically with the constellation cardinality, the ICGalgorithm is characterized by extremely low complexity. Simulation results demonstrate that the latter strategy allows to achieve an optimal trade-off between complexity and performance when compared to existing state-of-the-art solutions.

In the context of signal detection in the presence of an unknown time-varying channel parameter, receivers based on the Expectation Propagation (EP) framework appear to be very promising. EP is a message-passing algorithm based on factor graphs with an inherent ability to combine prior knowledge of system variables with channel observations. This suggests that an effective estimation of random channel parameters can be achieved even with a very limited number of pilot symbols, thus increasing the payload efficiency. However, achieving satisfactory performance often requires ad-hoc adjustments in the way the probability distributions of latent variables - both data and channel parameters - are combined and projected. Here, we provide, for the first time, an analysis of EP-based algorithms for the classical problem of coded transmission on a strong Wiener phase noise channel, employing soft-input soft-output decoding. The analysis includes possible improvements over the native application of EP, in order to identify its limitations and propose new strategies which reach the performance benchmark while maintaining low complexity, with a primary focus on challenging scenarios where the state-of-the-art algorithms fail.

We investigate the performance of free-space optical communication systems in the presence of atmospheric turbulence to assess the advantages that a coherent communication system can bring with respect to a conventional intensity modulation and direct detection (IM/DD) system. The perspective is an information-theoretic one, hence we evaluate the mutual information and the corresponding outage probability of both channels, with various traditional symbol constellations, as a pragmatic approximation to the capacity, or to the outage capacity, of those channels. In addition, we analyze non-uniform symbol constellations to evaluate the possible shaping gain that can be achieved under different channel conditions. We propose a method to quantify the gain that the coherent solution can achieve, in terms of signal-to-noise ratio (SNR), so that it can be compared, on a techno-economical basis, against the higher cost that it implies.

Expectation Propagation (EP) is a promising framework in message-passing algorithms based on factor-graphs. The inherent ability to combine prior (partial) knowledge of system variables with channel observations suggests that an effective estimation of random channel parameters can be achieved even with a very limited number of pilot symbols, thus increasing the payload efficiency. Yet, the way in which the probability distributions of latent variables (both data and parameters) are combined and projected often requires ad-hoc adjustments to reach satisfactory performance. Here, we apply EP to a classical problem of LDPC-coded transmission on a strong Wiener phase noise channel and discuss how and why, even in the simple case of binary modulation, EP can fail or succeed.

Motivated by automotive applications, we consider joint radar sensing and data communication for a system operating at millimeter wave (mmWave) frequency bands, where a Base Station (BS) is equipped with a co-located radar receiver and sends data using the Orthogonal Time Frequency Space (OTFS) modulation format. We consider two distinct modes of operation. In Discovery mode, a single common data stream is broadcast over a wide angular sector. The radar receiver must detect the presence of not yet acquired targets and performs coarse estimation of their parameters (angle of arrival, range, and velocity). In Tracking mode, the BS transmits multiple individual data streams to already acquired users via beamforming, while the radar receiver performs accurate estimation of the aforementioned parameters. Due to hardware complexity and power consumption constraints, we consider a hybrid digital-analog architecture where the number of RF chains and A/D converters is significantly smaller than the number of antenna array elements. In this case, a direct application of the conventional MIMO radar approach is not possible. Consequently, we advocate a beam-space approach where the vector observation at the radar receiver is obtained through a RF-domain beamforming matrix operating the dimensionality reduction from antennas to RF chains. Under this setup, we propose a likelihood function-based scheme to perform joint target detection and parameter estimation in Discovery, and high-resolution parameter estimation in Tracking mode, respectively. Our numerical results demonstrate that the proposed approach is able to reliably detect multiple targets while closely approaching the Cramér-Rao Lower Bound (CRLB) of the corresponding parameter estimation problem.

The recent developments in the field of direct-to-Earth (DTE) for low-Earth-orbit (LEO) satellite optical links have shown the potential benefits of on-off-keying-based communications with the variable data rate (VDR) technique, in contrast to the traditional constant data rate (CDR) approach. In this paper, relevant link level aspects are analyzed, namely: time, frame, and amplitude synchronization, showing that reliable and performing techniques allow to fully exploit the advantages offered by the VDR strategy.

We consider the phase noise affecting communication systems, where local oscillators are employed to obtain a reference signal for frequency and phase synchronizations. We try to fill the gap between measurements and analytical models, in case of free-running and phase-locked oscillators. In particular, we propose a closed form expression for the power spectral density of the phase noise described by few parameters that are explicitly linked to the oscillator measurements. We also propose an analytical model for the oscillator power spectral density.

We consider time-frequency-packed systems in an additive white Gaussian noise scenario. With respect to systems employing time packing, thus introducing intentional intersymbol interference only, a further improvement of the spectral efficiency is obtained by packing the adjacent carriers closer in frequency. The adoption of a multiuser detector can allow coping with the resulting intentional intercarrier interference. The optimal detector for time-frequency-packed systems has a complexity that increases exponentially with the number of interferers in both time and frequency dimensions and thus becomes unmanageable. We propose a suboptimal receiver, which is derived by using the framework based on factor graphs and the sum-product algorithm, with a complexity that is linear in the number of adjacent carriers and takes also advantage of a multi-user channel shortener to further reduce the complexity. We assess the performance by means of computer simulations and show that, when compared with other suboptimal receivers available in the literature and with the optimal detector, the proposed receiver results very promising in terms of trade-off between performance and computational complexity.

Fast and reliable synchronization in free-space optical (FSO) communications is a crucial task that has received little attention so far. Since in these applications the data rate is much higher than in traditional radio-frequency (RF) systems, novel technological constraints may arise in the design of the synchronization algorithms, as for example the need to operate at symbol rate instead with an oversampled data stream. In this work, we consider an FSO link and investigate the problem of channel estimation, symbol timing recovery and frame detection using a known synch pattern. The modulation format is on-off keying (OOK) and the received signal is plagued by a mixture of thermal and shot noise. By applying the least-squares criterion, we derive a novel synchronization scheme that can jointly retrieve all the unknown parameters using symbol-spaced samples. Although designed without taking the noise statistics into account, the estimator performance is assessed in a realistic scenario where shot noise is present. Comparisons are made with the relevant Cramér-Rao bound for the joint estimation of the synchronization parameters and signal-dependent noise variances. Numerical simulations and complexity analysis indicate that the resulting scheme performs satisfactorily with an affordable processing load. Hence, it represents a promising solution for fast synchronization in high-speed FSO communications.

Many recent works in the literature declare that Orthogonal Time-Frequency-Space (OTFS) modulation is a promising candidate technology for high mobility communication scenarios. However, a truly fair comparison with its direct concurrent and widely used Orthogonal Frequency-Division Multiplexing (OFDM) modulation has not yet been provided. In this paper, we present such a fair comparison between the two digital modulation formats in terms of achievable communication rate. In this context, we explicitly address the problem of channel estimation by considering, for each modulation, a pilot scheme and the associated channel estimation algorithm specifically adapted to sparse channels in the Doppler-delay domain, targeting the optimization of the pilot overhead to maximize the overall achievable rate. In our achievable rate analysis we consider also the presence of a guard interval or cyclic prefix. The results are supported by numerical simulations, for different time-frequency selective channels including multiple scattering components and under non-perfect channel state information resulting from the considered pilot schemes. This work does not claim to establish in a fully definitive way which is the best modulation format, since such choice depends on many other features which are outside the scope of this work (e.g., legacy, intellectual property, ease and know-how for implementation, and many other criteria). Nevertheless, we provide the foundations to properly compare multi-carrier communication systems in terms of their information theoretic achievable rate potential, within meaningful and sensible assumptions on the channel models and on the receiver complexity (both in terms of channel estimation and in terms of soft-output symbol detection).

