We address the post-compensation of nonlinear distortion in precoded orthogonal frequency division multiplexing signals caused by power amplifier impairments. An iterative message-passing receiver is proposed, using generalized approximate message passing to perform OFDM demodulation and nonlinearity compensation, while deriving new messages towards the equalizer to establish a turbo-equalization scheme. Additionally, the complex integral required for GAMP is simplified, reducing it to a one-dimensional integral that can be computed numerically. The proposed receiver significantly outperforms previous GAMPbased distortion compensation techniques.

We address joint channel estimation and data detection under unknown non-linearity caused by impaired power amplifiers. Using a Bayesian model with hidden variables for data, channel, and amplifier characteristics, we design a semi-blind probabilistic receiver for channel and non-linearity compensation coupled with decoding to minimize the number of pilot symbols. Simulations show high tolerance of the proposed receiver to unknown linear and non-linear impairments, with reasonable computation complexity.

This paper presents a new approach to reservoir computing (RC) optimization. Reservoir computing (RC) is a framework for building recurrent neural networks (RNNs) that alleviates the well-known learning difficulties in such neural networks by training only the output layer. While the weights of the input and the nonlinear hidden layers are randomly generated, the adjustment of critical hyperparameters, such as the input and the feedback scaling factor, is essential for optimal performance in RC. While recent hardware implementations of RC are crucial for high-speed processing, standard gradient-based hyperparameter optimization is often irrelevant due to potentially uncertain or time-varying internal functions and parameters. In this work, we propose and analyze a stochastic optimization approach using gradient approximations based solely on noisy measurements of the loss function to circumvent this problem. Our numerical and experimental results confirm that the proposed method can provide near-optimal RC hyperparameters with substantial complexity reduction compared to competing methods, validating its potential for RC optimization.

Grant-free non-orthogonal multiple access is an emerging communication paradigm, where devices transmit to an access point without explicit permission. However, unknown user activities add discrete latent variables on top of the usual hidden variables (accounting for channels and data), thus rendering exact inference - in the form a mixture of underlying distributions growing with time - intractable. Thus low-complexity user activity detection with reliable approximate distributed inference in the form of message-passing is relevant. We propose a new generic expectation propagation solution in the form of complex Gaussian distributions, that are consistently derived using a Wirtinger calculus-based second-order approximation. The proposed algorithm is then integrated with expectation propagation for other tasks (channel estimation, symbol detection and decoding) in a fully Bayesian inference setting. The main outcome is an excellent tradeoff between user missed detections and false alarms in a non-orthognal multiple access context, thus enabling further complexity reduction by gradually disabling message-passing for successfully identified inactive users. Numerical results demonstrate the superiority of the proposed method over similar approximations.

In grant-free non-orthogonal multiple access, the set of active users is unknown a priori. We address the challenging problem of dynamic channel estimation in this context. Assuming that inactive users are completely muted (in order to avoid unwanted pilot/preamble interference on active users), we investigate a channel estimation method performed jointly with user activity detection, multi-user detection and decoding. Leveraging conditional independence assumptions in probabilistic modeling, we introduce a low-complexity channel estimation performing expectation propagation in parallel for the measurements over all receive antennas. The proposed channel estimation technique is evaluated under different receive antenna correlation models and shows a good performance/complexity tradeoff with respect to joint measurement processing.

When the state space dimension increases, the computational burden can become a major challenge for optimal Kalman filtering in Gaussian triplet Markov models (TMMs). In this paper, we introduce a new model order reduction technique applicable to linear time-homogeneous Gaussian TMMs. Taking advantage of the lower state dimension of the resulting approximate model, a low-complexity suboptimal Kalman filter is obtained. The proposed estimator provides complexity reduction without significant accuracy loss and is shown to outperform two classical methods in the case of Markovian process noise.

A new lower bound is proposed in this article. Like Levenshtein bound, it relates to the maximum correlation value (autocorrelation and cross-correlation) a set of sequences can achieve. The novelty introduced here is that each sequence is associated with a mismatched filter. The proposed bound is inspired from Levenshtein's, holds for any set of unimodular sequences and can be applied in both aperiodic and periodic cases. It appears that the obtained expression does not deviate a lot from the (matched) Levenshtein, which indicates that the use of a mismatched filter will not guarantee much better sidelobe performance, as the number fo sequences is significant, contrary to the popular belief.

Digital self-interference cancellation is a major challenge for orthogonal frequency division multiplexing full-duplex transmissions. Therefore, reliable estimation of both the signal-of-interest and the self-interference channel, becomes the limiting factor in a mobile radio context. In this letter, improved estimation of the time-varying channels is obtained by solving the problem jointly with self-interference cancellation and decoding using a factor graph approach. Taking advantage of the per-subcarrier structure of message-passing, a low-complexity receiver is obtained. Our semianalytical and numerical results show the superiority of the proposed scheme over state-of-the art self-interference cancellation methods under limited pilot overhead.

