From Sigmoid Power Control Algorithm to Hopfield-like Neural Networks: “SIR” (“Signal”-to-“Interference”-Ratio)- Balancing Sigmoid-Based Networks- Part I: Continuous Time

Continuous-time Hopfield network has been an important focus of research area since 1980s whose applications vary from image restoration to combinatorial optimization from control engineering to associative memory systems. On the other hand, in wireless communications systems literature, power control has been intensively studied as an essential mechanism for increasing the system performance. A fully distributed power control algorithm (DPCA), called Sigmoid DPCA, is presented by Uykan in [10] and [11], which is obtained by discretizing the continuous-time system. In this paper, we present a Sigmoid-based “Signal-to-Interference Ratio, (SIR)” balancing dynamic networks, called Sgm”SIR”NN, which includes both the Sigmoid power control algorithm (SgmDPCA) and the Hopfield neural networks, two different areas whose scope of interest, motivations and settings are completely different. It’s shown that the Sgm”SIR”NN exhibits features which are generally attributed to Hopfield Networks. Computer simulations show the effectiveness of the proposed network as compared to traditional Hopfield Network.