We propose a novel discrete-time model for the phase noise signal, in case of free-running and phase-locked oscillators. In particular, we show how the PN can be described by an autoregressive process. The strength of the proposed model is that it can be easily expressed in terms of measurement parameters of practical oscillators. We then analyse the most common discrete-time phase noise channel model with reference to the measurement parameters and to the system bandwidth. The derived analytical models for the discrete-time phase noise signal can be used for the design of estimation/detection algorithms, for performance evaluation, or simply for fast simulations.

We consider a joint radar parameter estimation and communication system using orthogonal time frequency space (OTFS) modulation. The scenario is motivated by vehicular applications where a vehicle (or the infrastructure) equipped with a mono-static radar wishes to communicate data to its target receiver, while estimating parameters of interest related to this receiver. Provided that the radar-equipped transmitter is ready to send data to its target receiver, this setting naturally assumes that the receiver has been already detected. In a point-to-point communication setting over multipath time-frequency selective channels, we study the joint radar and communication system from two perspectives, i.e., the radar parameter estimation at the transmitter as well as the data detection at the receiver. For the radar parameter estimation part, we derive an efficient approximated Maximum Likelihood algorithm and the corresponding Cramér-Rao lower bound for range and velocity estimation. Numerical examples demonstrate that multi-carrier digital formats such as OTFS can achieve as accurate radar estimation as state-of-the-art radar waveforms such as frequency-modulated continuous wave (FMCW). For the data detection part, we focus on separate detection and decoding and consider a soft-output detector that exploits efficiently the channel sparsity in the Doppler-delay domain. We quantify the detector performance in terms of its pragmatic capacity, i.e., the achievable rate of the channel induced by the signal constellation and the detector soft-output. Simulations show that the proposed scheme outperforms concurrent state-of-the-art solutions. Overall, our work shows that a suitable digitally modulated waveform enables to efficiently operate joint radar parameter estimation and communication by achieving full information rate of the modulation and near-optimal radar estimation performance. Furthermore, OTFS appears to be particularly suited to the scope.

This paper considers the design of short non-binary low-density parity-check (LDPC) codes over finite fields of order m, for channels with phase noise. In particular, m-ary differential phase-shift keying (DPSK)-modulated code symbols are transmitted over an additive white Gaussian noise (AWGN) channel with the Wiener phase noise. At the receiver side, non-coherent detection takes place, with the help of a multi-symbol detection algorithm, followed by a non-binary decoding step. Both the detector and the decoder operate on a joint factor graph. As a benchmark, finite length bounds and information rate expressions are computed and compared with the codeword error rate (CER) performance, as well as the iterative threshold of the obtained codes. As a result, performance within 1.2 dB from finite-length bounds is obtained, down to a CER of 10-3.

Recent investigations show that high-rate telemetry systems, based on the CCSDS 131.2-B-1 standard and employed in Earth observation missions, do not fully exploit the available capacity. Thus, we propose and discuss possible ways to improve the data return of these systems that can be considered for a revision of the current standard. Some of them are represented by a revision and/or an extension of the currently adopted modulation and coding formats. The remaining techniques are related to an enhancement of the transceiver architecture. Different bandwidth allocation strategies are also considered. The benefits of the proposed techniques are assessed by means of computer simulations with reference to a realistic scenario where a real non-linear amplifier, real filters, and real impairments are considered.

This paper presents results on the achievable spectral efficiency and on the energy efficiency for a wireless multiple-input-multiple-output (MIMO) link operating at millimeter wave frequencies (mmWave) in a typical 5G scenario. Two different single-carrier modem schemes are considered, i.e., a traditional modulation scheme with linear equalization at the receiver, and a single-carrier modulation with cyclic prefix, frequency-domain equalization and fast Fourier transform-based processing at the receiver; these two schemes are compared with a conventional MIMO orthogonal frequency division multiplexing transceiver structure. Our analysis jointly takes into account the peculiar characteristics of MIMO channels at mmWave frequencies, the use of hybrid (analog-digital) pre-coding and post-coding beamformers, the finite cardinality of the modulation structure, and the non-linear behavior of the transmitter power amplifiers. Our results show that the best performance is achieved by single-carrier modulation with time-domain equalization, which exhibits the smallest loss due to the non-linear distortion, and whose performance can be further improved by using advanced equalization schemes. Results also confirm that performance gets severely degraded when the link length exceeds 90–100 m and the transmit power falls below 0 dBW.

In this paper, we study digital transmission over an additive white Gaussian noise (AWGN) channel with mary differential phase-shift keying (DPSK) modulation in the presence of phase noise. At the receiver side, non-coherent iterative detection and decoding is assumed. We present a non-binary low-density generator matrix (LDGM) code design which is suitable for both coherent and non-coherent channels. The code construction is strongly related to the one of non-binary irregular repeat-accumulate (IRA) low-density parity-check (LDPC) codes.

We consider the rates achievable by a user in a multibeam satellite system for unicast applications and propose alternatives to the conventional single-user symbol-by-symbol detection applied at user terminals. Single-user detection is known to suffer from strong degradation when the terminal is located near the edge of the coverage area of a beam and when aggressive frequency reuse is adopted. For this reason, we consider multiuser detection and take into account the strongest interfering signal. We also analyze two additional transmission strategies requiring modifications at medium access control layer. We describe an information-theoretic framework to compare the different strategies by computing the information rate of the user in the reference beam. Furthermore, we analyze the performance of coded schemes that could approach the information-theoretic limits. We show that classical codes from the DVB-S2(X) standard are not suitable when multiuser detection is adopted and we propose two ways to improve the performance based on the redesign of the code and of the bit mapping.

The need for increased data rates has led towards the development of advanced broadband satellite systems able to achieve higher capacity for providing Internet and backbone services in remote areas. Aside of the more conventional geostationary orbit (GEO), Medium Earth Orbit (MEO) satellite constellations are envisaged due to their advantages in terms of shorter link path and low latency; MEO satellite constellations are currently operating at Ka-band and are already showing signs of spectrum saturation in high demand areas in their coverage. In search of additional spectrum, in this paper, we employ the Q-band by investigating the performance of a multi-satellite MEO constellation network in terms of system capacity considering sophisticated propagation and physical layer tools. In particular, within the proposed Q-band solution, a higher throughput can be achieved with respect to a corresponding Ka-band system, by reaching up to 100% gain in terms of system capacity in a clear sky conditions.

We study the achievable rates by a single user in multibeam satellite scenarios. We show alternatives to the conventional symbol-by-symbol detection applied at user terminals. Single user detection is known to suffer from strong degradation when the terminal is located near the edge of the coverage area, and when aggressive frequency reuse is adopted. For this reason, we consider multiuser detection, and take into account the strongest interfering signal. Moreover, we analyze a different transmission strategy, where the signals from two adjacent beams jointly serve two users in a time division multiplexing fashion. We describe an information-theoretic framework to compare different transmission/detection strategies by computing the information rate of the user in the reference beam.

