In this paper, we propose generalizations of the de Bruijn identity based on extensions of the Shannon entropy, Fisher information and their associated divergences or relative measures. The foundations of these generalizations are the φ-entropies and divergences of the Csiszár (or Salicrú) class considered within a multidimensional context, including the one-dimensional case, and for several types of noisy channels characterized by a more general probability distribution beyond the well-known Gaussian noise. We found that the gradient and/or the Hessian of these entropies or divergences with respect to the noise parameter naturally give rise to generalized versions of the Fisher information or divergence, which are named the φ-Fisher information (divergence). The obtained identities can be viewed as further extensions of the classical de Bruijn identity. Analogously, it is shown that a similar relation holds between the φ-divergence and an extended mean-square error, named φ-mean square error, for the Gaussian channel.

In wireless networks, interferences between transmissions are modelled either in time or frequency domain. In this article, we jointly analyze interferences in the time-frequency domain using a stochastic geometry model assuming the total time-frequency resources to be a two-dimensional plane and transmissions from Internet of Things (IoT) devices time-frequency patterns on this plane. To evaluate the interference, we quantify the overlap between the information packets: provided that the overlap is not too strong, the packets are not necessarily lost due to capture effect. This flexible model can be used for multiple medium access scenarios and is especially adapted to the random time-frequency access schemes used in Low-Power Wide-Area Networks (LPWANs). By characterizing the outage probability and throughput, our approach permits to evaluate the performance of two representative LPWA technologies Sigfox®and LoRaWAN®.

We consider the joint detection and decoding of m-sequences. The receiver has to decide whether an m-sequence is received and possibly to decode its initial state. To do so, it implements an iterative message-passing decoding algorithm that operates on a parity check matrix, built upon a number of reference parity-check equations satisfied by the m-sequence. This matrix concatenates several elementary parity check matrices which are derived from reference equations. Unlike the conventional decoding case, the detection problem imposes to consider false alarms that may occur when the decoder is only fed with noise. While absorbing sets are known to be responsible for the error floor phenomenon of iterative message-passing decoders, we show that they may have a beneficial effect on the detection performance, in that they may prevent the decoder to produce false alarms. We further compute the number of hybrid cycles of length six and eight in the Tanner graph of the decoder and use the minimization of this number as criterion to derive an algorithm for selecting the reference parity check equations. This algorithm was found to be efficient for minimizing the probability of false alarm and decreases also the probability of wrong detection in the very small SNR region. This has been achieved at the cost of a reduction of the probability of correct detection.

Gold sequences are widely used in communications and positioning systems for synchronization purposes or spread spectrum transmissions. This paper addresses the decoding of the initial state of a Gold sequence. This can be used to detect a harmful interferer closed to a 3G femtocell base station and implement interference mitigation techniques. The decoder implements an iterative message-passing algorithm which is built upon a parity check matrix. Thus, it depends on the coding properties of Gold codes. In this paper, we synthesize the coding properties of Gold codes and use them to compute the number of parity check equations of weight t = 3, 4 or 5. Eventually, the impact of the parity check equations used for decoding is highlighted.

Estimation of a location parameter based on noisy and binary quantized measurements is considered in this letter. We study the behavior of the Cramér-Rao bound as a function of the quantizer threshold for different symmetric unimodal noise distributions. We show that, in some cases, the intuitive choice of threshold position given by the symmetry of the problem, placing the threshold on the true parameter value, can lead to locally worst estimation performance.

An adaptive algorithm to estimate jointly unknown location and scale parameters of a sequence of symmetrically distributed independent and identically distributed random variables using quantized measurements from a quantizer with adjustable input gain and input offset is presented. The asymptotic variance of estimation is obtained, simulations under Cauchy and Gaussian distributions are presented to validate the asymptotic results and they are compared to the continuous optimal estimator performance.

In this paper, the asymptotic approximation of the Fisher information for the estimation of a scalar parameter based on quantized measurements is studied. As the number of quantization intervals tends to infinity, it is shown that the loss of Fisher information due to quantization decreases exponentially as a function of the number of quantization bits. The optimal quantization interval density and the corresponding maximum Fisher information are obtained. Comparison between optimal nonuniform and uniform quantization for the location estimation problem indicates that nonuniform quantization is slightly better. At the end of the paper, an adaptive algorithm for jointly estimating and setting the thresholds is used to show that the theoretical results can be approximately obtained in practice.

