Channel Capacity Estimation using Free Probability Theory

In many channel measurement applications, one needs to estimate some characteristics of the channels based on a limited set of measurements. This is mainly due to the highly time varying characteristics of the channel. In this contribution, it will be shown how free probability can be used for channel capacity estimation in MIMO systems. Free probability has already been applied in various application fields such as digital communications, nuclear physics and mathematical finance, and has been shown to be an invaluable tool for describing the asymptotic behaviour of many large-dimensional systems. In particular, using the concept of free deconvolution, we provide an asymptotically (w.r.t. the number of observations) unbiased capacity estimator for MIMO channels impaired with noise called the free probability based estimator. Another estimator, called the Gaussian matrix mean based estimator, is also introduced by slightly modifying the free probability based estimator. This estimator is shown to give unbiased estimation of the moments of the channel matrix for any number of observations. Also, the estimator has this property when we extend to MIMO channels with phase off-set and frequency drift, for which no estimator has been provided so far in the literature. It is also shown that both the free probability based and the Gaussian matrix mean based estimator are asymptotically unbiased capacity estimators as the number of transmit antennas go to infinity, regardless of whether phase off-set and frequency drift are present. The limitations in the two estimators are also explained. Simulations are run to assess the performance of the estimators for a low number of antennas and samples to confirm the usefulness of the asymptotic results.Comment: Submitted to IEEE Transactions on Signal Processing. 12 pages, 9 figure

Melting of an Ising Quadrant

We consider an Ising ferromagnet endowed with zero-temperature spin-flip dynamics and examine the evolution of the Ising quadrant, namely the spin configuration when the minority phase initially occupies a quadrant while the majority phase occupies three remaining quadrants. The two phases are then always separated by a single interface which generically recedes into the minority phase in a self-similar diffusive manner. The area of the invaded region grows (on average) linearly with time and exhibits non-trivial fluctuations. We map the interface separating the two phases onto the one-dimensional symmetric simple exclusion process and utilize this isomorphism to compute basic cumulants of the area. First, we determine the variance via an exact microscopic analysis (the Bethe ansatz). Then we turn to a continuum treatment by recasting the underlying exclusion process into the framework of the macroscopic fluctuation theory. This provides a systematic way of analyzing the statistics of the invaded area and allows us to determine the asymptotic behaviors of the first four cumulants of the area.Comment: 28 pages, 3 figures, submitted to J. Phys.

Asymptotic Behaviour of Random Vandermonde Matrices with Entries on the Unit Circle

Analytical methods for finding moments of random Vandermonde matrices with entries on the unit circle are developed. Vandermonde Matrices play an important role in signal processing and wireless applications such as direction of arrival estimation, precoding, and sparse sampling theory, just to name a few. Within this framework, we extend classical freeness results on random matrices with independent, identically distributed (i.i.d.) entries and show that Vandermonde structured matrices can be treated in the same vein with different tools. We focus on various types of matrices, such as Vandermonde matrices with and without uniform phase distributions, as well as generalized Vandermonde matrices. In each case, we provide explicit expressions of the moments of the associated Gram matrix, as well as more advanced models involving the Vandermonde matrix. Comparisons with classical i.i.d. random matrix theory are provided, and deconvolution results are discussed. We review some applications of the results to the fields of signal processing and wireless communications.Comment: 28 pages. To appear in IEEE Transactions on Information Theor

Impact of jumps on returns and realised variances: econometric analysis of time-deformed Levy processes

In order to assess the effect of jumps on realised variance calculations, we study some of the econometric properties of time-changed Levy processes. We show that in general we can derive the second order properties of realised variances and use these to estimate the parameters of such models. Our analytic results give a first indication of the degrees of inconsistency of realised variance as an estimator of the time-change in the non-Brownian case. Further, our results suggest volatility is even more predictable than has been shown by the recent econometric work on realised variance.Kalman filter, Levy process, Long-memory, Quasi-likelihood, Realised variance, Stochastic volatility, Time-change.

Multi-stage Wireless Signal Identification for Blind Interception Receiver Design

Protection of critical wireless infrastructure from malicious attacks has become increasingly important in recent years, with the widespread deployment of various wireless technologies and dramatic growth in user populations. This brings substantial technical challenges to the interception receiver design to sense and identify various wireless signals using different transmission technologies. The key requirements for the receiver design include estimation of the signal parameters/features and classification of the modulation scheme. With the proper identification results, corresponding signal interception techniques can be developed, which can be further employed to enhance the network behaviour analysis and intrusion detection. In detail, the initial stage of the blind interception receiver design is to identify the signal parameters. In the thesis, two low-complexity approaches are provided to realize the parameter estimation, which are based on iterative cyclostationary analysis and envelope spectrum estimation, respectively. With the estimated signal parameters, automatic modulation classification (AMC) is performed to automatically identify the modulation schemes of the transmitted signals. A novel approach is presented based on Gaussian Mixture Models (GMM) in Chapter 4. The approach is capable of mitigating the negative effect from multipath fading channel. To validate the proposed design, the performance is evaluated under an experimental propagation environment. The results show that the proposed design is capable of adapting blind parameter estimation, realize timing and frequency synchronization and classifying the modulation schemes with improved performances