Flexible grid optical networks allow a better exploitation of fiber capacity, by enabling a denser frequency allocation. A tighter channel spacing, however, requires narrower filters, which increase linear intersymbol interference (ISI), and may dramatically reduce system reach. Commercial coherent receivers are based on symbol by symbol detectors, which are quite sensitive to ISI. In this context, Nyquist spacing is considered as the ultimate limit to wavelength-division multiplexing (WDM) packing. In this paper, we show that by introducing a limited-complexity trellis processing in the receiver, either the reach of Nyquist WDM flexi-grid networks can be significantly extended, or a higher spectral efficiency (SE) is possible at equal reach. By adopting information-theoretic techniques, we design a limited-complexity trellis processing and quantify its SE gain in flexi-grid architectures where wavelength selective switches over a frequency grid with 12.5GHz granularity are employed.

We consider binary continuous phase modulation (CPM) signals used in some recent low-cost and low-power consumption telecommunications standard. When these signals are generated through a low-cost transmitter, the real modulation index can end up being quite different from the nominal value employed at the receiver and a significant performance degradation is observed unless proper techniques for the estimation and compensation are employed. For this reason, we design new binary schemes with a much higher robustness. They are based on the concatenation of a suitable precoder with binary input and a ternary CPM format. The result is a family of CPM formats whose phase state is constrained to follow a specific evolution. Two of these precoders are considered. We will discuss many aspects related to these schemes, such as the power spectral density, the spectral efficiency, simplified detection, the minimum distance, and the uncoded performance. The adopted precoders do not change the recursive nature of CPM schemes. So these schemes are still suited for serial concatenation, through a pseudo-random interleaver, with an outer channel encoder.

We consider realistic long-haul optical links, with linear and nonlinear impairments, and investigate the application of time-frequency packing with low-order constellations as a possible solution to increase the spectral efficiency. A detailed comparison with available techniques from the literature will be also performed. We will see that this technique represents a feasible solution to overcome the relevant theoretical and technological issues related to this spectral efficiency increase and could be more effective than the simple adoption of high-order modulation formats.

We consider realistic long-haul optical links, where nonlinear effects represent the main impairment, and investigate the application of time-frequency packing with low-order constellations as a the most viable solution to increase the spectral efficiency. We will see that this technique allows to overcome the relevant theoretical and technological issues related to this spectral efficiency increase and is more effective than the simple adoption of high-order modulation formats which are more sensitive to nonlinear effects.

We consider intersymbol interference channels with reduced-complexity, mutual information optimized, channel-shortening detectors. For a given channel and receiver complexity, we optimize the transmit filter to use. The cost function we consider is the (Shannon) achievable information rate of the entire transceiver system. By functional analysis, we can establish a general form of the optimal transmit filter, which can then be optimized by standard numerical methods. As a side result, we also obtain an insight of the behaviour of the standard waterfilling algorithm for intersymbol interference channels.

We analyze the asymptotic performance of non-binary spatially-coupled low-density parity-check (SC-LDPC) codes built on the general linear group, when the transmission takes place over the binary erasure channel. We propose an efficient method to derive an upper bound to the maximum a posteriori probability (MAP) threshold for nonbinary LDPC codes, and observe that the MAP performance of regular LDPC codes improves with the alphabet size. We then consider nonbinary SC-LDPC codes. We show that the same threshold saturation effect experienced by binary SC-LDPC codes occurs for the nonbinary codes, hence we conjecture that the BP threshold for large termination length approaches the MAP threshold of the underlying regular ensemble.

In this paper, we address the problem of optimizing signal constellations for strong phase noise. The problem is investigated by considering three optimization formulations, which provide an analytical framework for constellation design. In the first formulation, we seek to design constellations that minimize the symbol error probability (SEP) for an approximate ML detector in the presence of phase noise. In the second formulation, we optimize constellations in terms of mutual information (MI) for the effective discrete channel consisting of phase noise, additive white Gaussian noise, and the approximate ML detector. To this end, we derive the MI of this discrete channel. Finally, we optimize constellations in terms of the MI for the phase noise channel. We give two analytical characterizations of the MI of this channel, which are shown to be accurate for a wide range of signal-to-noise ratios and phase noise variances. For each formulation, we present a detailed analysis of the optimal constellations and their performance in the presence of strong phase noise. We show that the optimal constellations significantly outperform conventional constellations and those proposed in the literature in terms of SEP, error floors, and MI.

We consider channels affected by intersymbol interference with reduced-complexity, mutual information optimized, channel-shortening detection. For such settings, we optimize the transmit filter, taking into consideration the reduced receiver complexity constraint. As figure of merit, we consider the achievable information rate of the entire system and with functional analysis, we establish a general form of the optimal transmit filter, which can then be optimized by standard numerical methods. As a corollary to our main result, we obtain some insight of the behavior of the standard waterfilling algorithm for intersymbol interference channels. With only some minor changes, the general form we derive can be applied to multiple-input multiple-output channels with intersymbol interference. To illuminate the practical use of our results, we provide applications of our theoretical results by deriving the optimal shaping pulse of a linear modulation transmitted over a bandlimited additive white Gaussian noise channel which has possible applications in the faster-than-Nyquist/time packing technique.

We consider realistic satellite communications systems for broadband and broadcasting applications, based on frequency-division-multiplexed linear modulations, where spectral efficiency is one of the main figures of merit. For these systems, we investigate their ultimate performance limits by using a framework to compute the spectral efficiency when suboptimal receivers are adopted and evaluating the performance improvements that can be obtained through the adoption of the time-frequency packing technique. Our analysis reveals that introducing controlled interference can significantly increase the efficiency of these systems. Moreover, if a receiver which is able to account for the interference and the nonlinear impairments is adopted, rather than a classical predistorter at the transmitter coupled with a simpler receiver, the benefits in terms of spectral efficiency can be even larger. Finally, we consider practical coded schemes and show the potential advantages of the optimized signaling formats when combined with iterative detection/decoding.

We propose a new spread spectrum (SS) system based on continuous-phase modulations (CPMs). The main idea is to exploit the sequence of modulation indices of a multi-h CPM as a frequency-hopping (FH) sequence. Spectral spreading, flatness and smoothness can be easily achieved by an appropriate choice of the maximum value of the modulation index and of the length of the index sequence. We will show that the proposed CPM-based spread spectrum system achieves an overall spectral efficiency larger than that of a single-user single-h CPM transmission even when a single-user detector is employed at the receiver. It also outperforms other solutions in the literature. In addition, we will also derive some suboptimal multi-user detectors.

This papers addresses the design of new energy-efficient Continuous Phase Modulation (CPM) waveforms suitable for being adopted in satellite mesh networks that are characterized by the absence of the Hub, and by small antennas and power amplifiers with moderate to low output saturated power at the user terminal. In particular, a CPM modulation format concatenated with a proper convolutional code for low spectral efficiency values has been selected to implement an efficient waveform for power-limited scenarios. Performance results show the gain obtained with respect to the DVB-RCS2 CPM waveforms at higher spectral efficiency also when transmission techniques, such as Burst Repetition, are considered, and confirm the suitability of the new designed CPM waveforms for satellite hub-less scenarios.

This paper addresses detailed waveform trade-offs for mesh satellite networks. The waveform analysis is carried out considering spectral efficiency, resilience against non linear distortion, channel impairments and interference for both linear and continuous phase modulation schemes defined in the DVB-RCS2 standard.

We consider a frequency-division-multiplexed satellite system where nonlinear distortions may originate from the presence of high power nonlinear devices and can cause significant performance degradations. The spectral efficiency is used as a performance measure to compare, from an information-theoretic point of view, different transmission strategies and modulation formats. More precisely, we will consider transmission schemes employing continuous phase modulations, which are robust to nonlinearities, and schemes based on linear modulations and employing a detector taking into account the nonlinear effects or more traditional techniques, such those based on predistortion of the nonlinear device.

