On the SIRs (Signal-to-Interference-Ratio) in Discrete-Time Autonomous Linear Networks

In this letter, we improve the results in [5] by relaxing the symmetry assumption and also taking the noise term into account. The author examines two discrete-time autonomous linear systems whose motivation comes from a neural network point of view in [5]. Here, we examine the following discrete-time autonomous linear system: ${\mathbf x}(k+1) = {\mathbf A} {\mathbf x}(k) + {\mathbf b}$ where ${\mathbf A}$ is any real square matrix with linearly independent eigenvectors whose largest eigenvalue is real and its norm is larger than 1, and vector ${\mathbf b}$ is constant. Using the same "SIR" ("Signal"-to-"Interference"-Ratio) concept as in [4] and [5], we show that the ultimate "SIR" is equal to $\frac{a_{ii}}{\lambda_{max} - a_{ii}}$, $i=1, 2, >..., N$, where $N$ is the number of states, $a_{ii}$ is the diagonal elements of matrix ${\bf A}$, and $\lambda_{max}$ is the (single or multiple) eigenvalue with maximum norm.Comment: 10 pages, 2 figures, has been submitted in March 2009 to IEEE International Conference on Artificial Neural Networks (ICANN) 2009, Cypru

Analysis of "SIR" ("Signal"-to-"Interference"-Ratio) in Discrete-Time Autonomous Linear Networks with Symmetric Weight Matrices

It's well-known that in a traditional discrete-time autonomous linear systems, the eigenvalues of the weigth (system) matrix solely determine the stability of the system. If the spectral radius of the system matrix is larger than 1, then the system is unstable. In this paper, we examine the linear systems with symmetric weight matrix whose spectral radius is larger than 1. The author introduced a dynamic-system-version of "Signal-to-Interference Ratio (SIR)" in nonlinear networks in [7] and [8] and in continuous-time linear networks in [9]. Using the same "SIR" concept, we, in this paper, analyse the "SIR" of the states in the following two $N$-dimensional discrete-time autonomous linear systems: 1) The system ${\mathbf x}(k+1) = \big({\bf I} + \alpha (-r {\bf I} + {\bf W}) \big) {\mathbf x}(k)$ which is obtained by discretizing the autonomous continuous-time linear system in \cite{Uykan09a} using Euler method; where ${\bf I}$ is the identity matrix, $r$ is a positive real number, and $\alpha >0$ is the step size. 2) A more general autonomous linear system descibed by ${\mathbf x}(k+1) = -\rho {\mathbf I + W} {\mathbf x}(k)$, where ${\mathbf W}$ is any real symmetric matrix whose diagonal elements are zero, and ${\bf I}$ denotes the identity matrix and $\rho$ is a positive real number. Our analysis shows that: 1) The "SIR" of any state converges to a constant value, called "Ultimate SIR", in a finite time in the above-mentioned discrete-time linear systems. 2) The "Ultimate SIR" in the first system above is equal to $\frac{\rho}{\lambda_{max}}$ where $\lambda_{max}$ is the maximum (positive) eigenvalue of the matrix ${\bf W}$. These results are in line with those of \cite{Uykan09a} where corresponding continuous-time linear system is examined. 3) The "Ultimate SIR" ...Comment: 35 pages, 4 figures, submitted to IEEE Trans. on Circuits and Systems 1 (TCAS1) in February 200

Discrete pseudo-SINR-balancing nonlinear recurrent system

Being inspired by the Hopfield neural networks (Hopfield (1982) and Hopfield and Tank (1985)) and the nonlinear sigmoid power control algorithm for cellular radio systems in Uykan and Koivo (2004), in this paper, we present a novel discrete recurrent nonlinear system and extend the results in Uykan (2009), which are for autonomous linear systems, to nonlinear case. The proposed system can be viewed as a discrete-time realization of a recently proposed continuous-time network in Uykan (2013). In this paper, we focus on discrete-time analysis and provide various novel key results concerning the discrete-time dynamics of the proposed system, some of which are as follows: (i) the proposed system is shown to be stable in synchronous and asynchronous work mode in discrete time; (ii) a novel concept called Pseudo-SINR (pseudo-signal-to-interference-noise ratio) is introduced for discrete-time nonlinear systems; (iii) it is shown that when the system states approach an equilibrium point, the instantaneous Pseudo-SINRs are balanced; that is, they are equal to a target value. The simulation results confirm the novel results presented and show the effectiveness of the proposed discrete-time network as applied to various associative memory systems and clustering problems

Continuous-time Hopfield neural network-based optimized solution to 2-channel allocation problem

Uykan, Zekeriya (Dogus Author)The channel allocation problem in cellular radio systems is NP-complete, and thus its general solution is not known for even the 2-channel case. It is well known that the link gain system matrix (or received-signal power system matrix) of the radio network is (and may be highly) asymmetric, and that as the Hopfield neural network is applied to optimization problems, its weight matrix should be symmetric. The main contribution of this paper is as follows: turning the channel allocation problem into a maxCut graph partitioning problem, we propose a simple and effective continuous-time Hopfield neural network-based solution by determining its symmetric weight matrix from the asymmetric received-signal-power-system matrix. Computer simulations confirm the effectiveness and superiority of the proposed solution as compared to standard algorithms for various illustrative cellular radio scenarios for the 2-channel case

Joint optimization of transmission-order selection and channel allocation for bidirectional wireless links-part II: algorithms

This is the second in a two-part series of papers on transmission order (TO) optimization in the presence of channel allocation (CA), i.e., joint optimization of the TO selection and CA problem, for interfering bidirectional wireless links. Part I of this paper thoroughly analyzes the joint optimization problem from a game theoretic perspective for a general deterministic setting. Here in Part II, we present novel distributed and centralized CA-TO algorithms, together with their performance analysis, for Device-to-Device (D2D) communications underlaying cellular networks based on the findings in Part I of this paper. Here, TO is a novel dimension for optimization. In Part II, we propose and analyze novel two distributed and one centralized joint CA-TO algorithms. Our investigations show that: i) our algorithms contain many of the existing TO algorithms and CA algorithms as its special cases and can thus be considered as a general framework for the joint CA and TO optimization. The computer simulations for TDD-based D2D communications underlaying cellular network show that the proposed distributed and centralized joint CA-TO algorithms remarkably outperform the reference algorithms.IEEE Communications Societ

N-GAIR: Non-greedy asynchronous interference reduction algorithm in wireless networks

In this paper, we consider optimum channel/frequency allocation problem in wireless networks by reducing total network interference signal powers, which is an NP-complete problem. Its optimum solution for general wireless networks for even 2-channel case is not known. Turning the channel/frequency allocation problem into a maxCut graph partitioning problem, we i) propose a spectral clustering based channel allocation algorithm, called SpecPure, and ii) propose and analyze a novel Non-Greedy Asynchronous Interference Reduction Algorithm for Wireless Networks, called N-GAIR, and iii) extend the results in [1] to the case where the number of channels is arbitrary. By simulating various CDMA based ad-hoc networks, we examine various scenarios to compare the performances of the proposed algorithms with the reference algorithm. We draw various conclusions for different network scenarios. For example, the results show that the SpecPure algorithm performs well for "symmetric" base locations scenarios, while the N-GAIR performs best for random base locations scenarios. The results confirm the effectiveness of the proposed algorithms, which can be adopted by any cellular, cognitive, ad-hoc or mesh type radio networks