Cognitive Radio Distributed Power Control Non-cooperative Game Nash Equilibrium Implementation

In this document, we explore the implementation of Nash Equilibrium for cognitive radio distributed power control in non-cooperative games. This implementation utilizes price functions and comparative analysis with DPC (Distributed Power Control) methods. Cognitive radio represents an innovative communication technology that enables devices to autonomously sense and utilize idle spectrum resources in wireless frequency bands. The power control algorithm typically involves iterative optimization where each device calculates its transmission power based on interference measurements and predefined utility functions.

In distributed power control systems, devices employ game-theoretic approaches to determine their transmission power levels, aiming to achieve equilibrium states. The implementation code structure generally includes modules for channel sensing, interference calculation, and power update mechanisms using gradient-based optimization methods. The non-cooperative Nash Equilibrium serves as a fundamental game theory solution concept where, after each participant selects their optimal strategy, no player can unilaterally improve their outcome by changing strategies. This equilibrium point can be computationally achieved through iterative algorithms that converge when power updates become negligible.

Our implementation incorporates price functions as penalty mechanisms to regulate interference and DPC power control methods for performance comparison. The algorithmic framework typically involves initializing transmission powers, computing signal-to-interference ratios (SIR), and updating powers using response functions that consider both utility maximization and price-based constraints. Key functions in the code implementation include calculate_nash_equilibrium() for equilibrium computation, update_power_levels() for iterative optimization, and compare_dpc_strategies() for performance benchmarking. Through this methodology, we can effectively analyze and optimize power control challenges in cognitive radio systems, achieving efficient spectrum utilization while maintaining quality of service requirements.