We propose a new spread spectrum (SS) system based on continuous phase modulations (CPMs). The main idea is to exploit the sequence of modulation indices of a multi-h CPM as a frequency hopping (FH) sequence. We will show how the sequence of indices impacts on the CPM signal bandwidth and power spectral density (PSD). Spectral spreading, flatness and smoothness can be easily achieved by an appropriate choice of the maximum value of the modulation index and of the length of the index sequence. We will show that a CPM-based spread spectrum system achieves an overall spectral efficiency larger than that of a single-user single-h CPM signal even when a single-user detector is employed at the receiver.

We recently investigated the spectral efficiency, achievable with a symbol-by-symbol receiver, for linear modulations employing time-frequency packing. In this paper, we will investigate the improvements that can be obtained by increasing the receiver complexity. In the numerical results, we will mainly concentrate on time packing (an extension of the so called faster-than-Nyquist signaling technique) and on (i) receivers based on linear processing plus symbol-by-symbol detection or (ii) receivers based on a more sophisticated trellis processing with constrained complexity. Finally, the potential advantage of the proposed signalling scheme when combined with conventional low-density parity-check (LDPC) coding of the DVB-S2 air interface will be presented.

We propose novel detection algorithms for linear modulations transmitted over nonlinear satellite channels, also impaired by additive white Gaussian noise. These algorithms are derived by using a Volterra-series expansion of the useful signal and by applying the sum-product algorithm to a suitably-designed factor graph. Being soft-input soft-output (SISO) in nature, the proposed detectors can be adopted in turbo processing without additional modifications. Typical linear modulations employed in satellite transmissions are considered in the numerical results. When compared with the optimal detection algorithm for these channels, whose complexity is exponential in the channel memory, the proposed schemes result very appealing in terms of tradeoff between performance and computational complexity. Particularly, the proposed schemes can approach the optimal performance with a complexity only linear in the channel memory.

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.

In coherent optical systems, the phase noise due to transmit and receive lasers has a significant impact on the receiver performance - the sensitivity to phase noise and the capability of electronic processing to compensate for its effects are reduced for increasing lasers'' linewidths. However, a detailed analysis of the effects of phase noise on the system performance cannot leave other aspects out of consideration. In fact, the picture is completely different for optical systems using single-carrier or orthogonal frequency division multiplexing, in the presence or absence of inline dispersion compensation, or when an unmodulated carrier is also transmitted for phase noise compensation purposes. In addition, transmit and receive phase noise components may have a different impact. All these aspects are analyzed and discussed in this paper. A novel digital coherence enhancement technique, able to significantly reduce the phase noise of transmit or receive lasers by using an interferometric device plus a very simple electronic processing, is also proposed.

Orthogonal frequency division multiplexing (OFDM) and single-carrier (SC) data transmission are compared as potential candidates for the next generation coherent long-haul 100 Gbps optical communication systems. The comparison takes into account impairments either general or mainly related to coherent detection, e.g., group velocity dispersion (GVD), polarization mode dispersion (PMD), non-linear effects, phase noise due to transmit and receive lasers, uncompensated frequency offset, other synchronization aspects, overall complexity, power and spectral efficiency, technological constraints.

We consider a frequency division multiplexed (FDM) system where each user employs a continuous phase modulation (CPM), serially concatenated with an outer code through an interleaver, and iterative detection/decoding. In such a system, the spectral efficiency can be increased by reducing the spacing between two adjacent channels, thus increasing the relevant interference. Hence, we address the design of low-complexity suboptimal multiuser detectors able to effectively cope with such an interference. We extend some well known multiuser detection algorithms proposed for code division multiple access (CDMA) systems. Moreover, we introduce a new detection scheme using the framework based on factor graphs (FGs) and the sum-product algorithm (SPA). The simulation results show that the described algorithms allow to effectively reduce the spacing, thus increasing the spectral efficiency, and in particular, the proposed detection scheme results to be the most effective one in terms of performance and computational complexity.

We consider a frequency division multiplexed (FDM) satellite system where each user employs a continuous phase modulation (CPM), serially concatenated with an outer code through an interleaver, and iterative detection/decoding. In such a system, the spectral efficiency can be increased by reducing the spacing between two adjacent channels, thus increasing the relevant interference. Hence, we address the design of low-complexity suboptimal multiuser detectors able to effectively cope with such an interference. We extend some well known multiuser detection algorithms proposed for code division multiple access (CDMA) systems. Moreover, we introduce a new detection scheme using the framework based on factor graphs (FGs) and the sum-product algorithm (SPA). The simulation results show that the described algorithms allow to effectively reduce the spacing, thus increasing the spectral efficiency, and in particular, the proposed detection scheme results to be the most effective one in terms of performance and computational complexity.

We propose a novel simulation-based method to evaluate the performance of Viterbi decoders. In particular, we address scenarios where the error probability is very low, that is, scenarios where classical Monte Carlo simulations would require impractical execution times before producing reliable results. As other recent fast-simulation approaches, the proposed method relies on the multicanonical Monte Carlo technique, but, unlike the existing general-purpose methods, it is specifically designed for Viterbi decoders, the algorithm being driven by a control variable that depends on the state metrics of the various survivors over the trellis. In simple scenarios for which analytical tools are available, the simulation results agree with them, while, in the most common scenarios, no analytical tool is available and the proposed method gives the fastest way for the estimation of low error probabilities.

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.

Digital communications over channels impaired by impulse noise are considered. We first address the problem from an information-theoretical viewpoint, discussing the performance limits imposed by the channel model. Then, we describe and compare a couple of practical communication schemes employing powerful channel codes and iterative decoding, with focus on a very simple and robust detection scheme that does not require the estimation of the statistics of the impulse noise.

Digital communications over channels impaired by impulse noise are addressed. We adopt a two-state Markov model that allows to describe the typical bursty nature of the impulse noise, in contrast to the memoryless models generally considered in the literature. For this channel, we evaluate the achievable information rate and propose a couple of practical communication systems based on powerful codes and iterative receivers. Moreover, we discuss the effectiveness of the considered receivers in terms of performance/latency tradeoff as well as in terms of robustness to erroneous channel estimations. The proposed schemes are shown to perform fairly close to the theoretical limits, and significantly better than the conventional schemes employing memoryless detection.

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.

We consider a terrestrial wireless channel, whose statistical model under flat-fading conditions is due to Clarke. A lot of papers in the literature deal with receivers for this scenario, aiming at estimating and tracking the time-varying channel, possibly with the aid of known (pilot) symbols. A common approach to derive receivers of reasonable complexity is to resort to a Kalman filter which is based on an approximation of the actual fading process as autoregressive moving-average (ARMA) of a given order. The aim of this paper is to show that the approximation of the actual fading process, usually exploited in the literature, is far from effective. Thus, we present a novel technique, based on an off-line minimization of the mean square error of the channel estimate, which ensures a considerable gain in terms of bit-error rate for Kalman-based receivers without increasing the receiver complexity. Moreover, we also propose a novel approximation, to be employed in Kalman smoothers proposed for iterative detection schemes, which allows further performance improvements without a significant increase of the computational complexity.

We address the design of low-complexity algorithms for soft-output detection over channels impaired by intersymbol interference. Unlike most works with similar aims, which assume the presence of the whitened matched filter at the receiver (Forney approach), algorithms that can directly work on the matched filter output (Ungerboeck approach) are considered. We introduce a novel (cyclic) factor graph describing the channel and, by applying the sum-product algorithm to it, we derive soft-output detection schemes that can provide impressive complexity reductions with respect to the benchmark algorithms, since their complexity is linear, instead of exponential, in the channel memory. Finally, we report simulation results proving that the performance of the proposed algorithms makes them appealing for turbo equalization in various practical scenarios.

