Stéphane Azou

Performance Analysis of a Spreading Sequence Estimator for Spread Spectrum Transmissions

Abstract Direct sequence spread spectrum transmissions (DS-SS) are now widely used for secure communications, as well as for multiple access. They have many interesting properties, including low probability of interception. Indeed, DS-SS transmitters use a periodical pseudo-random sequence to modulate the baseband signal before transmission. A receiver which does not know the sequence cannot demodulate the signal. In this paper, we propose a new method which can estimate the spreading sequence in a noncooperative context. The method is based on eigenanalysis techniques. The received signal is divided into windows, from which a covariance matrix is computed. We show that the sequence can be reconstructed from the two first eigenvectors of this matrix, and that useful information, such as desynchronisation time, can be extracted from the eigenvalues. The main achievement of the present paper is a performance analysis of the proposed spreading sequence estimation procedure. An analytical approach is first considered owing to matrix perturbation theory and Wishart matrix properties. Then, complementary Monte Carlo simulations are performed to show the effectiveness of the proposed method.

On exact Kalman filtering of polynomial systems

A closed-form state estimator for some polynomial nonlinear systems is derived in this paper. Exploiting full Taylor series expansion we first give exact matrix expressions to compute mean and covariance of any random variable distribution that has been transformed through a polynomial function. An original discrete-time Kalman filtering implementation relying on this exact polynomial transformation is proposed. The important problem of chaotic synchronization of Chebyshev maps is then considered to illustrate the significance of these results. Mean square error between synchronized signals and consistency criteria are chosen as performance measures under various signal-to-noise ratios. Comparisons to the popular extended Kalman filter and to the recent unscented Kalman filter are also conducted to show the pertinence of our filtering formulation

A chaotic Direct-Sequence Spread-Spectrum system for underwater communication

The recent advances in acoustic modem technology have enabled the development of Underwater Acoustic Networks (UAN). Application interests include oceanographic information gathering, environmental monitoring or coastal defense. Due to its ability of simultaneously sharing the same frequency band for various users and the poor propagation conditions usually encountered in shallow water environment, the Code Division Multiple Access (CDMA) is a promising scheme for UAN. Recent results show that a standard CDMA direct-sequence spread spectrum approach is not sufficient to ensure Low Probabilities of Detection (LPD) and/or Interception (LPI), that is an unauthorized observer may notice that a communication signal is present. For many applications, this drawback is not acceptable. In this paper, the application of chaos to transmission of information is under investigation to achieve an LPI/LPD objective in an UAN context. Performance results of two receivers are shown for a single user through a realistic simulation scenario. An experiment at sea will be conducted by GESMA soon to confirm these first results.

A robust synchronization procedure for blind estimation of the symbol period and the timing offset in spread spectrum transmissions

In the context of spectrum surveillance (non cooperative context), a robust synchronization procedure is presented, in order to estimate the period symbol and timing offset of a direct sequence spread spectrum signal. Experimental results are given to illustrate the performances of the algorithm.

A complete receiver solution for a chaotic direct-sequence spread spectrum communication system

This paper is devoted to receiver design in a chaotic direct-sequence spread spectrum (CD3S) digital communication system. The demodulation is achieved through chaos synchronization in an efficient manner thanks to dual unscented Kalman filtering. The problem of carrier phase recovery, frequently neglected in chaos-based communication systems, is addressed either through Costas loop prior to demodulation or by dual estimation of the code, symbol and phase in baseband. The input signal power fluctuations, which often causes large errors in synchronizing chaotic waveforms, is also taken into account. Numerical simulations are provided to show the significance of the proposed receiver for both additive white Gaussian noise (AWGN) channel and a nonstationary channel.

Sea trial results of a chaotic direct-sequence spread spectrum underwater communication system

Recent theoretical results show that use of chaotic dynamics can significantly increase privacy of digital communication signals. The purpose of this paper is to report sea trial results of a chaotic spread spectrum system. Due to its ability to simultaneously sharing the same frequency band for various users (through Code Division Multiple Access) and its robustness against channel imperfections, it is the Direct-Sequence scheme that we use in our system. This is done by using a chaotic dynamic for the spreading code generator. Two receiver structures are discussed; one is similar to the matched filter structure usually encountered in standard DS-SS systems; the other, more original, is based on a state-space formulation to recover various parameters of the incoming chaotic signal. Through these first sea trials, we aim to prove the feasibility of a chaos-based transmission for a single user that operates without any covertness constraint. Other tests will be conducted soon to evaluate the performances for a Signal-to-Noise Ratio below 0 dB.

A new discrete impulse response Gramian and its application to model reduction

Some fundamental properties of an impulse response Gramian for linear, time-invariant, asymptotically stable, discrete single-input-single-output (SISO) systems are derived. This Gramian is system invariant and can be found by solving a Lyapunov equation. The connection with standard controllability, observability, and cross Gramians is proven. The significance of these results in model-order reduction is highlighted with an efficient procedure.

Energy detection based blind synchronization for pulse shape modulated IR-UWB systems

Synchronization is a key performance-limiting factor in any communication system and a challenging task to accomplish. In this paper, an energy detection based non data-aided (NDA) algorithm for orthogonal pulse shape modulated (PSM) impulse radio ultra wideband (IR-UWB) system is proposed. Relying on unique signal structure, simple overlap-add operation followed by energy detection enables synchronization. The algorithm remains functional under practical scenarios i.e. in the presence of inter-frame and inter-symbol interference (IFI & ISI) and with M-ary modulation. Simulation results are provided to demonstrate the performance of proposed algorithm.

On the Blind Estimation of Chip Time of Time-Hopping Signals Through Minimization of a Multimodal Cost Function

In this correspondence, we focus on blind estimation of the chip duration of time-hopping signals by introducing a cost function based on time-of-arrival (ToA) folding over multiple observation sets. An optimization algorithm that takes advantage of the highly oscillatory behavior in the nearby of the global minimum is proposed and a performance bound for the chip time estimate is derived. The pertinence of our approach is shown through numerical results, considering alternative methods like periodogram and separable least squares line search. The proposed technique enables a good tradeoff between statistical accuracy and computational complexity.

Linear predictive speech coding using fermat number transform

This paper is about the reduction of the computational complexity of a speech codec. A linear predictive coding procedure is developed to allow its implementation with number theoretic transforms. The use of fermat number transform can reduce, in a significant way, the cost of linear predictive algorithm implantation on digital signal processor.