[Paper Review] Adaptive Resource Allocation in Jamming Teams Using Game Theory

Ali Khanafer, Sourabh Bhattacharya+1 more|arXiv (Cornell University)|Feb 6, 2011

Advanced Wireless Network Optimization12 references14 citations

TL;DR

This paper proposes a game-theoretic framework for adaptive resource allocation in jamming teams, where each agent splits its power between internal communication and jamming the opposing team. Using zero-sum matrix games and continuous kernel games, it establishes sufficient conditions for pure strategy saddle-point equilibria and demonstrates that teams adapt modulation schemes (e.g., 256-QAM) to balance communication reliability and jamming effectiveness under power and energy constraints.

ABSTRACT

In this work, we study the problem of power allocation and adaptive modulation in teams of decision makers. We consider the special case of two teams with each team consisting of two mobile agents. Agents belonging to the same team communicate over wireless ad hoc networks, and they try to split their available power between the tasks of communication and jamming the nodes of the other team. The agents have constraints on their total energy and instantaneous power usage. The cost function adopted is the difference between the rates of erroneously transmitted bits of each team. We model the adaptive modulation problem as a zero-sum matrix game which in turn gives rise to a a continuous kernel game to handle power control. Based on the communications model, we present sufficient conditions on the physical parameters of the agents for the existence of a pure strategy saddle-point equilibrium (PSSPE).

Motivation & Objective

• To address the challenge of power allocation between communication and jamming in mobile, energy-constrained ad hoc networks.
• To model adaptive modulation as a zero-sum matrix game to optimize spectral efficiency and jamming effectiveness.
• To ensure a non-zero communication rate by introducing minimum rate constraints in power allocation.
• To establish sufficient conditions for the existence of pure strategy saddle-point equilibria (PSSPE) based on physical parameters.
• To develop a games-within-games framework integrating trajectory planning, power allocation, and adaptive modulation for decentralized decision-making.

Proposed method

• Formulates the power allocation problem as a continuous kernel game to handle dynamic power control under energy and instantaneous power constraints.
• Models adaptive modulation as a zero-sum matrix game where each team selects modulation schemes (e.g., 16-, 64-, 256-QAM) to minimize BER difference.
• Uses the saddle-point equilibrium condition: min_i max_j A_ij = max_j min_i A_ij, to determine PSSPE existence.
• Applies Theorem 2 to prove existence of mixed-strategy saddle-point equilibria (MSSPE) for the modulation game.
• Employs the ordered interchangeability property to resolve ambiguity in multiple equilibria without inter-team coordination.
• Integrates the three-layered game structure: pursuit-evasion for trajectories, continuous kernel games for power allocation, and matrix games for modulation adaptation.

Experimental results

Research questions

• RQ1 Under what physical conditions does a pure strategy saddle-point equilibrium exist for power allocation in jamming teams?
• RQ2 How can adaptive modulation be optimally selected in a decentralized, noncooperative setting to balance communication and jamming?
• RQ3 What is the impact of energy and power constraints on the equilibrium strategies of jamming teams?
• RQ4 How does the choice of modulation scheme affect the BER difference and overall system performance under varying SNR conditions?
• RQ5 Can a games-within-games framework ensure robust, adaptive resource allocation across multiple decision layers (trajectory, power, modulation) in mobile ad hoc networks?

Key findings

• A sufficient condition for the existence of a pure strategy saddle-point equilibrium (PSSPE) in the power allocation game is derived based on physical parameters such as path loss, noise, and interference levels.
• In the simulation example, the unique PSSPE is found at {256, 256} modulation schemes, where the third row of the payoff matrix strictly dominates all others.
• At high SNR (50 dB), both teams switch to smaller modulation constellations (e.g., 16-QAM) to preserve communication reliability while allocating power to jamming.
• The adaptive modulation strategy dynamically shifts from high-rate communication to joint communication and jamming as environmental conditions change.
• The ordered interchangeability property ensures that teams can independently select from multiple equilibria without coordination, maintaining system stability.
• The framework successfully generalizes prior work by incorporating minimum rate constraints and enabling non-zero communication rates even under jamming pressure.