The optimal receiver processing based on maximum-likelihood sequence detection (MLSD) is employed with high-order phase and amplitude modulations in optical transmission systems affected by typical channel impairments such as group velocity dispersion (GVD), polarization mode dispersion (PMD), and phase uncertainties due to phase noise. A couple of widely known front ends, with proper modifications, can be used to extract the required sufficient statistics from the received signal. Receiver adaptivity and complexity reduction are also discussed. It is demonstrated that, as long as a sufficient receiver complexity is employed, GVD and PMD entail no performance degradation with respect to the case of no channel distortions (the back-to-back case).

We consider digital communications over channels impaired by impulse noise. A two-state Markov channel model is adopted, which, unlike the memoryless models generally considered in the literature, allows to describe the typical bursty nature of the impulse noise. First, by means of information-theoretical arguments, we compute and discuss the ultimate performance limits of such systems. Then, we derive an algorithm for optimal maximum-a-posteriori symbol detection, and explain how to exploit it in receivers employing iterative detection/decoding. Finally, we report simulation results showing the effectiveness of the proposed schemes, as well as an excellent agreement with the computed theoretical limits.

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 system model, consisting of the superposition of two independent signals and a receiver based on successive interference cancellation, showing that it allows a further increase of the spectral efficiency.

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, that 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 efficiency achieved without optimizing the channel spacing can be achieved. I.

We compare low-complexity schemes for soft-output detection of continuous phase modulations (CPMs). In particular, we address the problem of minimizing the complexity of the front end filters and that of the trellis exploited by the detection algorithm, with the aim of assuring a negligible performance degradation with respect to the optimal full-complexity receiver. We show that the approach providing the simplest front end is that based on the CPM decomposition proposed by Moqvist and Aulin. On the other hand, we prove that the most convenient solution in terms of trellis complexity is provided by the CPM decomposition proposed by Mengali and Morelli, possibly combined with suitable techniques for reduced trellis search.

We consider digital communications over channels affected by Class-A impulse noise. First, by means of information theoretic arguments, the performance limits of such systems are derived and discussed. Then, practical communication schemes employing powerful channel codes with iterative decoding are presented. Together with an ideal detection scheme which perfectly knows the statistics of the impulse noise, we describe a sub- optimal scheme which ensures a limited performance degradation even when a reliable statistical characterization of the noise is not available. Finally, by means of computer simulations, we show the effectiveness of the described schemes, whose performance is fairly close to the derived theoretical limits.

We propose a novel iterative method, similar to the generalized Blahut-Arimoto algorithm recently proposed by Kavcic, to evaluate the Markov capacity of a continuous phase modulated signal over an additive white Gaussian noise channel. One of the novelty of our approach is that we maximize, with respect to the input distribution, the spectral efficiency in bps/Hz rather than the mutual information in bits per channel use. We address this problem by taking into account the bandwidth occupancy of the CPM signal by means of the Carson's rule bandwidth definition, and solving a linearly constrained nonlinear optimization problem. The results show that Markov capacity obtained with the proposed input optimization algorithm strongly outperforms the capacity for independent and uniformly distributed input.

We consider a terrestrial wireless channel, whose statistical model under flat-fading conditions is due to Clarke. A lot of papers in the literature deal with receivers for this scenario, aiming at estimating and tracking the time-varying channel, possibly with the aid of known (pilot) symbols. A common approach to derive receivers of reasonable complexity is to resort to a Kalman filter which is based on an approximation of the actual fading process as autoregressive moving-average (ARMA) of a given order. The aim of this paper is to show that the approximation of the actual fading process, usually exploited in the literature, is far from optimal. Thus, we present a novel technique, based on an off-line minimization of the mean square error of the channel estimate, which ensures a considerable gain in terms of bit-error rate for Kalman-based receivers without increasing the receiver complexity. Moreover, we also propose a novel approximation, to be employed in Kalman smoothers proposed for iterative detection schemes, which allows to further improve the performance without a significant increase of the computational complexity.

In this paper, we present an overview on the design of algorithms for iterative detection over channels with memory. The starting point for all the algorithms is the implementation of soft-input soft-ouput maximum a posteriori (MAP) symbol detection strategies for transmissions over channels encompassing unknown parameters, either stochastic or deterministic. The proposed solutions represent effective ways to reach this goal. The described algorithms are grouped into three categories: i) we first introduce algorithms for adaptive iterative detection, where the unknown channel parameters are explicitly estimated; ii) then, we consider finite-memory iterative detection algorithms, based on ad hoc truncation of the channel memory and often interpretable as based on an implicit estimation of the channel parameters; and iii) finally, we present a general detection-theoretic approach to derive optimal detection algorithms with polynomial complexity. A few illustrative numerical results are also presented.

We consider rotationally invariant (RI) trellis-coded modulations transmitted over channels affected by phase noise. To describe the main ideas of this paper, we first concentrate, as a case study, on the simplest RI scheme, namely the differentially encodedM-ary phase-shift keying signal. For this problem, we use the framework based on factor graphs and the sum–product algorithm to derive the exact maximuma posteriorisymbol detection algorithm. By analyzing its properties, we demonstrate that it can be implemented by a forward–backward estimator of the phase probability density function, followed by a symbol-by-symbol completion to produce thea posterioriprobabilities of the information symbols. To practically implement the forward–backward phase estimator, we propose a couple of schemes with different complexity. The resulting algorithms exhibit an excellent performance, and in one case, only a limited complexity increases with respect to the algorithm that perfectly knows the channel phase. The properties of the optimal decoder and the proposed practical decoding schemes are then extended to the case of a generic RI code. The proposed soft-output algorithms can also be used in iterative decoding schemes for concatenated codes employing RI inner components. Among them, in the numerical results, we consider repeat-accumulate codes and other serially concatenated schemes recently proposed in the technical literature.

We consider rotationally invariant (RI) trellis-coded modulations (TCMs) transmitted over channels affected by phase noise. To describe the main ideas of this paper, we first concentrate, as a case study, on the simplest RI scheme, namely the differentially encoded M-ary phase-shift keying (M-PSK) signal. For this problem, we use the framework based on factor graphs (FGs) and the sum-product algorithm (SPA), to derive the exact maximum a posteriori (MAP) symbol detection algorithm. By analyzing its properties, we demonstrate that it can be implemented by a forward-backward estimator of the phase probability density function, followed by a symbol-by-symbol completion to produce the a posteriori probabilities of the information symbols. To practically implement the forward-backward phase estimator, we propose a couple of schemes with different complexity. The resulting algorithms exhibit an excellent performance and, in one case, only a limited complexity increases with respect to the algorithm that perfectly knows the channel phase. The properties of the optimal decoder and the proposed practical decoding schemes are then extended to the case of a generic RI code. The proposed soft-output algorithms can also be used in iterative decoding schemes for concatenated codes employing RI inner components. Among them, in the numerical results, we consider repeat-accumulate (RA) codes and other serially concatenated schemes recently proposed in the technical literature.

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

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 maximuma posterioricriterion. 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.

We propose novel techniques to reduce the complexity of the well-known Bahl, Cocke, Jelinek, and 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 one for deriving reduced-complexity techniques, we describe three reduced-complexity algorithms, each of them particularly effective over one of the three different classes of channels affected by intersymbol interference (minimum-phase, maximum-phase, and mixed-phase channels). The proposed algorithms do not explore all paths on the trellis describing the channel memory, but they work only on the most promising ones, chosen according to the maximum a posteriori criterion. Moreover, some optimization techniques 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 we compare them with other solutions in the literature.

