Optimization methods for base station placement in wireless applications

Wireless design tools contain one or more propagation models whose purpose is to predict quantitative measures of system performance as a function of system parameters. A logical next step is to optimize predicted overall performance by choosing the best values for parameters that can be controlled by the provider and/or maintainer of the system. However, because the function to be optimized is often highly nonlinear and nasty (for example, unpredictably discontinuous, nondifferentiable, or noisy), only a limited number of optimization techniques can be applied. Direct search methods are well suited to finding the optimal placement of base stations, since they require only the value of the function to be optimized. In extensive numerical testing, we have found a customized variant of the Nelder-Mead "simplex" method to be reasonably efficient and reliable at finding local optima. Our experience with producing improved or optimal base station placements suggests that optimization can enhance understanding of propagation models as well as improve wireless system designs.