Nash Bargaining Game-Theoretic Framework for Power Control in Distributed Multiple-Radar Architecture Underlying Wireless Communication System
<p>Illustration of the system model for spectrum sharing between DMRS and the wireless communication system with their corresponding channel gains.</p> "> Figure 2
<p>Simulated 2D scenario with locations of multiple radars, communication user and target.</p> "> Figure 3
<p>Convergence of power control results in different cases: (<b>a</b>) Case 1 with <math display="inline"> <semantics> <msub> <mi mathvariant="bold">σ</mi> <mrow> <mi>RCS</mi> <mo>,</mo> <mn>1</mn> </mrow> </msub> </semantics> </math>; (<b>b</b>) Case 1 with <math display="inline"> <semantics> <msub> <mi mathvariant="bold">σ</mi> <mrow> <mi>RCS</mi> <mo>,</mo> <mn>2</mn> </mrow> </msub> </semantics> </math>; (<b>c</b>) Case 2 with <math display="inline"> <semantics> <msub> <mi mathvariant="bold">σ</mi> <mrow> <mi>RCS</mi> <mo>,</mo> <mn>1</mn> </mrow> </msub> </semantics> </math>; (<b>d</b>) Case 2 with <math display="inline"> <semantics> <msub> <mi mathvariant="bold">σ</mi> <mrow> <mi>RCS</mi> <mo>,</mo> <mn>2</mn> </mrow> </msub> </semantics> </math>.</p> "> Figure 4
<p>The power ratio results in different cases: (<b>a</b>) Case 1 with <math display="inline"> <semantics> <msub> <mi mathvariant="bold">σ</mi> <mrow> <mi>RCS</mi> <mo>,</mo> <mn>1</mn> </mrow> </msub> </semantics> </math>; (<b>b</b>) Case 1 with <math display="inline"> <semantics> <msub> <mi mathvariant="bold">σ</mi> <mrow> <mi>RCS</mi> <mo>,</mo> <mn>2</mn> </mrow> </msub> </semantics> </math>; (<b>c</b>) Case 2 with <math display="inline"> <semantics> <msub> <mi mathvariant="bold">σ</mi> <mrow> <mi>RCS</mi> <mo>,</mo> <mn>1</mn> </mrow> </msub> </semantics> </math>; (<b>d</b>) Case 2 with <math display="inline"> <semantics> <msub> <mi mathvariant="bold">σ</mi> <mrow> <mi>RCS</mi> <mo>,</mo> <mn>2</mn> </mrow> </msub> </semantics> </math>.</p> "> Figure 5
<p>Convergence of SINR in different cases: (<b>a</b>) Case 1 with <math display="inline"> <semantics> <msub> <mi mathvariant="bold">σ</mi> <mrow> <mi>RCS</mi> <mo>,</mo> <mn>1</mn> </mrow> </msub> </semantics> </math>; (<b>b</b>) Case 1 with <math display="inline"> <semantics> <msub> <mi mathvariant="bold">σ</mi> <mrow> <mi>RCS</mi> <mo>,</mo> <mn>2</mn> </mrow> </msub> </semantics> </math>; (<b>c</b>) Case 2 with <math display="inline"> <semantics> <msub> <mi mathvariant="bold">σ</mi> <mrow> <mi>RCS</mi> <mo>,</mo> <mn>1</mn> </mrow> </msub> </semantics> </math>; (<b>d</b>) Case 2 with <math display="inline"> <semantics> <msub> <mi mathvariant="bold">σ</mi> <mrow> <mi>RCS</mi> <mo>,</mo> <mn>2</mn> </mrow> </msub> </semantics> </math>.</p> "> Figure 6
<p>Comparisons of equilibrium transmit power in different cases employing various methods: (<b>a</b>) Case 1 with <math display="inline"> <semantics> <msub> <mi mathvariant="bold">σ</mi> <mrow> <mi>RCS</mi> <mo>,</mo> <mn>1</mn> </mrow> </msub> </semantics> </math>; (<b>b</b>) Case 1 with <math display="inline"> <semantics> <msub> <mi mathvariant="bold">σ</mi> <mrow> <mi>RCS</mi> <mo>,</mo> <mn>2</mn> </mrow> </msub> </semantics> </math>; (<b>c</b>) Case 2 with <math display="inline"> <semantics> <msub> <mi mathvariant="bold">σ</mi> <mrow> <mi>RCS</mi> <mo>,</mo> <mn>1</mn> </mrow> </msub> </semantics> </math>; (<b>d</b>) Case 2 with <math display="inline"> <semantics> <msub> <mi mathvariant="bold">σ</mi> <mrow> <mi>RCS</mi> <mo>,</mo> <mn>2</mn> </mrow> </msub> </semantics> </math>.</p> "> Figure 7
<p>Comparisons of equilibrium SINR in different cases employing various methods: (<b>a</b>) Case 1 with <math display="inline"> <semantics> <msub> <mi mathvariant="bold">σ</mi> <mrow> <mi>RCS</mi> <mo>,</mo> <mn>1</mn> </mrow> </msub> </semantics> </math>; (<b>b</b>) Case 1 with <math display="inline"> <semantics> <msub> <mi mathvariant="bold">σ</mi> <mrow> <mi>RCS</mi> <mo>,</mo> <mn>2</mn> </mrow> </msub> </semantics> </math>; (<b>c</b>) Case 2 with <math display="inline"> <semantics> <msub> <mi mathvariant="bold">σ</mi> <mrow> <mi>RCS</mi> <mo>,</mo> <mn>1</mn> </mrow> </msub> </semantics> </math>; (<b>d</b>) Case 2 with <math display="inline"> <semantics> <msub> <mi mathvariant="bold">σ</mi> <mrow> <mi>RCS</mi> <mo>,</mo> <mn>2</mn> </mrow> </msub> </semantics> </math>.</p> "> Figure 8
