Using the Eigenvalue Relaxation for Binary Least-Squares Estimation Problems

The goal of this paper is to survey the properties of the eigenvalue relaxation for least squares binary problems. This relaxation is a convex program which is obtained as the Lagrangian dual of the original problem with an implicit compact constraint and as such, is a convex problem with polynomial time complexity. Moreover, as a main pratical advantage of this relaxation over the standard Semi-Definite Programming approach, several efficient bundle methods are available for this problem allowing to address problems of very large dimension. The necessary tools from convex analysis are recalled and shown at work for handling the problem of exactness of this relaxation. Two applications are described. The first one is the problem of binary image reconstruction and the second is the problem of multiuser detection in CDMA systems

Finite quantum tomography via semidefinite programming

Using the the convex semidefinite programming method and superoperator formalism we obtain the finite quantum tomography of some mixed quantum states such as: qudit tomography, N-qubit tomography, phase tomography and coherent spin state tomography, where that obtained results are in agreement with those of References \cite{schack,Pegg,Barnett,Buzek,Weigert}.Comment: 25 page

Adaptive interference suppression for DS-CDMA systems based on interpolated FIR filters with adaptive interpolators in multipath channels

In this work we propose an adaptive linear receiver structure based on interpolated finite impulse response (FIR) filters with adaptive interpolators for direct sequence code division multiple access (DS-CDMA) systems in multipath channels. The interpolated minimum mean-squared error (MMSE) and the interpolated constrained minimum variance (CMV) solutions are described for a novel scheme where the interpolator is rendered time-varying in order to mitigate multiple access interference (MAI) and multiple-path propagation effects. Based upon the interpolated MMSE and CMV solutions we present computationally efficient stochastic gradient (SG) and exponentially weighted recursive least squares type (RLS) algorithms for both receiver and interpolator filters in the supervised and blind modes of operation. A convergence analysis of the algorithms and a discussion of the convergence properties of the method are carried out for both modes of operation. Simulation experiments for a downlink scenario show that the proposed structures achieve a superior BER convergence and steady-state performance to previously reported reduced-rank receivers at lower complexity

Combined Semi-definite Relaxation and Sphere Decoding Method for Multiple Antennas Systems

In this paper, a new detection method which combines the semi-definite programming relaxation (SDR) with the sphere decoding (SD) is proposed for 256-QAM multiple-input multiple-output (MIMO) system. In this method, the SDR algorithms are engaged to obtain a primary result. Then, a hyper-sphere is constructed which is centered at the received signal and has its radius equals to the Euclidean distance between the primary result and the received signal. Finally, the SD searching strategy is employed to determine the final result which satisfies the principle of maximum likelihood. Simulation results show that the proposed method can offer optimum BLER performance as well as lower computational complexity than the conventional SD detectors. © 2011 IEEE.published_or_final_versio