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 重庆邮电大学学报(自然科学版)  2020, Vol. 32 Issue (3): 394-399  DOI: 10.3979/j.issn.1673-825X.2020.03.008 0

### 引用本文

ZHANG Gongguo, WU Cuixian, XU Yongjun. Interference efficiency-based power allocation for cognitive OFDMA networks[J]. Journal of Chongqing University of Posts and Telecommunications (Natural Science Edition), 2020, 32(3): 394-399.   DOI: 10.3979/j.issn.1673-825X.2020.03.008.

### Foundation item

The National Natural Science Foundation of China (61601071); The Science and Technology Research Program of Chongqing Municipal Education Commission (KJQN201800606); The Open Research Fund from Shandong Provincial Key Lab of Wireless Communication Technologies (SDKLWCT-2019-04)

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### 文章历史

1. 重庆邮电大学 通信与信息工程学院, 重庆 400065;
2. 重庆信科通信工程有限公司 通信工程应用新技术研究所, 重庆 401121;
3. 山东大学 山东省无线通信技术重点实验室, 济南 250100

Interference efficiency-based power allocation for cognitive OFDMA networks
ZHANG Gongguo1,2 , WU Cuixian1 , XU Yongjun1,3
1. School of Communication and Information Engineering, Chongqing University of Posts and Telecommunications, Chongqing 400065, P. R. China;
2. Chongqing Information Technology Communication Engineering Co. Ltd, Chongqing 401121, P. R. China;
3. Shandong Provincial Key Lab. of Wireless Communication Technologies, Shandong University, Jinan 250100, P. R. China
Abstract: In order to improve the energy efficiency of cognitive radio networks and reduce the total interference to the primary users, this paper proposed a new interference efficiency-based maximization power allocation algorithm for downlink cognitive orthogonal frequency division multiplexing access (OFDMA) networks. Interference efficiency is defined as the total rate of secondary users over the total interference to the primary users. Since the original problem is a non-convex fractional programming problem, it is difficult to obtain the analytical solution for power allocation. Based on the Dinkelbach method, the original problem is firstly converted into a convex optimization problem. Then it is solved by using Lagrange dual methods and the subgradient updating methods. Lastly, simulation results show that the proposed algorithm has good convergence, and it outperforms the traditional energy efficiency maximization-based power allocation algorithm in terms of interference efficiency and the protection for primary users.
Keywords: cognitive OFDM networks    power allocation    Lagrange dual method    interference efficiency
0 引言

1 系统模型

 $\sum\limits_{n = 1}^N {{p_n}} {g_{n, m}} \le I_m^{{\rm{th}}}, \forall m, m = 1, 2, \cdots , M$ (1)

(1) 式中：pn为次用户基站分配给次用户n的发射功率；gn, m表示次用户n与主用户m之间的信道增益；Imth为每个主用户接收机m处的干扰温度门限值。如果次用户的发射功率满足上述约束，那么主用户的通信质量将得到保护。

 ${\sum\limits_{n = 1}^N {{p_n}} \le {p^{{\rm{max}}}}}$ (2)
 ${{p_n} \le p_n^{{\rm{max}}}, \forall n}$ (3)

(2)—(3)式中：pmax为次用户发射功率的最大值；pnmax为子载波n上的峰值发射功率门限。

 ${R_n} = {\rm{lb}} \left( {1 + \frac{{{p_n}{h_n}}}{\sigma }} \right)$ (4)

(4) 式中：hn表示次用户基站到用户n的信道增益；σ表示接收机端的背景噪声。

 $\begin{array}{l} \mathop {{\rm{max}}}\limits_{{p_n}} \frac{{\sum\limits_{n = 1}^N { {\rm{lb}} } (1 + {p_n}{h_n}/\sigma )}}{{\sum\limits_{m = 1}^M {\sum\limits_{n = 1}^N {{p_n}} } {g_{n, m}}}}\\ \begin{array}{*{20}{l}} {{\rm{s}}{\rm{.t}}{\rm{.}}{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\rm{C1}}:\sum\limits_{n = 1}^N {{p_n}} \le {p^{{\rm{max}}}}}\\ {{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\rm{C2}}:{p_n} \le p_n^{{\rm{max}}}, \forall n}\\ {{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\rm{C3}}:\sum\limits_{n = 1}^N {{p_n}} {g_{n, m}} \le I_m^{{\rm{th}}}, \forall m} \end{array} \end{array}$ (5)

 $\begin{array}{l} \mathop {{\rm{max}}}\limits_{{p_n}} \sum\limits_{n = 1}^N { {\rm{lb}} } (1 + {p_n}{h_n}/\sigma ) - \eta \sum\limits_{m = 1}^M {\sum\limits_{n = 1}^N {{p_n}} } {g_{n, m}}\\ \begin{array}{*{20}{l}} {{\rm{s}}{\rm{.t}}{\rm{.}}{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\rm{C1}}:\sum\limits_{n = 1}^N {{p_n}} \le {p^{{\rm{max}}}}}\\ {{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\rm{C2}}:{p_n} \le p_n^{{\rm{max}}}, \forall n}\\ {{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\rm{C3}}:\sum\limits_{n = 1}^N {{p_n}} {g_{n, m}} \le I_m^{{\rm{th}}}, \forall m} \end{array} \end{array}$ (6)

(6) 式中，η可以考虑成对总干扰功率的代价因子。对于给定的η，目标函数可以重新定义为

 $f(\eta ) = \sum\limits_{n = 1}^N { {\rm{lb}} } (1 + {p_n}{h_n}/\sigma ) - \eta \sum\limits_{m = 1}^M {\sum\limits_{n = 1}^N {{p_n}} } {g_{n, m}}$ (7)

