The key point in design of radial basis function networks is to specify the number and the locations of the centers. Several heuristic hybrid learning methods, which apply a clustering algorithm for locating the centers and subsequently a linear leastsquares method for the linear weights, have been previously suggested. These hybrid methods can be put into two groups, which will be called as input clustering (IC) and input-output clustering (IOC), depending on whether the output vector is also involved in the clustering process. The idea of concatenating the output vector to the input vector in the clustering process has independently been proposed by several papers in the literature although none of them presented a theoretical analysis on such procedures, but rather demonstrated their effectiveness in several applications. The main contribution of this paper is to present an approach for investigating the relationship between clustering process on input-output training samples and the mean squared output error in the context of a radial basis function netowork (RBFN). We may summarize our investigations in that matter as follows: 1) A weighted mean squared input-output quantization error, which is to be minimized by IOC, yields an upper bound to the mean squared output error. 2) This upper bound and consequently the output error can be made arbitrarily small (zero in the limit case) by decreasing the quantization error which can be accomplished through increasing the number of hidden units.

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PO BOX 5400, FIN-02015 HUT, FINLAND. AbstractConvergence speed and distributiveness are important properties of a power control algorithm to determine its potentialforpractical usage in cellular radio systems. Most of the power control algorithms in literature are derived from numerical linear algebra or linear control theory, and consequently are in linear form This paper, on the other hand, proposes a (sigmoid-basis) nonlinear power control algorithm, which is fully distributed and first ordel: The algorithm is obtained by discretization of the direrential equation form of the algorithm shown to be stable in the case of feasible system. We cam'ed out computational experiments on a CDMA system The results indicate that our algorithm significantly enhances the convergence speed of power control in comparison with linear distributed power control algorithm of Foschini and Miuanic CIS a reference algorithm.

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Device-to-Device(D2D) communications underlaying cellular networks is as a promising concept which has several advantages over the traditional cellular networks. In TDD system, the frame structure defines the order of uplink and downlink transmission slots. Typically a TDD system is synchronized and the same transmissionorder (TO) is used in all cells. In a direct D2D link, we have the freedom of selecting the TO of the devices freely. To our best knowledge, no paper has explicitly examined the TO optimization problem in D2D communications underlaying cellular network so far. In this paper, we focus exactly on this problem: Once the proper co-channel D2D pairs are determined in the network, how to minimize the network interference by optimally determining the TOs in all D2D links (together with co-channel cellular links) in the network, which is an NP-complete problem. In this paper, we formulate the TO optimization problem from a graph theoretic point of view: i) We show that TO optimization problem is equal to a constraint balanced min-cut graph partitioning problem of our defined augmented graph, ii) we propose and analyze a distributed and a centralized efficient asynchronous clustering algorithm for solving the TO optimization problem, equivalently, for the min-cut of our proposed augmented graph. Computer simulations for TDD-based D2D underlaying cellular network show that the proposed distributed and centralized algorithms, called ABCAMiC and CABCAMiC, respectively, i) remarkably outperform the reference case where all TOs are fixed, and, ii) converge within relatively small number of steps and generally converge in only a few epochs even for large number of cellular and D2D users, and, iii) the expected Manuscript performance of the (partly/fully) distributed ABCAMiC is almost equal to that of the centralized solution CABCAMiC, which generally gives near-global optimal solution to the TO optimization problem.Index Terms-Device-to-Device (D2D) communications underlaying TDD cellular network, transmission order optimization, graph representation of wireless systems, balanced min-cut graph partitioning, clustering. involvement and thus enhancing the BS resource utilization, (and by low transmit power because the MSs are relatively close to each other) or (b) The local MSs still communicate via the BS using the BS uplink (UL) and downlink (DL) resources unnecessarily (and by relatively high transmit powers if the MSs are relatively far from the BS).The answer is clear: Option (a). It's evidently resource inefficient (in terms of transmit power and bandwidth) for two proximate devices to communicate via a relatively far entity (BS) when there is a direct local path between the devices. The idea of re-using the radio resources (same frequency and time) in the spatial domain (due to the propagation loss or due to the fact that some parts of the network are shielded from other areas by natural obstructions etc) is presented in [63], and is not an innovation as pointed out by e.g. [66]. Direct D2D communication be...

The Hopfield neural network (HNN) has been widely used in numerous different optimization problems since the early 1980s. The convergence speed of the HNN (already in high gain) eventually plays a critical role in various real-time applications. In this brief, we propose and analyze a generalized HNN which drastically improves the convergence speed of the network, and thus allows benefiting from the HNN capabilities in solving the optimization problems in real time. By examining the channel allocation optimization problem in cellular radio systems, which is NP-complete and in which fast solution is necessary due to time-varying link gains, as well as the associative memory problem, computer simulations confirm the dramatic improvement in convergence speed at the expense of using a second nonlinear function in the proposed network.

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 discretetime autonomous linear system: x(k + 1) = Ax(k) + b where A is any real square matrix with linearly independent eigenvectors whose largest eigenvalue is real and its norm is larger than 1, and vector 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 aii λmax−aii , i = 1, 2, . . . , N , where N is the number of states, a ii is the diagonal elements of matrix A, and λ max is the (single or multiple) eigenvalue with maximum norm.

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