<p>Comparisons of interference power levels in different cases employing various methods: (<b>a</b>) Case 1 with <math display="inline"> <semantics> <msub> <mi mathvariant="bold">σ</mi> <mrow> <mi>RCS</mi> <mo>,</mo> <mn>1</mn> </mrow> </msub> </semantics> </math>; (<b>b</b>) Case 1 with <math display="inline"> <semantics> <msub> <mi mathvariant="bold">σ</mi> <mrow> <mi>RCS</mi> <mo>,</mo> <mn>2</mn> </mrow> </msub> </semantics> </math>; (<b>c</b>) Case 2 with <math display="inline"> <semantics> <msub> <mi mathvariant="bold">σ</mi> <mrow> <mi>RCS</mi> <mo>,</mo> <mn>1</mn> </mrow> </msub> </semantics> </math>; (<b>d</b>) Case 2 with <math display="inline"> <semantics> <msub> <mi mathvariant="bold">σ</mi> <mrow> <mi>RCS</mi> <mo>,</mo> <mn>2</mn> </mrow> </msub> </semantics> </math>.</p> ">
Abstract
:1. Introduction
1.1. Background and Motivation
1.2. Literature Review
1.3. Major Contributions
- (1)
- We formulate the power control problem for DMRS underlying a wireless communication system as a cooperative Nash bargaining game, which complies fully with the Nash bargaining axioms. A unified analytical framework is proposed to maximize the overall utility function of the DMRS, where the interference power constraints (IPCs) are imposed to protect the communication user’s transmission, a minimum SINR requirement is employed to provide reliable target detection performance and the maximum power resource limitations are considered. The power control decisions of all radars are coupled in the IPCs, which makes the distributed optimization much more complex. To solve this difficulty, the IPCs are transformed into an extra pricing term in the constructed mathematical formulation [34], which not only reflects the spectrum sharing between DMRS and the communication system, but also complies with all the axioms in the Nash theorem.
- (2)
- The existence, uniqueness and fairness of the NBS to this game are proven. Then, an iterative Nash bargaining power control algorithm is developed, which is shown to converge to a Pareto-optimal equilibrium for the cooperative bargaining game.
- (3)
- The proposed algorithm is evaluated by extensive numerical simulations, which demonstrate that the proposed cooperative Nash bargaining power control algorithm outperforms other existing approaches in terms of power saving, target detection and spectrum coexistence performance between DMRS and communication system in the same frequency band.
1.4. Organization of the Paper
2. System Model
2.1. Problem Scenario
2.2. Signal Model
3. Nash Bargaining Game-theoretic Power Control in DMRS
3.1. Basis of the Technique
3.2. Basics of Nash Bargaining Games
3.3. Utility Function Design and Power Control Game Formulation
3.4. Potential Extension
4. Nash Bargaining Power Control Solutions for DMRS
4.1. Solution of the Cooperative Game
4.2. Update of the Lagrange Multipliers
4.3. Iterative Nash Bargaining Power Control Algorithm
Algorithm 1 Cooperative bargaining power control algorithm. |
|
5. Simulation Results and Discussion
5.1. Simulation Settings
5.2. Simulation Results
5.2.1. Convergence Performance
5.2.2. Superiority of Our Proposed Algorithm
5.2.3. Spectrum Sharing Performance
6. Conclusion Remarks
Acknowledgments
Author Contributions
Conflicts of Interest
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Shi, C.; Wang, F.; Salous, S.; Zhou, J.; Hu, Z. Nash Bargaining Game-Theoretic Framework for Power Control in Distributed Multiple-Radar Architecture Underlying Wireless Communication System. Entropy 2018, 20, 267. https://doi.org/10.3390/e20040267
Shi C, Wang F, Salous S, Zhou J, Hu Z. Nash Bargaining Game-Theoretic Framework for Power Control in Distributed Multiple-Radar Architecture Underlying Wireless Communication System. Entropy. 2018; 20(4):267. https://doi.org/10.3390/e20040267
Chicago/Turabian StyleShi, Chenguang, Fei Wang, Sana Salous, Jianjiang Zhou, and Zhentao Hu. 2018. "Nash Bargaining Game-Theoretic Framework for Power Control in Distributed Multiple-Radar Architecture Underlying Wireless Communication System" Entropy 20, no. 4: 267. https://doi.org/10.3390/e20040267
APA StyleShi, C., Wang, F., Salous, S., Zhou, J., & Hu, Z. (2018). Nash Bargaining Game-Theoretic Framework for Power Control in Distributed Multiple-Radar Architecture Underlying Wireless Communication System. Entropy, 20(4), 267. https://doi.org/10.3390/e20040267