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

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.

We present innovative techniques to reduce the complexity of the well known BCJR detection algorithm applied on channels affected by intersymbol interference. On a general channel with mixed phase, we independently perform two reduced trellis searches in the forward and backward recursions, and propose a modified completion stage for combining them. When iterative detection/decoding is performed, the reduced searches are defined on the basis of a probabilistic criterion which provides a noticeable performance improvement with respect to the other reduced-complexity algorithms. On the other hand, for channels with minimum phase, we show that the simplified backward recursion can operate on the same set of paths selected during the forward search. Computer simulations confirm the effectiveness of the proposed algorithms in various turbo equalization schemes.

We consider rotationally invariant (RI) trellis-coded modulations (TCMs) transmitted over channels affected by phase noise. For this problem, we use the framework based on factor graphs (FGs) and the sum-product algorithm (SPA) to derive the exact maximum a posteriori (MAP) symbol detection algorithm. We demonstrate that it can be implemented by a reduced number of forward-backward estimators of the phase probability density function, followed by a symbol-by-symbol completion to compute the a posteriori probabilities of the information symbols. To practically implement the forward-backward phase estimators, we propose a couple of schemes with different complexity. The resulting algorithms exhibit an excellent performance and a limited complexity. The proposed soft-output algorithms can be also used in iterative decoding schemes for concatenated codes employing RI inner components

The problem of detection and decoding of low-density parity-check (LDPC) codes transmitted over channels with memory is addressed. A new general method to build a factor graph which takes into account both the code constraints and the channel behavior is proposed and the a posteriori probabilities of the information symbols, necessary to implement maximum a posteriori (MAP) symbol detection, are derived by using the sum-product algorithm. With respect to the case of a LDPC code transmitted on a memoryless channel, the derived factor graphs have additional factor nodes taking into account the channel behavior and not the code constraints. It is shown that the function associated to the generic factor node modeling the channel is related to the basic branch metric used in the Viterbi algorithm when MAP sequence detection is applied or in the BCJR algorithm implementing MAP symbol detection. This fact suggests that all the previously proposed solutions for those algorithms can be systematically extended to LDPC codes and graph-based detection. When the sum-product algorithm works on the derived factor graphs, the most demanding computation is in general that performed at factor nodes modeling the channel. In fact, the complexity of the computation at these factor nodes is in general exponential in a suitably defined channel memory parameter. In these cases, a technique for complexity reduction is illustrated. In some particular cases of practical relevance, the above mentioned complexity becomes linear in the channel memory. This does not happen in the same cases when detection is performed by using the Viterbi algorithm or the BCJR algorithm, suggesting that the use of factor graphs and the sum-product algorithm might be computationally more appealing. As an example of application of the described framework, the cases of noncoherent and flat fading channels are considered

We consider the carrier frequency offset estimation in a digital burst-mode 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 is shown, the presence of the phase noise produces a remarkable performance degradation of the frequency estimation accuracy. In addition, we bound and we also gain some important hints on the estimators to be used in this scenario.

In this paper, we derive low-complexity MAP symbol detection algorithms for continuous phase modulations (CPMs). To obtain this result, the well-known problem of a transmission over an additive white Gaussian noise (AWGN) channel affected by known intersymbol interference (ISI) is first 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, and in the derivation of the simplified algorithms for CPM signals.

In this paper, we present an iterative decoding algorithm for turbo and LDPC codes transmitted over channels affected by a time-varying phase noise and an uncompensated 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 numerical results for binary LDPC codes and LDPC-coded modulation schemes, showing that, despite its low complexity, the algorithm is able to cope with a strong phase noise and a significant uncompensated frequency offset, thus avoiding the use of complicated data-aided frequency estimation schemes operating on a known preamble.

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.

In this paper, we present a general approach to finite-memory detection. From a semi-tutorial perspective, a number of previous results are rederived and new insights are gained within a unified framework. A probabilistic derivation of the well-known Viterbi algorithm, forward-backward, and sum-product algorithms, shows that a basic metric emerges naturally under very general causality and finite-memory conditions. This result implies that detection solutions based on one algorithm can be systematically extended to other algorithms. For stochastic channels described by a suitable parametric model, a conditional Markov property is shown to imply this finite-memory condition. This conditional Markov property, although seldom met exactly in practice, is shown to represent a reasonable and useful approximation in all considered cases. We consider, as examples, linear predictive and noncoherent detection schemes. While good performance for increasing complexity can often be achieved with a finite-memory detection strategy, key issues in the design of detection algorithms are the computational efficiency and the performance for limited complexity.

In this paper, based on the application of the sum-product (SP) algorithm to factor graphs (FGs) representing the joint a posteriori probability (APP) of the transmitted symbols, we propose new iterative soft-input soft-output (SISO) detection schemes for intersymbol interference (ISI) channels. We have verified by computer simulations that the SP algorithm converges to a good approximation of the exact marginal APPs of the transmitted symbols if the FG has girth at least 6. For ISI channels whose corresponding FG has girth 4, the application of a stretching technique allows us to obtain an equivalent girth-6 graph. For sparse ISI channels, the proposed algorithms have advantages in terms of complexity over optimal detection schemes based on the Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm. They also allow a parallel implementation of the receiver and the possibility of a more efficient complexity reduction. The application to joint detection and decoding of low-density parity-check (LDPC) codes is also considered and results are shown for some partial-response magnetic channels. Also in these cases, we show that the proposed algorithms have a limited performance loss with respect to that can be obtained when the optimal "serial" BCJR algorithm is used for detection. Therefore, for their parallel implementation, they represent a favorable alternative to the modified "parallel" BCJR algorithm proposed in the literature for the application to magnetic channels.

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.

This paper presents a 2048 bit, rate 1/2 soft decision decoder for a new class of codes known as turbo Gallager codes. The decoder can support up to 1 Gbit/s code rate and performs up to 48 decoding iteration ensuring at the same time high throughput and good coding gain. In order to evaluate the performance and the gate complexity of the decoder VLSI architecture, it has been synthesized in a 0.18 /spl mu/m standard-cell CMOS technology.

In this paper, the problem of detection and decoding of low-density parity-check (LDPC) codes transmitted over channels with memory is addressed. A general method to build a factor graph which takes into account both the code constraints and the channel behavior is described and the a posteriori probabilities of the transmitted symbols are derived by using the sum-product algorithm. A noncoherent channel and a flat fading channel are considered as examples of application.

This paper proposes new algorithms for joint iterative decoding and parameter estimation in Bayesian and nonBayesian method. The low-density parity-check (LDPC) codes in the presence of phase noise is focused in this paper. The nonBayesian algorithm for an unknown phase channel is based on the application of the expectation-maximization (EM) algorithm. The proposed Bayesian algorithms are obtained as an application of the sum-product algorithm to the factor graph. Comparing the performance of the considered algorithms in the case of LDPC code, the EM-KL (EM-Karhunen-Loeve) algorithm performs better than EM-SW (sliding window) algorithm.

