High-order statistical methods for blind channel identification and source detection with applications to wireless communications

Abstract

Current telecommunications systems offer services that require very high transmission rates. The channel identification problem arises in this context with a major issue. The use of blind techniques have been of great interest in the search for a better balance between an appropriate binary rates and the quality of the retrieved information. Relying on special properties of cumulants of 4th order of the signals to the channel output, this thesis introduces new signal processing tools with applications in mobile radio communication systems. Exploring the symmetrical structure of the output cumulants, the problem of blind channel identification is approached from a multilinear model tensor 4th order cumulant based on a decomposition into parallel factors (PARAFAC). If SISO, the components of the new model have a tensor Hankel structure. In the case of MIMO channels without memory, the redundancy of tensor factors is explored in the estimation of the coefficients of the channel. In this context, new blind channel identification algorithms developed in this thesis are based on a least squares optimization problem single step (SS-LS). The proposed methods fully exploit the multilinear structure of the cumulant tensor and their symmetries and redundancies, thus avoiding any form of preprocessing. Indeed, the SS-LS approach induces a solution based on a single minimization procedure without intermediate steps, contrary to what happens in most of the existing literature methods. Using only the cumulants of order 4 and exploring the concept of Virtual Arrangement, this is also the problem of location of sources, in a multiuser environment. An original Contribution is to increase the number of virtual sensors based on a particular decomposition of cumulants tensioner, thereby improving the resolution of the arrangement whose structure is typically obtained when using order statistics 6. It is considered also the estimation physical of a MIMO channel of communication with muti-routes. Via a fully blind approach, the multipath channel is first treated as a convolutional model and a new technique is proposed to estimate its coefficients. This non-parametric technique generalizes the methods previously proposed for SISO and MIMO cases (out of memory). Making use of a tensor formalism to represent the multipath MIMO channel, its physical parameters may be obtained using a combined technique of ALS-MUSIC type, based on a subspace algorithm. Finally, it will be considered the problem of determining the order of FIR channels, particularly in the case of MISO systems. A complete procedure is introduced to the detection and estimation of selective MISO communication channels in frequency. The new algorithm, based on a deflation approach successively detects each signal source, determines the order of their individual broadcast channel and estimates the associated coefficients.