We consider cooperative communications between a source node and a destination node with the help of two relays. In order to overcome the half-duplex constraint, the amplify-and-forward two-path relaying protocol is used. We adopt orthogonal frequency-division multiplexing modulation to combat frequency-selective channels and asynchronous reception at the destination node. In this paper, we develop a coherent receiver architecture suitable for unknown block fading channels. A factor graph representing the joint a posteriori probability of the coded symbols and the channels in the frequency domain is introduced. Then, we derive a Bayesian inference algorithm based on message passing over the factor graph. The resulting iterative receiver maintains low-complexity, based on the interaction between an off-the-shelf soft-input soft-output decoder and a newly introduced per-subcarrier processor for two-path relaying channel estimation and symbol detection. Simulation results show that the proposed solution maintains the full diversity order, even with a limited number of training blocks.

Wireless sensor networks (WSN) are specially distributed sensors deployed for the purpose of sensing and monitoring physical or environmental conditions. Sensor measurements in WSN usually suffer from both random errors (noise) and systematic errors (bias). This poses a major problem in the end application, as the data from the network become progressively uninformative.

We present a method for joint decode-and-forward physical layer network coding in two-way relay networks. The two source nodes send their packets simultaneously over time-varying channels to a relay node, then the relay broadcasts the received superimposed packets to the source nodes using network coding. The nodes use trellis coding for the sake of error correction and multi-antenna equipments to combat multipath fading. A challenging multiple access problem occurs at the relay node, which performs joint channel estimation and decoding for the individual source packets. We design message passing algorithms based on factor-graphs to solve this problem. The relay has two separate modules that perform channel estimation and decoding for the packets received from each source node. The interference generated by the other source node is taken into account by exchanging messages between the two modules.

We consider physical network coding on a two-way relay channel. Two source nodes send their packets simultaneously over time-varying MIMO channels to a relay node. Assuming that the relay employs the joint decode-and-forward strategy, the relay must be able to decode the individual source packets. This task requires a robust estimation of the source-to-relay channels. We design a message passing algorithm based on factor-graphs to solve this problem efficiently.

We consider the problem of semi-supervised segmentation of textured images. Recently, reweighted belief propagation has been introduced as a solution for Bayesian inference with respect to the maximum posterior mode criterion. In this pa per, we show how to adapt reweighted belief propagation to the problem of segmentation of textured images. An adaptive parameter estimation technique is also provided. Then, we compare classical simulated annealing with the recently introduced reweighted belief propagation algorithm, in terms of segmentation results.

We consider the problem of semi-supervised segmentation of textured images. Existing model-based approaches model the intensity field of textured images as a Gauss-Markov random field to take into account the local spatial dependencies between the pixels. Classical Bayesian segmentation consists of also modeling the label field as a Markov random field to ensure that neighboring pixels correspond to the same texture class with high probability. Well-known relaxation techniques are available which find the optimal label field with respect to the maximum a posteriori or the maximum posterior mode criterion. But, these techniques are usually computationally intensive because they require a large number of iterations to converge. In this paper, we propose a new Bayesian framework by modeling two-dimensional textured images as the concatenation of two one-dimensional hidden Markov autoregressive models for the lines and the columns, respectively. A segmentation algorithm, which is similar to turbo decoding in the context of error-correcting codes, is obtained based on a factor graph approach. The proposed method estimates the unknown parameters using the Expectation-Maximization algorithm.

We consider the equalization of two-dimensional intersymbol interference (2D ISI) channels. We propose a message passing algorithm based on Gaussian belief propagation (GaBP) to perform joint decoding and equalization. While in existing 2D equalizers the complexity is exponential in the length of the state-space, the complexity is only polynomial for the proposed algorithm. This enables to handle 2D channels with long memory with a tractable computational complexity.

We consider blind equalization for block transmissions over the frequency selective Rayleigh fading channel. In the absence of pilot symbols, the receiver must be able to perform joint equalization and blind channel identification. Relying on a mixed discrete-continuous state-space representation of the communication system, we introduce a blind Bayesian equalization algorithm based on a Gaussian mixture parameterization of the a posteriori probability density function (pdf) of the transmitted data and the channel. The performances of the proposed algorithm are compared with existing blind equalization techniques using numerical simulations.

Blind coherent detection of convolutional turbo codes is a hard problem in the presence of strong phase noise. Since the operating signal-to-noise ratio is usually very low, phase synchronisation algorithms suffer from phase ambiguities and cycle slips. A possible remedy is to perform joint phase estimation and decoding on a combined state-space model for the time-varying phase and the component convolutional codes. We demonstrate that joint phase estimation and decoding is in fact mandatory only for one component code, while ordinary BCJR decoding can be used for the second component code. Monte Carlo simulations for the turbo code used in the DVB-RCS standard show that the performances of the proposed scheme are close to decoding with perfect knowledge of the phase.

We present a joint phase estimation and decoding method for convolutional turbo codes in the presence of strong phase noise. In order to overcome the problem of phase ambiguity and cycle slips, a combined state-space model for the time varying phase and the component convolutional codes is introduced. The proposed algorithm uses a Gaussian sum approach to approximate the multimodal a posteriori probability density function (pdf) of the phase in a blind context. We compare our method to the well known alternative consisting in discretizing the phase.Monte-Carlo simulations for the turbo code used in the DVB-RCS standard show that the performances of the proposed scheme are close to decoding with perfect knowledge of the phase.