In this paper, the tracking of a slowly varying scalar Wiener process based on quantized noisy measurements is studied. An adaptive algorithm using a quantizer with adjustable input gain and bias is presented as a low complexity solution. The mean and asymptotic mean squared error of the algorithm are derived. Simulations under Cauchy and Gaussian noise are presented to validate the results and a comparison with the optimal estimator in the Gaussian and real-valued measurement case shows that the loss of performance due to quantization is negligible using 4 or 5 bits of resolution.

Interference between macro and femtocells is an important issue for the development of WCDMA femtocell networks. More specifically, the uplink signal of a macro User Equipment may generate an unacceptable level of interference at the femto Base Station. To avoid this situation, interference mitigation techniques could be implemented. All the proposed techniques require the knowledge of the uplink scrambling code index of the interferer. Unfortunately, if the femto BS is in a closed access mode, there are no signalling links with the surrounding macro BSs. The femto BS has to estimate blindly this scrambling code index. An algorithm which performs a blind identification of the uplink scrambling code index of a WCDMA transmission is proposed in this article. This gives the possibility to implement interference cancelation algorithm at the femto BS.

Interference between macro and femtocells is an important issue for the development of CDMA2000 femtocell networks. More specifically, the reverse link signal of a macro User Equipment may generate an unacceptable level of interference at the femto Base Station. To avoid this situation, interference mitigation techniques could be implemented. All the proposed techniques require to know the state of the scrambling code of the interferer in the reverse link. Unfortunately, it depends on the code mask of the terminal which is unknown by the femto BS. The femto BS has to estimate blindly the state of the scrambling code. An algorithm which performs a blind identification of the scrambling code of a CDMA2000 reverse link transmission is proposed in this article. This gives the possibility to implement interference cancelation algorithm at the femto BS.

In this paper, the issue of audio source separation from a single channel is addressed, i.e., the estimation of several source signals from a single observation of their mixture. This challenging problem is tackled with a specific two levels coder-decoder configuration. At the coder, source signals are assumed to be available before the mix is processed. Each source signal is characterized by a set of parameters that provide additional information useful for separation. We propose an original method using a watermarking technique to imperceptibly embed this information about the source signals into the mix signal. At the decoder, the watermark is extracted from the mix signal to enable an end-user who has no access to the original sources to separate these signals from their mixture. Hence, we call this separation process informed source separation (ISS). Thereby, several instruments or voice signals can be segregated from a single piece of music to enable post-mixing processing such as volume control, echo addition, spatialization, or timbre transformation. Good performances are obtained for the separation of up to four source signals, from mixtures of speech or music signals. Promising results open up new perspectives in both under-determined source separation and audio watermarking domains.

This paper addresses the joint path delay and time-varying complex gain estimation for continuous phase modulation (CPM) over a time-selective slowly varying flat Rayleigh fading channel. We propose an expectation-maximization (EM) algorithm for path delay estimation in a Kalman smoother framework. The time-varying complex gain is modeled by a first order autoregressive (AR) process. Such a modeling yields to the representation of the problem by a dynamic Bayesian system in a state-space form that allows the application of EM algorithm in the context of unobserved data for obtaining an estimate of the path delay. This is used with Kalman smoother for state estimation. We derive analytically a closed-form expression of the modified hybrid Cramer-Rao bound (MHCRB) for path delay and complex gain parameters. Finally, some numerical examples are presented to illustrate the performance of the proposed algorithm compared to the conventional generalized correlation method and to the MHCRB.

This paper deals with the on-line estimation of a dynamical carrier phase and a frequency offset in a digital receiver. We consider a Brownian phase evolution with a linear drift in a data aided scenario. The proposed study is relative to the use of an oversampled signal model after matched filtering, leading to a coloured reception noise and a non-stationary power signal. We derive a closed-form expression of the hybrid Cramer-Rao bound (HCRB) for this estimation problem. We use a binary offset carrier (BOC) function as shaping pulse. Our numerical results show the potential gain of using the oversampled signal for estimating the dynamical phase and frequency offset, obtaining better performances than using a classical synchronizer.

In this paper, we address the issue of audio source separation with a single channel, i.e. the estimation of source signals from a single mixture of these signals. This problem is addressed with a specific configuration: source signals are assumed to be available before the mix is processed. We propose an original method that uses a watermarking technique to embed information about the source signals into the mix signal. Extracting this watermark enables an end-user who has no access to the original sources to separate these signals from their mixture. Thereby several instruments or voice signals can be segregated from a single piece of music to enable post-mixing processing such as volume control.

