In this paper, we apply the random walk model in designing a raindrop algorithm to find the global optimal solution of a non-linear programming problem. The raindrop algorithm does not require the information of the first or second order derivatives
of the object function. Hence it is a direct method. We investigate the properties of raindrop algorithm. Besides, we apply the raindrop algorithm to solve a non-linear optimization problem, where the object function is highly irregular (neither convex nor concave). And the global optimal solution can be found with small number of iterations.
The Radio Environment Map (REM) provides an effective approach to Dynamic Spectrum Access (DSA) in Cognitive Radio Networks (CRNs). Previous results on REM construction show that there exists a tradeoff between the number of measurements (sensors) an
d REM accuracy. In this paper, we analyze this tradeoff and determine that the REM error is a decreasing and convex function of the number of measurements (sensors). The concept of geographic entropy is introduced to quantify this relationship. And the influence of sensor deployment on REM accuracy is examined using information theory techniques. The results obtained in this paper are applicable not only for the REM, but also for wireless sensor network deployment.
