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Thus far, most of the power control (PC) algorithms derived from numerical algebra envisage a system where the link gains are fixed, and the PC command can take any value in the real field. These two assumptions are quite unrealistic in actual communication systems, since link gains are time varying and PC commands must be sent over capacity limited channels. Most of the power control algorithms derived from control theory, on the other hand, analyze the PC problem from the point of view of one link. In this paper, we propose a fully distributed and nonlinearly proportional PC algorithm for time-varying link gain environments that can possibly be implemented also as a 1-bit increase/decrease PC command, and analyze it from system point of view. We construct a simple direct bridge between the link gain changes and the parameters of the proposed algorithm. It is shown that the proposed algorithm drives the carrier-to-interference + noise + ratio (CIR) to an interval in time-changing link gain environments. Simulation results for urban speeds show that the proposed algorithm is more robust against link gain changes as compared to the linear distributed PC algorithm of Foschini and Miljanic as a reference algorithm. The proposed algorithm was also verified with an advanced dynamic system simulator. Index Terms--Cellular radio systems, distributed power control (PC) algorithms, proportional power control (PropPC).

In this paper we present and analyze a new structure for designing a radial basis function neural network (RBFNN). In the training phase, input layer of RBFNN is augmented with desired output vector. Generalization phase involves the following steps: 1) identify the cluster to which a previously unseen input vector belongs; 2) augment the input layer with an average of the targets of the input vectors in the identified cluster; and 3) use the augmented network to estimate the unknown target. It is shown that, under some reasonable assumptions, the generalization error function admits an upper bound in terms of the quantization errors minimized when determining the centers of the proposed method over the training set and the difference between training samples and generalization samples in a deterministic setting. When the difference between the training and generalization samples goes to zero, the upper bound can be made arbitrarily small by increasing the number of hidden neurons. Computer simulations verified the effectiveness of the proposed method. Index Terms--Clustering, input-output clustering, radial basis function neural network (RBFNN).

Convergence speed and distributiveness are important properties of a power-control algorithm in order to evaluate its potential for use 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 that is fully distributed and first order. The algorithm is obtained by discretization of the differential equation forms of the algorithm shown to be stable in the case of a feasible system. It is shown to be quadratically convergent in the neighborhood of its fixed point. We carried out computational experiments on a code-division multiple-access system. The results indicate that our algorithm significantly enhances the convergence speed of power control in an estimation error-free scenario and is more robust against estimation errors as compared with the linear distributed power-control algorithm of Foschini and Miljanic as a reference algorithm. The proposed algorithm was also verified with an advanced dynamic system simulator. Index Terms--Code-division multiple-access (CDMA) radio systems, distributed power-control algorithms, sigmoid function.

Gradient-descent type supervised learning is the most commonly used algorithm for design of standard sigmoid perceptron (SP). However, it is computationally expensive (slow) and has local-minima problem. Moody and Darken proposed an input-clustering based hierarchical algorithm for fast learning in networks of locally tuned neurons in the context of radial basis function networks. In this paper, we propose and analyze input clustering (IC) and input-output clustering (IOC)-based algorithms for fast learning in networks of globally tuned neurons in the context of the SP. It is shown that 'localizing' the input layer weights of the SP by the IC and the IOC minimizes an upper bound to the SP output error. The proposed algorithms could possibly be used also to initialize the SP weights for the conventional gradient-descent learning. Simulation results offer that the SPs designed by the IC and the IOC yield comparable performance in comparison with its radial basis function network counterparts. Index Terms--Gradient-descent learning, input clustering (IC), input-output clustering (ITC), radial basis function networks, single-hidden-layer sigmoid perceptron (SP).

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 least-squares 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. Index Terms--Input/output clustering, radial basis function neural networks.