Polynomial Moment Relaxation for MIMO Detection

We develop a polynomial-time detector for maximum likelihood (ML) detection over multiple-input multiple-output (MIMO) channels. Our proposed polynomial moment relaxation (PMR) detection gives a unified framework for MIMO detection with relaxation including semi-definite relaxation as a special case. We give three approaches to replace a finite alphabet constraint with a polynomial constraint. Since both the objective function and the constraints are polynomials, we use a moment relaxation approach by applying the dual theories of moments and positive polynomials solvable by semi-definite programming. With different relaxation orders, our PMR achieve a flexible trade-off between complexity and performance

Waveform Design for Secure SISO Transmissions and Multicasting

Wireless physical-layer security is an emerging field of research aiming at preventing eavesdropping in an open wireless medium. In this paper, we propose a novel waveform design approach to minimize the likelihood that a message transmitted between trusted single-antenna nodes is intercepted by an eavesdropper. In particular, with knowledge first of the eavesdropper's channel state information (CSI), we find the optimum waveform and transmit energy that minimize the signal-to-interference-plus-noise ratio (SINR) at the output of the eavesdropper's maximum-SINR linear filter, while at the same time provide the intended receiver with a required pre-specified SINR at the output of its own max-SINR filter. Next, if prior knowledge of the eavesdropper's CSI is unavailable, we design a waveform that maximizes the amount of energy available for generating disturbance to eavesdroppers, termed artificial noise (AN), while the SINR of the intended receiver is maintained at the pre-specified level. The extensions of the secure waveform design problem to multiple intended receivers are also investigated and semidefinite relaxation (SDR) -an approximation technique based on convex optimization- is utilized to solve the arising NP-hard design problems. Extensive simulation studies confirm our analytical performance predictions and illustrate the benefits of the designed waveforms on securing single-input single-output (SISO) transmissions and multicasting

Outage Probability and Outage-Based Robust Beamforming for MIMO Interference Channels with Imperfect Channel State Information

In this paper, the outage probability and outage-based beam design for multiple-input multiple-output (MIMO) interference channels are considered. First, closed-form expressions for the outage probability in MIMO interference channels are derived under the assumption of Gaussian-distributed channel state information (CSI) error, and the asymptotic behavior of the outage probability as a function of several system parameters is examined by using the Chernoff bound. It is shown that the outage probability decreases exponentially with respect to the quality of CSI measured by the inverse of the mean square error of CSI. Second, based on the derived outage probability expressions, an iterative beam design algorithm for maximizing the sum outage rate is proposed. Numerical results show that the proposed beam design algorithm yields better sum outage rate performance than conventional algorithms such as interference alignment developed under the assumption of perfect CSI.Comment: 41 pages, 14 figures. accepted to IEEE Transactions on Wireless Communication

Solving Fractional Polynomial Problems by Polynomial Optimization Theory

This work aims to introduce the framework of polynomial optimization theory to solve fractional polynomial problems (FPPs). Unlike other widely used optimization frameworks, the proposed one applies to a larger class of FPPs, not necessarily defined by concave and convex functions. An iterative algorithm that is provably convergent and enjoys asymptotic optimality properties is proposed. Numerical results are used to validate its accuracy in the non-asymptotic regime when applied to the energy efficiency maximization in multiuser multiple-input multiple-output communication systems.Comment: 5 pages, 2 figures, 1 table, submitted to Signal Processing Letter