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 应用科技  2020, Vol. 47 Issue (6): 1-4  DOI: 10.11991/yykj.202007014 0

### 引用本文

LYU Wei, ZHANG Yu, LI Yibing. A power control algorithm based on non-cooperative game for cognitive heterogeneous cellular networks[J]. Applied Science and Technology, 2020, 47(6): 1-4. DOI: 10.11991/yykj.202007014.

### 文章历史

1. 联通(黑龙江)产业互联网有限公司，黑龙江 哈尔滨 150001;
2. 哈尔滨工程大学 信息与通信工程学院，黑龙江 哈尔滨 150001

A power control algorithm based on non-cooperative game for cognitive heterogeneous cellular networks
LYU Wei1, ZHANG Yu2, LI Yibing2
1. China Unicom (Heilongjiang) Industrial Internet Company Limited, Harbin 150001, China;
2. College of Information and Communication Engineering, Harbin Engineering University, Harbin 150001, China
Abstract: Aiming at the energy consumption problem of downlink in cognitive heterogeneous cellular networks, a power control algorithm based on non-cooperative game model is proposed in this paper. The cross layer interference is suppressed by limiting power and the total power of the secondary network base station. At the same time, the algorithm transforms the power control problem into a linear problem about the price factor to solve the optimal transmitting power of the cognitive femtocell base station, which can ensure the user service quality of the primary network and effectively improve the energy efficiency of the cognitive network.
Keywords: cognitive heterogeneous cellular network    non-cooperative game    energy efficiency    power control    interference suppression    price factor

1 系统模型

 ${{\rm{SINR}} _n} = \frac{{{p_n}{h_n}}}{{{p_m}{h_{mn}} + {\sigma ^2}}}$

 ${{\rm{SINR}} _m} = \frac{{{p_m}{h_m}}}{{{p_n}{h_{nm}} + {\sigma ^2}}}$

 ${p_n} \leqslant \dfrac{{\dfrac{{{p_m}{h_m}}}{{\gamma _0^{{\rm{th}}}}} - {\sigma ^2}}}{{{h_{nm}}}} = P_n^0$ (1)

 ${P_{n\max }} = \min \left\{ {P_n^0,P_n^1} \right\}$ (2)

 ${E_n} = \dfrac{{{R_n}}}{{{p_n} + {p_c}}}{\rm{ = }}\dfrac{{{B_n}{\rm{lb} }\Bigg(1{\rm{ + }}\dfrac{{{p_n}{h_n}}}{{{p_m}{h_{mn}} + {\sigma ^2}}}\Bigg)}}{{{p_n} + {p_c}}}$

2 功率控制 2.1 非合作博弈功率控制算法

 $G = \left\{ {N,\left\{ {{p_n}} \right\},\left\{ {{U_n}} \right\}} \right\}$

 $\begin{array}{l} {U_n} = {E_n} - {\lambda _n}{p_n}{\rm{ = }}\dfrac{{{B_n}{\rm{lb} }\Bigg(1{\rm{ + }}\dfrac{{{p_n}{h_n}}}{{{p_m}{h_{mn}} + {\sigma ^2}}}\Bigg)}}{{{p_n} + {p_c}}} - {\lambda _n}{p_n}{\rm{ }} \\ {\rm{s}}{\rm{.t}}{\rm{.}}\displaystyle\sum\limits_{n = 1}^N {{p_n}} \leqslant {P_{{\rm{total}}}} \end{array}$ (3)

2.2 最优解

 $p_n^* =\left\{ \begin{array}{l} {0}, \quad {{w_n}{\rm{ < 0}}{\text{且}}{w_n}{\rm{(}}{P_{n{\rm{max}}}}{\rm{) < 0}}}\\ {{P_{n\max }}}, \quad {{w_n}{\rm{ > 0}}{\text{且}}{w_n}{\rm{(}}{P_{n{\rm{max}}}}{\rm{) > 0}}}\\ {\mathop {\arg }\limits_{{p_n}} ({w_n} = 0)}, \quad {{w_n}{\rm{ > 0}}{\text{且}}{w_n}{\rm{(}}{P_{n{\rm{max}}}}{\rm{) < 0}}} \end{array} \right.$

 $\begin{array}{l} \;\; {w_n} = ({p_n} + {p_c}){\rm{lb}}\dfrac{{\rm{e}}{{h_n}}}{{{p_m}{h_{mn}} + {\sigma ^2}}} - \\ \Bigg(1 + \dfrac{{{h_n}{p_n}}}{{{p_m}{h_{mn}} + {\sigma ^2}}}\Bigg){\rm{lb}}\Bigg(1 + \dfrac{{{h_n}{p_n}}}{{{p_m}{h_{mn}} + {\sigma ^2}}}\Bigg) - \\ \;\;\;\;\;\; {\lambda _n}\Bigg(1 + \dfrac{{{h_n}{p_n}}}{{{p_m}{h_{mn}} + {\sigma ^2}}}\Bigg){({p_n} + {p_c})^2} \end{array}$

 $\begin{array}{c} \;\; {f_n} = \dfrac{{({p_n} + {p_c}){\rm{lb}}\dfrac{{\rm{e}}{{h_n}}}{{{p_m}{h_{mn}} + {\sigma ^2}}}}}{{\Bigg(1 + \dfrac{{{h_n}{p_n}}}{{{p_m}{h_{mn}} + {\sigma ^2}}}\Bigg){{({p_n} + {p_c})}^2}}} - \\ \dfrac{{\Bigg(1 + \dfrac{{{h_n}{p_n}}}{{{p_m}{h_{mn}} + {\sigma ^2}}}\Bigg){\rm{lb}}\Bigg(1 + \dfrac{{{h_n}{p_n}}}{{{p_m}{h_{mn}} + {\sigma ^2}}}\Bigg)}}{{\Bigg(1 + \dfrac{{{h_n}{p_n}}}{{{p_m}{h_{mn}} + {\sigma ^2}}}\Bigg){{({p_n} + {p_c})}^2}}} \\ \;\;\;\;{f_{n\min }} = {f_n}({P_{n\max}}) = {\tilde \lambda ^0}\\ \;\;\;\;{f_{n\min }} = {f_n}({p_{{g_n} = 0}}) = {\tilde \lambda ^1}\\ \;\;\;\; \;\;\;\;{\tilde \lambda _{\max }} = {f_n}(0)\end{array}$

 ${\tilde \lambda _n} \in [\max\{ {\tilde \lambda ^0},{\tilde \lambda ^1}\} ,{\tilde \lambda _{\max }}]$
3 仿真分析