Stabilizing Relaxed Nonlinear FMA Yields a (Combinatorial) Optimizer

Abstract

In this paper, we focus on so-called nonlinear and unfeasible FMA (Foschini-Miljanic Algorithm) case, where the system matrix is unfeasible and the transmit powers are limited. We stabilize the nonlinear dynamic system by a normalization term, as in Oja's approach for his model. We draw various conclusions regarding the linear and nonlinear cases: i) In linear case, we show that the SINRs in the stabilized linear wireless network converge to some constants which are inversely related to the dominant eigenvalue of normalized link gain matrix. ii) In nonlinear case, we show that the proposed nonlinear network, which includes also Oja's principal component analyzer as a special case, can be applied to solving (combinatorial) optimization problems. The performance of the proposed network is examined in channel allocation problem in cellular radio systems, which is NP complete, and in content-addressable memory design problem. The simulation results confirm the effectiveness and the superiority of the proposed nonlinear network as compared to the Hopfield Neural Network for the very same weight matrices in optimization problems.