[Paper Review] Non-cooperative games for spreading code optimization, power control and receiver design in wireless data networks

Stefano Buzzi, H. Vincent Poor|ArXiv.org|May 6, 2007

Wireless Communication Networks Research10 references3 citations

TL;DR

This paper proposes non-cooperative game-theoretic frameworks for joint optimization of spreading codes, transmit power, and receiver design in DS-CDMA wireless networks to maximize user-specific energy efficiency (throughput per unit power). It demonstrates that both linear and non-linear multiuser receivers—especially with spreading code optimization—achieve significant performance gains, with unique Nash equilibria proven to exist, outperforming prior approaches in simulations across various system loads.

ABSTRACT

This paper focuses on the issue of energy efficiency in wireless data networks through a game theoretic approach. The case considered is that in which each user is allowed to vary its transmit power, spreading code, and uplink receiver in order to maximize its own utility, which is here defined as the ratio of data throughput to transmit power. In particular, the case in which linear multiuser detectors are employed at the receiver is treated first, and, then, the more challenging case in which non-linear decision feedback multiuser receivers are adopted is addressed. It is shown that, for both receivers, the problem at hand of utility maximization can be regarded as a non-cooperative game, and it is proved that a unique Nash equilibrium point exists. Simulation results show that significant performance gains can be obtained through both non-linear processing and spreading code optimization; in particular, for systems with a number of users not larger than the processing gain, remarkable gains come from spreading code optimization, while, for overloaded systems, the largest gainscome from the use of non-linear processing. In every case, however, the non-cooperative games proposed here are shown to outperform competing alternatives.

Motivation & Objective

• To address energy efficiency in uplink DS-CDMA networks by enabling users to independently optimize their transmit power, spreading codes, and receiver structures.
• To model the joint optimization of power control, spreading code selection, and receiver design as a non-cooperative game, where each user maximizes its own utility (throughput per transmit power).
• To prove the existence and uniqueness of a Nash equilibrium in both linear and non-linear receiver scenarios, ensuring stable system operation.
• To evaluate the performance gains from spreading code optimization and non-linear interference cancellation under varying system loads (underloaded vs. overloaded).

Proposed method

• Formulates a non-cooperative game where each user independently selects its transmit power, spreading code, and receiver structure to maximize its utility (throughput/power ratio).
• For linear receivers, uses a game-theoretic framework with iterative power and code optimization, leveraging large-system analysis to derive convergence properties.
• For non-linear decision feedback receivers, introduces two-stage games: first optimizing power, then jointly optimizing spreading codes and power using iterative algorithms.
• Employs a modified minimum mean square error (MMSE) receiver with decision feedback to suppress multiuser interference, enhancing SINR and throughput.
• Derives conditions for unit-norm spreading codes via eigen-decomposition and iterative adjustment of regularization parameters (μk) in the receiver design.
• Uses large-system analysis to characterize system behavior in the limit of large processing gain N, enabling tractable equilibrium analysis.

Experimental results

Research questions

• RQ1 Does a unique Nash equilibrium exist in a non-cooperative game where users jointly optimize power, spreading codes, and receiver design in a CDMA uplink?
• RQ2 How do spreading code optimization and non-linear receiver design impact energy efficiency and system performance in lightly loaded (K ≤ N) versus heavily loaded (K > N) CDMA systems?
• RQ3 What are the relative performance gains from spreading code optimization versus non-linear interference cancellation across different system loads?
• RQ4 How does the proposed game-theoretic framework compare to prior approaches that fix the receiver or omit spreading code optimization?
• RQ5 Can iterative algorithms based on the game structure converge to the unique equilibrium while maintaining unit-norm spreading codes?

Key findings

• A unique Nash equilibrium exists for both linear and non-linear receiver scenarios, ensuring stable and predictable system operation under non-cooperative user behavior.
• For systems with K ≤ N (underloaded), spreading code optimization provides the most significant performance gains, significantly improving average output SINR and reducing the fraction of users transmitting at maximum power.
• For overloaded systems (K > N), non-linear decision feedback receivers (especially SIC/MMSE) deliver the largest gains, outperforming linear receivers and fixed-code schemes.
• The proposed non-cooperative games consistently outperform the benchmark game from [7], which only optimizes power and linear receiver design, across all system loads.
• Even with fading and path loss, the SIC/MMSE receiver with code optimization maintains an average output SINR below the target γ̄, indicating that some users cannot achieve optimal SINR without exceeding power limits.
• The fraction of users transmitting at maximum power exceeds 10% in the SIC/MMSE case with code optimization, highlighting the need for adaptive power control in practical deployments.