Application of Jacobi Algorithm in Frequency Selective Channels

In this paper, we apply the Jacobi iterative algorithm to combat intersymbol interference caused by frequency selective channels. An analytical bound of the proposed equalizer is analyzed in order to gain an insight into its asymptotic performance. Due to the error propagation problem, the potential of this algorithm is not reached in an uncoded system. However, its extension to a coded system with the application of the turbo processing principle results in a new turbo equalization algorithm which demonstrates comparable performance with reduced complexity compared to some existing filter based turbo equalization schemes

Decomposition by Partial Linearization: Parallel Optimization of Multi-Agent Systems

We propose a novel decomposition framework for the distributed optimization of general nonconvex sum-utility functions arising naturally in the system design of wireless multiuser interfering systems. Our main contributions are: i) the development of the first class of (inexact) Jacobi best-response algorithms with provable convergence, where all the users simultaneously and iteratively solve a suitably convexified version of the original sum-utility optimization problem; ii) the derivation of a general dynamic pricing mechanism that provides a unified view of existing pricing schemes that are based, instead, on heuristics; and iii) a framework that can be easily particularized to well-known applications, giving rise to very efficient practical (Jacobi or Gauss-Seidel) algorithms that outperform existing adhoc methods proposed for very specific problems. Interestingly, our framework contains as special cases well-known gradient algorithms for nonconvex sum-utility problems, and many blockcoordinate descent schemes for convex functions.Comment: submitted to IEEE Transactions on Signal Processin

Polynomial matrix decomposition techniques for frequency selective MIMO channels

For a narrowband, instantaneous mixing multi-input, multi-output (MIMO) communications system, the channel is represented as a scalar matrix. In this scenario, singular value decomposition (SVD) provides a number of independent spatial subchannels which can be used to enhance data rates or to increase diversity. Alternatively, a QR decomposition can be used to reduce the MIMO channel equalization problem to a set of single channel equalization problems. In the case of a frequency selective MIMO system, the multipath channel is represented as a polynomial matrix. Thus conventional matrix decomposition techniques can no longer be applied. The traditional solution to this broadband problem is to reduce it to narrowband form by using a discrete Fourier transform (DFT) to split the broadband channel into N narrow uniformly spaced frequency bands and applying scalar decomposition techniques within each band. This describes an orthogonal frequency division multiplexing (OFDM) based system. However, a novel algorithm has been developed for calculating the eigenvalue decomposition of a para-Hermitian polynomial matrix, known as the sequential best rotation (SBR2) algorithm. SBR2 and its QR based derivatives allow a true polynomial singular value and QR decomposition to be formulated. The application of these algorithms within frequency selective MIMO systems results in a fundamentally new approach to exploiting spatial diversity. Polynomial matrix decomposition and OFDM based solutions are compared for a wide variety of broadband MIMO communication systems. SVD is used to create a robust, high gain communications channel for ultra low signal-to-noise ratio (SNR) environments. Due to the frequency selective nature of the channels produced by polynomial matrix decomposition, additional processing is required at the receiver resulting in two distinct equalization techniques based around turbo and Viterbi equalization. The proposed approach is found to provide identical performance to that of an existing OFDM scheme while supporting a wider range of access schemes. This work is then extended to QR decomposition based communications systems, where the proposed polynomial approach is found to not only provide superior bit-error-rate (BER) performance but significantly reduce the complexity of transmitter design. Finally both techniques are combined to create a nulti-user MIMO system that provides superior BER performance over an OFDM based scheme. Throughout the work the robustness of the proposed scheme to channel state information (CSI) error is considered, resulting in a rigorous demonstration of the capabilities of the polynomial approach

Real and Complex Monotone Communication Games

Noncooperative game-theoretic tools have been increasingly used to study many important resource allocation problems in communications, networking, smart grids, and portfolio optimization. In this paper, we consider a general class of convex Nash Equilibrium Problems (NEPs), where each player aims to solve an arbitrary smooth convex optimization problem. Differently from most of current works, we do not assume any specific structure for the players' problems, and we allow the optimization variables of the players to be matrices in the complex domain. Our main contribution is the design of a novel class of distributed (asynchronous) best-response- algorithms suitable for solving the proposed NEPs, even in the presence of multiple solutions. The new methods, whose convergence analysis is based on Variational Inequality (VI) techniques, can select, among all the equilibria of a game, those that optimize a given performance criterion, at the cost of limited signaling among the players. This is a major departure from existing best-response algorithms, whose convergence conditions imply the uniqueness of the NE. Some of our results hinge on the use of VI problems directly in the complex domain; the study of these new kind of VIs also represents a noteworthy innovative contribution. We then apply the developed methods to solve some new generalizations of SISO and MIMO games in cognitive radios and femtocell systems, showing a considerable performance improvement over classical pure noncooperative schemes.Comment: to appear on IEEE Transactions in Information Theor

