Performance analysis of a spreading sequence estimator for spread spectrum transmissions

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.