The subject of this paper is the asymptotic optimality of finite-memory detection for transmission over a channel characterized by a single multiplicative time-invariant stochastic parameter (e.g., block frequency nonselective fading). It is known that any finite-memory detection algorithm, either trellis-based or graph-based, is characterized by a single basic metric. We present a theorem which proves that this metric tends, asymptotically, to that of a receiver with perfect channel state information

The most powerful channel-coding schemes, namely, those based on turbo codes and low-density parity-check (LDPC) Gallager codes, have in common the principle of iterative decoding. However, the relative coding structures and decoding algorithms are substantially different. This paper shows that recently proposed novel coding structures bridge the gap between these two schemes. In fact, with properly chosen component convolutional codes, a turbo code can be successfully decoded by means of the decoding algorithm used for LDPC codes, i.e., the belief-propagation algorithm working on the code Tanner graph. These new turbo codes are here nicknamed "turbo Gallager codes." Besides being interesting from a conceptual viewpoint, these schemes are important on the practical side because they can be decoded in a fully parallel manner. In addition to the encoding complexity advantage of turbo codes, the low decoding complexity allows the design of very efficient channel-coding schemes.

We propose a general framework for detection over channels with infinite memory. A general truncation assumption leads automatically to the definition of a trellis diagram. A general approach to the design of forward-backward (FB) algorithms is proposed and two main classes of FB algorithms (with coupled and decoupled recursions, respectively) are presented. Moreover, it is shown that sequence detection algorithms, in the form of a Viterbi algorithm (VA), follow easily from one of the proposed classes. The generality of the proposed framework is shown by applying it to a few stochastic channels. The performance of the proposed algorithms seems to depend ultimately on the truncation length, almost irrespective of the specific detection strategy.

We propose a new space-time coding scheme for the quasi-static multiple-antenna channel with perfect channel state information at the receiver and no channel state information at the transmitter. In our scheme, codewords produced by a trellis encoder are formatted into space-time codeword arrays such that decoding can be implemented efficiently by minimum mean-square error (MMSE) decision-feedback interference mitigation coupled with Viterbi decoding, through the use of per-survivor processing. We discuss the code design for the new scheme, and show that finding codes with optimal diversity is much easier than for conventional trellis space-time codes (STCs). We provide an upper bound on the word-error rate (WER) of our scheme which is both accurate and easy to evaluate. Then, we find upper and lower bounds on the information outage probability with discrete independent and identically distributed (i.i.d). inputs (as opposed to Gaussian inputs, as in most previous works) and we show that the MMSE front-end yields a large advantage over the whitened matched filter (i.e., zero-forcing) front-end. Finally, we provide a comprehensive performance/complexity comparison of our scheme with coded vertical Bell Labs layered space-time (V-BLAST) architecture and with the recently proposed threaded space-time codes. We also discuss the concatenation of our scheme with block space-time precoders, such as the linear dispersion codes.

In this paper we consider iterative detection over bandpass channels which introduce an unknown phase rotation in the transmitted signal. We first introduce a unified formulation of adaptive forward-backward algorithms for channels with parametric uncertainty, including both recursive and non-recursive estimation strategies, and then apply this framework to a phase noncoherent channel. Two main classes of adaptive forward-backward algorithms are then considered and compared: closed-loop algorithms, which use explicit recursive phase estimation, and open-loop algorithms, which use implicit non-recursive phase estimation. We consider schemes with combined detection and decoding. Pilot symbols are inserted in order to cope with the unknown time-varying channel phase.

Provides an abstract of articles to be presented in a forthcoming issue.

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.

In a paper by Cavallini et al. (see IEEE Trans. Commun., vol. 45, p.456-63, Apr. 1997), chip-level differential encoding/detection for direct-sequence spread-spectrum signals was proposed to cope with frequency-nonselective fast fading channels. It was shown that, unlike in the additive white Gaussian noise channel, in time-varying fading channels the system performance may be considerably improved, especially when the spreading factor is increased. In this paper, noncoherent sequence detection, recently proposed by the authors, is the starting point for the derivation of receivers with improved performance with respect to that of standard differential detection. For M-ary phase-shift keying signals, a theoretical analysis is performed and the results are confirmed by means of computer simulation. The performance advantage of taking into account a larger phase memory, with respect to the minimum accounted for by differential detection, is demonstrated. In particular, the amount of phase memory is optimized as a function of the Doppler spread for a Rayleigh frequency-nonselective fading channel. The robustness in the presence of phase noise is also investigated by means of computer simulation.

We propose a new space-time coding scheme for the quasi-static multiple-antenna channel with perfect channel state information at the receiver and no channel state information at the transmitter. The new scheme includes both trellis space-time codes and layered space-time codes as special cases. Our scheme can be efficiently decoded by minimum mean-square error (MMSE) decision-feedback interference cancellation coupled with Viterbi decoding through the use of per-survivor processing (PSP). We discuss the code design for the new scheme, and show that finding codes with optimal diversity is much easier than for conventional trellis space-time codes.

We consider possible solutions for noncoherent decoding of concatenated codes with spectrally efficient modulations. Serially concatenated coding structures and possible schemes derived from turbo trellis coded modulation (T-TCM) are considered. In both cases, at the receiver side we consider joint detection and decoding. Since taking into account an augmented channel memory leads to an intolerable trellis size, we consider a recently proposed state-reduction technique.

We propose a technique to reduce the number of trellis states in BCJR-type algorithms, i.e., algorithms. with a structure similar to that of the well-known algorithm by Bahl, Cocke, Jelinek, and Raviv (1974). This work is inspired by reduced-state sequence detection (RSSD). The key idea is the construction, during one of the recursions in the reduced-state trellis, of a "survivor map" to be used in the other recursion. In a more general setting, two distinct survivor maps could be determined in the two recursions and used jointly to approximate the a posteriori probabilities. Three examples of application to iterative decoding are shown: (1) coherent detection for intersymbol interference (ISI) channels; (2) noncoherent detection based on an algorithm previously proposed by the authors; and (3) detection based on linear prediction for Rayleigh fading channels. As in classical RSSD, the proposed algorithm allows significant state-complexity reduction with limited performance degradation.

We address the use of the extrinsic information generated by each component decoder in an iterative decoding process. The BJCR algorithm proposed by Bahl et al. (1974) and the soft-output Viterbi algorithm (SOVA) are considered as component decoders. In both cases, we consider, in a unified view, various feedback schemes which use the extrinsic information in different fashions. Numerical results for a classical rate-1/2 turbo code and a serially concatenated code transmitted over a memoryless additive white Gaussian noise (AWGN) channel are provided. The performance of the considered schemes leads to interesting remarks about the nature of the extrinsic information.

We address maximum likelihood sequence detection (MLSD) for communications on flat Rayleigh fading channels. Making use of linear prediction we derive the structure of an oversampled detector which is computationally efficient and can easily accommodate a time varying Doppler frequency. This goal is achieved through a specific analytical derivation of the prediction coefficients which appear in the metric of the sequence detector. For fractionally-spaced observations, we derive the constraints which allows one to establish an explicit relationship between the set of observation predictors and the set of fading predictors. Then, the equivalence between different classes of prediction-based detectors is shown. The numerical results give useful indications to balance the complexity of these detectors in terms of prediction order, description of intersymbol interference and oversampling.

We propose a technique to reduce the number of trellis states in BCJR-type algorithms, i.e., algorithms with a structure similar to that of the well-known algorithm by Bahl, Cocke, Jelinek and Raviv (1974). This work is inspired by reduced-state sequence detection (RSSD). The key idea is the construction, during one of the recursions, of a "survivor map", on a reduced-state trellis, to be used in the other recursion. Two examples of application of the proposed technique to iterative decoding structures are shown, namely coherent detection over intersymbol interference (ISI) channels and noncoherent detection based on an algorithm previously proposed by the authors.