 $\begin{array}{*{20}{l}} {f({\eta ^*}) = \sum\limits_{n = 1}^N { {\rm{lb}} } (1 + p_n^*{h_n}/\sigma ) - }\\ {{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\eta ^*}\sum\limits_{m = 1}^M {\sum\limits_{n = 1}^N {p_n^*} } {g_{n, m}} = 0} \end{array}$ (8)

 ${\eta ^*} = \frac{{\sum\limits_{n = 1}^N { {\rm{lb}} } (1 + p_n^*{h_n}/\sigma )}}{{\sum\limits_{m = 1}^M {\sum\limits_{n = 1}^N {p_n^*} } {g_{n, m}}}}$ (9)

2 功率分配算法设计

 $\begin{array}{l} \mathop {{\rm{max}}}\limits_{{p_n}} \sum\limits_{n = 1}^N { {\rm{lb}} } (1 + {p_n}{h_n}/\sigma ) - \eta \sum\limits_{m = 1}^M {\sum\limits_{n = 1}^N {{p_n}} } {g_{n, m}}\\ \begin{array}{*{20}{l}} {{\rm{s}}{\rm{.t}}{\rm{.}}{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\rm{C1}}:\sum\limits_{n = 1}^N {{p_n}} \le {p^{{\rm{max}}}}}\\ {{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\rm{C2}}:{p_n} \le p_n^{{\rm{max}}}, \forall n}\\ {{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\rm{C3}}:\sum\limits_{n = 1}^N {{p_n}} {g_{n, m}} \le I_m^{{\rm{th}}}, \forall m} \end{array} \end{array}$ (10)

 $\begin{array}{*{20}{c}} {L(\{ {p_n}\} , \eta , \alpha , \{ {\beta _m}\} ) = \sum\limits_{n = 1}^N { {\rm{lb}} } (1 + {p_n}{h_n}/\sigma ) - }\\ {\eta \sum\limits_{m = 1}^M {\sum\limits_{n = 1}^N {{p_n}} } {g_{n, m}} + \alpha ({p^{{\rm{max}}}} - \sum\limits_{n = 1}^N {{p_n}} ) + }\\ {\sum\limits_{m = 1}^M {{\beta _m}} (I_m^{{\rm{th}}} - \sum\limits_{n = 1}^N {{p_n}} {g_{n, m}})} \end{array}$ (11)

(11) 式中，α≥0和βm≥0表示发射功率和干扰温度约束对应的拉格朗日乘子(或称之为对偶变量)。该拉格朗日函数可以写成的分解形式为

 $\begin{array}{*{20}{l}} {L(\{ {p_n}\} , \eta , \alpha , \{ {\beta _m}\} ) = \sum\limits_{n = 1}^N {{L_n}} (\{ {p_n}\} , \eta , \alpha , \{ {\beta _m}\} ) + }\\ {{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} \alpha {p^{{\rm{max}}}} + \sum\limits_{m = 1}^M {{\beta _m}} I_m^{{\rm{th}}}} \end{array}$ (12)

(12) 式中

 $\begin{array}{*{20}{l}} {{L_n}(\{ {p_n}\} , \eta , \alpha , \{ {\beta _m}\} ) = {\rm{lb}} (1 + {p_n}{h_n}/\sigma ) - }\\ {{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} \sum\limits_{m = 1}^M {(\eta + {\beta _m}){p_n}{g_{n, m}} - \alpha {p_n}} } \end{array}$ (13)

 $\begin{array}{l} \mathop {{\rm{min}}}\limits_{\alpha , {\beta _m}} D(\alpha , \{ {\beta _m}\} )\\ {\rm{s}}{\rm{.t}}{\rm{.}}{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} \alpha \ge 0, {\beta _m} \ge 0 \end{array}$ (14)

(14) 式中，对偶函数为

 $D(\alpha , \{ {\beta _m}\} ) = \mathop {{\rm{max}}}\limits_{{p_n}} L(\{ {p_n}\} , \eta , \alpha , \{ {\beta _m}\} )$ (15)

 $p_n^* = \left[ {\frac{1}{{{\rm{ln}}2(\alpha + \sum\limits_{m = 1}^M {(\eta + {\beta _m})} {g_{n, m}})}} - \frac{\sigma }{{{h_n}}}} \right]_0^{p_n^{{\rm{max}}}}$ (16)

(16) 式中，[x]ab=min(b, max(a, x))。基于次梯度更新算法，拉格朗日乘子可以描述为

 $\alpha (t + 1) = {[\alpha (t) - {t_1} \times ({p^{{\rm{max}}}} - \sum\limits_{n = 1}^N {{p_n}} )]^ + }$ (17)
 ${\beta _m}(t + 1) = {[{\beta _m}(t) - {t_2} \times (I_m^{{\rm{th}}} - \sum\limits_{n = 1}^N {{p_n}} {g_{n, m}})]^ + }$ (18)

(17)—(18)式中：[y]+=max(0, y)；t表示迭代次数；t1>0和t2>0表示迭代步长。当选择合适的步长，可以保证算法快速收敛到最优值。

3 仿真分析

 图 1 干扰效率收敛性能 Fig.1 Convergence performance of interference efficiency

 图 2 不同算法干扰效率与能量效率对比 Fig.2 Interference efficiency and energy efficiency under different schemes

 图 4 不同用户数量对系统干扰功率的影响 Fig.4 Received interference power versus the number of secondary users

 图 5 不同用户数量对系统干扰效率的影响 Fig.5 Total interference efficiency versus the number of secondary users
4 结论

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