Paraunitary oversampled filter bank design for channel coding

Oversampled filter banks (OSFBs) have been considered for channel coding, since their redundancy can be utilised to permit the detection and correction of channel errors. In this paper, we propose an OSFB-based channel coder for a correlated additive Gaussian noise channel, of which the noise covariance matrix is assumed to be known. Based on a suitable factorisation of this matrix, we develop a design for the decoder's synthesis filter bank in order to minimise the noise power in the decoded signal, subject to admitting perfect reconstruction through paraunitarity of the filter bank. We demonstrate that this approach can lead to a significant reduction of the noise interference by exploiting both the correlation of the channel and the redundancy of the filter banks. Simulation results providing some insight into these mechanisms are provided

Competitive Design of Multiuser MIMO Systems based on Game Theory: A Unified View

This paper considers the noncooperative maximization of mutual information in the Gaussian interference channel in a fully distributed fashion via game theory. This problem has been studied in a number of papers during the past decade for the case of frequency-selective channels. A variety of conditions guaranteeing the uniqueness of the Nash Equilibrium (NE) and convergence of many different distributed algorithms have been derived. In this paper we provide a unified view of the state-of-the-art results, showing that most of the techniques proposed in the literature to study the game, even though apparently different, can be unified using our recent interpretation of the waterfilling operator as a projection onto a proper polyhedral set. Based on this interpretation, we then provide a mathematical framework, useful to derive a unified set of sufficient conditions guaranteeing the uniqueness of the NE and the global convergence of waterfilling based asynchronous distributed algorithms. The proposed mathematical framework is also instrumental to study the extension of the game to the more general MIMO case, for which only few results are available in the current literature. The resulting algorithm is, similarly to the frequency-selective case, an iterative asynchronous MIMO waterfilling algorithm. The proof of convergence hinges again on the interpretation of the MIMO waterfilling as a matrix projection, which is the natural generalization of our results obtained for the waterfilling mapping in the frequency-selective case.Comment: To appear on IEEE Journal on Selected Areas in Communications (JSAC), September 200

Using Anisotropic Micro-Scale Topography to Manipulate the Wettability of Aluminum and Reduce the Retention of Water

A method is described for fabricating controlled micro-scale, topographical features on aluminum surfaces for the purpose of exploiting those features to affect the surface wettability. Using a photolithographic approach, a photoresist-masked surface is subjected to a plasma etch in a mixture of gaseous BCl3 and Cl2. Parallel grooves, microns to tens of microns in width, depth and spacing are studied, because this geometry is scaleable for mass production by roll-to-roll micro-embossing, and because the anisotropic nature of these features provides a directional change in wettability that can reduce the retention of water on the surface. Aluminum was studied because it is naturally hydrophilic and widely used in wet-surface heat exchanger applications, because of its low cost and excellent mechanical and thermal properties. Water droplets placed on a micro-grooved aluminum surface using a micro-syringe exhibit significantly increased apparent contact angles, and for water condensed onto an inclined, micro-grooved surface, the droplet volume at incipient sliding is reduced by more than 50% compared to droplets on a surface without micro-grooves. No chemical surface treatment is necessary to achieve this water repellency; it is accomplished solely through the anisotropic surface topography. The droplet geometry shows an elongated base contour relative to a surface without micro-grooves, and discontinuities in the three-phase contact line are also introduced by the grooves. A mechanistic model is presented for predicting the critical droplet size on micro-grooved surfaces. This model extends earlier work by accounting for the droplet geometry and contact-line changes caused by the micro-grooves. The model is validated through comparisons of predicted to measured critical droplet sizes, and it is then used to provide guidance for the development of surfaces with enhanced water drainage behavior. In a broad range of air-cooling applications, water retention on the air-side surface of metallic heat exchangers is problematic, because it can reduce the air-side heat transfer coefficient, increase core pressure drop, and provide a site for biological activity. In refrigeration systems, the accumulation of frost on metallic fins requires periodic defrosting and reduces energy efficiency. When water is retained on these surfaces following the defrost cycle, ice is more readily formed in the subsequent cooling period, and such ice can lead to shorter operation times before the next defrost is required. Thus the management and control of water droplets on heat-transfer and airhandling surfaces is vital to energy efficiency, functionality, and maintenance in air-cooling systems. The microstructured surfaces introduced in this work are proposed for use in air-cooling and dehumidifying applications, but they may have other applications where the management of liquids on a surface is important.Air Conditioning and Refrigeration Project 166Air Conditioning and Refrigeration Project 20