In this paper, we present an application of the Extended Kalman Filter for the on-line estimation of a dynamical carrier phase offset. The novel approach implies deriving the filter in an oversampled scenario in a digital receiver. We consider a Brownian phase evolution in a Data Aided scenario. Our numerical results using a BOC shaping pulse show that using the oversampled signal for estimating the phase offset we can obtain better performances than using a classical synchronizer.

This paper presents a near-optimum, low-complexity, fixed-interval smoothing algorithm that approaches the performance of an optimal smoother for the price of two low-complexity sequential estimators (two PLLs). The proposed Smoothing PLL (S-PLL) algorithm is easy to implement and fits the Cramer-Rao bounds over a wide range of signal-to-noise ratios. Moreover we show that, compared to the conventional forward loop, the proposed scheme allows to have a large gain of several dBs and is able to track frequency offsets.

This letter deals with the CramrRao bound for the estimation of a hybrid vector with both random and deterministic parameters. We point out the specificity of the case when the deterministic and the random vectors of parameters are statistically dependent. The relevance of this expression is illustrated by studying a practical phase estimation problem in a non-data-aided communication context.

In this letter we present a low-complexity architecture designed for the decoding of block turbo codes. In particular we simplify the implementation of Pyndiah's algorithm by not storing any of the concurrent codewords generated by the list decoder.

Iterated function systems (EFS) is a relevant model to produce fractal functions, whether deterministic (with strict self-similarity) or random (self-similar up to probability distribution). The basic idea of such a construction is to start with an initial function and then compress, dilate and translate it such that by doing so over and over again, we end up with a self-similar signal. This construction relies on a construction tree which has always been deterministic in the literature for signals. Here we introduce new fractals, called Galton Watson fractals, as fixed points of IFS with a random underlying construction tree and deterministic operators. We give a proof of the existence and uniqueness of a fixed point at the random and distribution level.

This paper describes several power mask designs for local loop multi-carrier transmission. The proposed algorithms exploit the signal to noise and interference ratio knowledge at the transmitter in order to maximize the overall bit rate. This design prevents from the multiple large constellations soft-demapping burden by using a single mid-size Quadrature Amplitude Modulation (QAM). We illustrate the algorithms performance by giving results for Very high bit rate Digital Suscriber Line (VDSL) systems.

This letter presents an original phase synchronization scheme designed for block turbo coded systems. This is a low-complexity scheme. It copes with low signal-to-noise ratios, taking complete advantage of the turbo coding possibilities. We display various results, showing that the proposed algorithm is able to process blocks of a few hundreds bits and that it tackles the case of large quadrature amplitude modulation constellations very well and with no phase ambiguity.

This paper concerns a new synchronizing scheme designed for block turbo coded system. The phase estimation relies on the feedback of the extrinsic information. A near optimum version of the algorithm based on the block turbo decoder devised by Pyndiah allows easy implementation. We display various results showing that the proposed algorithm is able to track frequency shifts and that it works very well in the case of general Quadrature Amplitude Modulation (QAM) constellations. We also show that this turbo synchronizer works at low Signal to Noise Ratios (SNR) taking completely advantage of the turbo coding possibilities.

Use of antenna arrays at both sides of the communication link can result in high channel capacities provided that the propagation medium is rich scattering. Previous studies on MIMO wireless structures have mostly considered Rayleigh fading conditions. Here a study is made on the capacity of Rician channels; it is shown that depending on the number of antennas, the MIMO capacity achieved under the condition of Rician fading may be greater or smaller than the capacity in the case of Rayleigh fading. In particular, for a large number of antennas, Rician channels exhibit smaller capacity than Rayleigh channels. On the other hand, for Rician channels, if the line-of-sight component is not very significant, the increase in capacity by an increase in the number of antennas can still be considerable.

MIMO channels can attain high capacities provided that the propagation medium contains enough scatterers. The capacity of MIMO channels can further be increased by performing optimal power distribution over transmit antennas. This, in turn, necessitates knowledge of the channel at the transmitter. It is shown in this paper that for low signal-to-noise ratios (SNR) and small number of antennas, this increase in capacity can be of interest. Rayleigh fading conditions are considered.