The previously proposed noncoherent sequence detection (NSD) algorithms have a performance which approaches that of coherent detectors and are robust to phase 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, two 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 (M-PSK) and quadrature amplitude modulation (M-QAM).

A new class of noncoherent sequence detection (NSD) algorithms for combined demodulation and decoding of any coded linear and continuous phase modulations, transmitted over additive white Gaussian noise (AWGN) channels, has been previously presented. In this paper, this class is generalized to the case of frequency nonselective Rayleigh or Rice slowly fading channels, in the presence or absence of channel state information. Coded linear modulations, namely M-ary phase shift keying (M-PSK) and quadrature amplitude modulation (M-QAM), are considered. The proposed detection schemes have a performance which approaches that of coherent detectors, are very robust to phase and frequency instabilities, and compare favorably to other solutions previously proposed in the technical literature.

Previously, noncoherent sequence detection schemes for coded linear and continuous phase modulations have been proposed, which deliver hard decisions by means of a Viterbi algorithm. The current trend in digital transmission systems toward iterative decoding algorithms motivates an extension of these schemes. In this paper, we propose two noncoherent soft-output decoding algorithms. The first solution has a structure similar to that of the well-known algorithm by Bahl et al. (1974), whereas the second is based on noncoherent sequence detection and a reduced-state soft-output Viterbi algorithm. Applications to the combined detection and decoding of differential or convolutional codes are considered. Further applications to noncoherent iterative decoding of turbo codes and serially concatenated interleaved codes are also considered. The proposed noncoherent detection schemes exhibit moderate performance loss with respect to corresponding coherent schemes and are very robust to phase and frequency instabilities.

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).

The capacity of a random-phase additive white Gaussian noise (AWGN) channel, referred to as noncoherent channel, is investigated in the case of a transmission of N information symbols. The non-Gaussianity of the capacity achieving distribution is shown and a lower bound on the channel capacity is derived. For increasing values of the number of transmitted symbols N, the capacity of a noncoherent channel is shown to asymptotically approach that of a coherent channel, i.e., a known-phase AWGN channel. The asymptotical Gaussianity of the capacity-achieving distribution is also shown. Based on the derived lower bound, the inherent capacity loss of a noncoherent channel, as compared to a coherent one may be considered very limited for values of N of a few units or a ten. This result may be viewed as the information theoretic counterpart of a similar conclusion derived by many authors with reference to the probability of detection error.

Colavolpe and Raheli have proposed (see Proc. IEEE Intern. Conf. Univ. Pers. Commun. (ICUPC'98), Florence, Italy, October 1998, and Proc. Global Commun. Conf., (GLOBECOM'98), Sydney, Australia, 1998), noncoherent sequence detection schemes for any coded modulation. These schemes produce hard decisions via a Viterbi algorithm. The current trend in digital transmission systems toward iterative decoding algorithms motivates an extension of these schemes. We propose a noncoherent soft-output algorithm for coded linear modulations whose structure is similar to that of the well-known algorithm by Bahl et al. (1974). The application to the case of combined detection and decoding of differential or convolutional codes is considered and comparisons with noncoherent sequence detection are performed. As an example of application to iterative processing, noncoherent decoding of turbo codes is considered.

In this paper, noncoherent sequence detection, proposed in a companion paper by Colavolpe and Raheli (see ibid. vol.47, no.9, p.1376-85, 1999), is extended to the case of continuous phase modulations (CPMs). The results in the companion paper on linear modulations with intersymbol interference (ISI) are used here because a CPM signal is mathematically equivalent to a sum of ISI-affected linearly modulated components, according to the Laurent decomposition. The proposed suboptimal detection schemes have a performance which approaches that of coherent detection with acceptable complexity, allow for time-varying phase models, and compare favorably with previously proposed solutions.

New noncoherent sequence detection algorithms for combined demodulation and decoding of coded linear modulations transmitted over additive white Gaussian noise channels, possibly affected by intersymbol interference, are presented. Optimal sequence detection in the presence of a random rotation of the signal phase, assumed to be constant during the entire transmission, requires a receiver complexity exponentially increasing with the duration of the transmission. Based on proper approximations, simple suboptimal detection schemes based on the Viterbi algorithm are presented, whose performance approaches that of coherent detection. In a companion paper by Colavolpe and Raheli (see ibid., vol.47, no.9, p.1303-7, 1999), noncoherent sequence detection is extended to continuous phase modulations. In the proposed schemes, the tradeoff between complexity and performance is simply controlled by a parameter, referred to as implicit phase memory, and the number of states of a trellis diagram. Besides being realizable, these schemes have the convenient feature of allowing us to remove the constant phase assumption and encompass time-varying phase models. The proposed schemes compare favorably with other solutions previously proposed in the technical literature.

In this paper, we present a theoretical performance analysis of noncoherent schemes for the combined sequence detection and decoding of coded M-ary phase shift keying (M-PSK) signals (Colavolpe and Raheli 1997). Based on the classical union bound, we describe a method for the numerical evaluation of the pairwise error probability, for which no closed-form expressions exist, and compare results with computer simulations. We also present an upper bound to this pairwise error probability which may be effectively used for an exhaustive search of optimal codes. This bound allows us to prove that the noncoherent sequence detection schemes proposed in Colavolpe and Raheli perform as well as an optimal coherent receiver when an implicit phase memory parameter is sufficiently large. In the case of differentially encoded M-PSK, we derive a simple expression for the asymptotic bit error probability which is in agreement with simulations for high as well as low signal-to-noise ratio.

Based on an extension of Laurent (1986) decomposition of continuous phase modulation (CPM) signals into a sum of linearly modulated components, we derive a class of reduced-complexity maximum-likelihood (ML) coherent detection and closed-loop phase synchronization schemes. The complexity of the resulting detection schemes is significantly reduced with respect to that of optimal coherent receivers with negligible performance loss. This result extends a known one valid for the binary case to multilevel CPM. The proposed synchronization schemes are perfectly suitable to be used in conjunction with these receivers.

We present new non-coherent sequence detection algorithms for M-ary phase shift keying (M-PSK) signals transmitted over additive white Gaussian noise (AWGN) channels. We first consider the problem of optimal sequence detection in the presence of an unknown channel phase modeled as stochastic with uniform distribution and constant during the entire transmission. In this case, the complexity of the optimal receiver depends exponentially on the duration of the transmission. We then introduce some approximations in order to realize simple suboptimal detection schemes based on the Viterbi algorithm (VA) whose performance approaches that of coherent detection. Besides being realizable, the proposed suboptimal schemes have the convenient feature of allowing us to remove the assumption of constant phase during transmission. We show that our detection schemes compare favorably with other solutions previously proposed in the literature for both differentially and non-coherent coded modulations.

Based on an extension of Laurent (1986) decomposition of continuous phase modulation (CPM) signals into a sum of linearly modulated components, we derive a class of reduced-complexity maximum-likelihood (ML) coherent detection and closed-loop phase synchronization schemes. The complexity of the resulting detection schemes, expressed in terms of the number of matched filters and states of a Viterbi algorithm, is significantly reduced with respect to that of optimal coherent receivers with negligible performance loss. This result extends a known one valid for the binary case to multilevel CPM. The proposed synchronization schemes do not require an increased number of matched filters, and are perfectly suitable to be used in conjunction with these receivers. Based on the phase-locked loop (PLL) equivalent linear model, a method for optimizing the parameters of digital second-order PLL's is presented. Numerical examples, based on theoretical analysis and computer simulation, are provided for two specific formats in the CPM class: tamed frequency modulation (TFM) and a quaternary raised-cosine (RC) modulation.