Abstract
Small cell is an emerging and promising technology for improving hotspots coverage and capacity, which tends to be densely deployed in populated areas. However, in a dense small cell network, the performances of users differ vastly due to the random deployments and the interferences. To guarantee fair performance among users in different cells, we propose a new distributed strategy for fairness constrained power control, referred to as the diffusion adaptive power control (DAPC). DAPC achieves overall network fairness in a distributed manner, in which each base station optimizes a local fairness with little information exchanged with neighboring cells. We study several adaptive algorithms to implement the proposed DAPC strategy. To improve the efficiency of the standard least mean square algorithm (LMS), we derive an adaptive step-size logarithm LMS algorithm, and discuss its convergence properties. Simulation results confirm the efficiency of the proposed methods.
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Acknowledgements
This work is supported by the National Natural Science Foundation of China under Grant No. 61372092 and “863” Fund under Grants 2014AA01A701
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Appendix
Appendix
1.1 Proof of (13)
We define the transmit power in dB, \(p\_dB_{FAP_{i,t} } \), as
Since the update is in logarithm, the gradient should also be changed as the gradient of \(p\_dB_{FAP_{i,t} } \).
where \(\mu \) is a fixed value and \(\frac{10}{p_{FAP_{i,t} } \ln 10}\) is always positive. In this way, the update is adaptive step-size and it is redefined as
which completes the proof. \(\square \)
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Luan, Z., Qu, H., Zhao, J. et al. Fairness constrained diffusion adaptive power control for dense small cell network. Telecommun Syst 68, 373–384 (2018). https://doi.org/10.1007/s11235-017-0387-z
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DOI: https://doi.org/10.1007/s11235-017-0387-z