In this work, we present a new techniques to solve the integral equations of the second kind with logarithmic kernel. First, we show the existence and uniqueness of the solution for the given problem in a Hilbert space. Next, we discuss a projection method for solving integral equations with logarithmic kernel of the second kind; the present method based on the shifted Legendre polynomials. We examine the existence of the solution for the approximate equation, and we provide a new error estimate for the numerical solutions. At the end, numerical examples are provided to illustrate the theoretical results.

In any wireless cellular network, power control is one of the most important dynamic radio resource management (RRM) schemes which increases the capacity and performance of the system. In this paper, we present a modified scheme to Distributed Power control that optimize the transmission power of mobile’s and signal-to-interference-plus-noise ratio (SINR) error. This method, based on minimization of performance criterion, achieves the minimum SINR error and power consumption at the next time instant. The Mixed Kalman/H$ınfty$ Filter with covariance intersection has been applied in the proposed scheme to estimate and predict the channel variation and still ensure a good robustness. Finally, the mixed Kalman/H$ınfty$ filter based power control method is compared with Kalman filter and H$ınfty$ filter based power control results show that our method provides robustness against practical impairments, such as measurement uncertainties and fast channel variations.