Giulio Colavolpe

Algorithms for iterative decoding in the presence of strong phase noise

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

Modulation Formats and Waveforms for 5G Networks: Who Will Be the Heir of OFDM?: An overview of alternative modulation schemes for improved spectral efficiency

Fifth-generation (5G) cellular communications promise to deliver the gigabit experience to mobile users, with a capacity increase of up to three orders of magnitude with respect to current long-term evolution (LTE) systems. There is widespread agreement that such an ambitious goal will be realized through a combination of innovative techniques involving different network layers. At the physical layer, the orthogonal frequency division multiplexing (OFDM) modulation format, along with its multiple-access strategy orthogonal frequency division multiple access (OFDMA), is not taken for granted, and several alternatives promising larger values of spectral efficiency are being considered. This article provides a review of some modulation formats suited for 5G, enriched by a comparative analysis of their performance in a cellular environment, and by a discussion on their interactions with specific 5G ingredients. The interaction with a massive multiple-input, multiple-output (MIMO) system is also discussed by employing real channel measurements.

Noncoherent sequence detection

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.

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

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

Noncoherent iterative (turbo) decoding

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.

Noncoherent sequence detection of continuous phase modulations

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.

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

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

Robust Multilevel Coherent Optical Systems With Linear Processing at the Receiver

This paper investigates optical coherent systems based on polarization multiplexing and high-order modulations such as phase-shift keying (PSK) signals and quadrature amplitude modulations (QAM). It is shown that a simple linear receiver processing is sufficient to perfectly demultiplex the two transmitted streams and to perfectly compensate for group velocity dispersion (GVD) and polarization mode dispersion (PMD). In addition, in the presence of a strong phase noise of the lasers at the transmitter and receiver, a symbol-by-symbol detector with decision feedback is able to considerably improve the receiver robustness with a limited complexity increase. We will also discuss the channel estimation and the receiver adaptivity to time-varying channel conditions as well as the problem of the frequency acquisition and tracking. Finally, a new two-dimensional (polarization/time) differential encoding rule is proposed to overcome a polarization-ambiguity problem. In the numerical results, the receiver performance will be assessed versus the receiver complexity.

Extrinsic information in iterative decoding: a unified view

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.

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

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