We present a joint channel estimation and decoding method for space-time trellis codes (STTC) transmitted over an unknown flat fading multiple-input multiple-output (MIMO) channel. In a blind context, i.e. when pilot symbols are not available, we will show that the probability density function (pdf) of the MIMO channel becomes multimodal due to phase ambiguities. To address this problem, a combined state-space model for the time-varying MIMO channel and the STTC is introduced. The proposed algorithm then uses a Gaussian mixture approach to perform joint channel estimation and soft-output detection. We compare our method to several well known algorithms obtained by collapsing the Gaussian mixture to a single Gaussian distribution. A comparison with sequential Monte Carlo methods is also included. Numerical simulations show that the performances of the proposed blind STTC decoder are close to decoding with perfect channel state information (CSI). As a useful application of the proposed soft-output algorithm, we provide an example of blind iterative decoding of concatenated space-time codes.

We present a joint phase estimation and decoding method for convolutional turbo codes in the presence of strong phase noise. In order to overcome the problem of phase ambiguity and cycle slips, a combined state-space model for the time-varying phase and the component convolutional codes is introduced. The proposed algorithm uses a Gaussian sum approach to approximate the multimodal a posteriori probability density function (pdf) of the phase in a blind context. Monte-Carlo simulations for the turbo code used in the DVB-RCS standard show that the performances of the proposed scheme are close to decoding with perfect knowledge of the phase.

We present a joint channel estimation and detection method of space-time trellis codes (STTC) in the context of an unknown flat fading multiple-input multiple-output (MIMO) channel. A combined state-space model for the space-time code and the Rayleigh fading MIMO channel is introduced, in order to use deterministic particle filtering at the receiver side. An important feature of the proposed method is that the fading rate need not be known to the receiver. Monte-Carlo simulations show that the performances of the proposed scheme are close to decoding with perfect channel state information (CSI) using the Viterbi algorithm (VA).

Iterative decoding algorithms may be viewed as high-dimensional nonlinear dynamical systems, depending on a large number of parameters. In this work, we introduce a simplified description of several iterative decoding algorithms in terms of the a posteriori average entropy, and study them as a function of a single parameter that closely approximates the signal-to-noise ratio (SNR). Using this approach, we show that virtually all the iterative decoding schemes in use today exhibit similar qualitative dynamics. In particular, a whole range of phenomena known to occur in nonlinear systems, such as existence of multiple fixed points, oscillatory behavior, bifurcations, chaos, and transient chaos are found in iterative decoding algorithms. As an application, we develop an adaptive technique to control transient chaos in the turbo-decoding algorithm, leading to a substantial improvement in performance. We also propose a new stopping criterion for turbo codes that achieves the same performance with considerably fewer iterations.

In this correspondence, we introduce a simple one-dimensional (1-D) nonlinear map to describe the iterates of the bit-error rate (BER) of parallel-concatenated convolutional codes (PCCC) on the binary-input Gaussian channel. A lower bound on this map is derived based upon the weight enumerator of the constituent codes, thus enabling the characterization of the dynamics of the decoder in terms of fixed points, along with the associated stability analysis.

Interleaved convolutional time hopping (ICTH) is a recently proposed coding/modulation scheme for UWB impulse radio. ICTH is based upon a low-rate convolutional code, with optimized distance properties, combined with multilevel pulse-position modulation (PPM). In this context, bit-interleaved coded modulation (BICM) is used to decorrelate the bit errors and, more importantly, to obtain a flat spectrum. We present analytical bounds for the BER (bit-error-rate) performance of ICTH and an analysis of its spectral properties.

We propose a novel density evolution approach to analyze the iterative decoding algorithms of low-density parity-check (LDPC) codes and product codes, based on Gaussian densities. Namely, for these classes of codes we derive a one-dimensional (1D) map whose iterates directly represent the error probability both for the additive white Gaussian noise (AWGN) and the Rayleigh-fading channel. These simple models allow a qualitative analysis of the nonlinear dynamics of the decoding algorithm. As an application, we compute the decoding thresholds and show that they are consistent with the simulation results available in the literature.

In this paper we introduce a model of the iterative decoding of product codes. For each iteration, an approximation of the bit error rate (BER) at the output of the decoders is used to evaluate the density of the extrinsic information. The decoding thresholds obtained for the additive white Gaussian noise (AWGN) and the Rayleigh fading channel are consistent with the simulation results available in the literature.

Pseudochaotic time hopping (PCTH) is a previously proposed encoding/modulation scheme for ultra-wideband (UWB) impulse radio. PCTH exploits concepts from symbolic dynamics to generate aperiodic spreading sequences, resulting in a noise-like spectrum. We present a multiple-access technique suitable for the PCTH scheme. In particular, we provide an analytical expression of the bit-error rate performance as a function of the number of users and validate it by simulation.