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Tong检测算法性能分析及参数设置

1. 北京航空航天大学 机械工程及自动化学院, 北京 100191;
2. 北京航空航天大学 电子信息工程学院, 北京 100191

Performance analysis and parameter setting for Tong detection algorithm
ZHU Yunlong1, CHOU Wusheng1, YANG Dongkai2
1. School of Mechanical Engineering and Automation, Beijing University of Aeronautics and Astronautics, Beijing 100191, China;
2. School of Electronic and Information Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100191, China
Abstract:Tong detection algorithm is a common used signal detection algorithm. But the overall conclusions about statistical performance and parameter setting of Tong detection algorithm are absent. Aiming at these problems, statistical and recursive analysis methods were used to carry on theoretical analysis about mean value and variance of dwell times in signal search unit in detail, the corresponding expressions were given, a maximum dwell times constraint method was offered according to the 3Sigma principle. The relationships between detection probability, average dwell times of noise search unit and signal search unit, initial value and maximum value of algorithm counter, pre-detection signal to noise ratio were analyzed. Analysis results indicate that the parameters of Tong detection algorithm should be set according to signal strength and search modes, and the influence of parameter setting on detection probability and average dwell times of noise search unit or signal search unit should be balanced.

1 Tong检测算法结构

Tong算法结构如图 1所示[2].该算法设定一个向上/向下计数器k,最大值为A,初始值为B.若检测量超过判决门限Vt,则k加1,否则减1,当K=A时捕获成功,k=0时该搜索单元被否决,进入下一搜索单元进行检测.为防止kA与0之间徘徊,可规定一个最大滞留次数Nmax,如在某一单元的滞留次数超过Nmax,则放弃此单元.

 图 1 Tong检测算法结构Fig. 1 Structure of Tong detection algorithm

H1表示信号存在,H0表示信号不存在.对功率检测量做归一化处理:z=l/σn2.其中,σn2是I路或Q路预检测积分结果中噪声的功率.可以证明[2],z满足如式(2)和式(3)所示的卡方分布：

2 滞留次数的统计特性 2.1 平均滞留次数 2.1.1 噪声搜索单元平均滞留次数

2.1.2 信号搜索单元平均滞留次数

P(X(i－1)=Ai|k=i－1)=P(X(i－1)=Ai－1|k=i－1)=0

a=(1－Pd)/Pd,b=1/Pd,解差分方程得
i等于计数器初始值B,并将ab表达式代入式(12),可得检测信号单元的平均滞留次数为
2.2 信号搜索单元滞留次数方差

Ds(i)为计数器值为i时滞留次数X(i)的方差,由方差的定义容易得到

Rs(i)=E[X2(i)k=i].对Rs(i)的讨论也分为成功捕获和发生漏检两种情况.使用与推导均值时类似的方法处理Rs(i),可以得到两种情况下相同的递推表达式.计数器到达0和A的时候,X(i)为确定性事件,且等于0,因此Rs(0)=Rs(A)=0.递推模型为

Δ(i)=Rs(i)－Rs(i+1),对式(15)变形可得

2.3 最大滞留次数的选择方法

3 Tong检测算法性能分析

 图 2 Tong算法总检测概率Fig. 2 Total detection probabilities of Tong algorithm
3.2 平均滞留次数分析 3.2.1 噪声搜索单元中的平均滞留次数

 A B 4 6 8 10 12 1 1.02 1.14 1.33 1.57 1.83 2 2.04 2.27 2.65 3.11 3.61
3.2.2 信号搜索单元中的平均滞留次数

 B A 4 6 8 10 12 1 2.93 6.04 8.05 10.00 11.98 2 4.00 6.81 8.44 10.22 12.13

 B A 4 6 8 10 12 1 3.26 5.15 7.10 9.08 11.07 2 2.62 4.32 6.21 8.17 10.15

A一定时,若s/n较低,则B较小时,平均滞留次数也较小,B较大时,平均滞留次数也较大.这是由于当s/n较低时,尤其当A也较小时,检测概率也较低,例如s/n=6 dB,A=4,B=1时,Pd=48.36%,PD=22.60%;A=4,B=2时,Pd=48.32%,PD=36.02%,这种情况下很容易发生漏检,计数器值减小并到达0的概率较大,此时不同B值下的单次检测概率较为接近,则B越小,计数器越容易到达0,平均滞留次数也越小.随着A的增大,检测概率也在增大,计数器值增加并到达A的可能性变大,但单次检测概率仍不是很高,中间过程有可能出现反复,例如s/n=6 dB,A=8,B=1时,Pd=83.99%,PD=80.94%;A=8,B=2时,Pd=83.78%,PD=96.25%,B较小时单次检测概率稍大,因此平均滞留次数稍小.

A一定时,若s/n较高,则B较小时,平均滞留次数较大,B较大时,平均滞留次数较小.这是由于,若s/n较高,则检测概率也较高,例如s/n=9 dB时,A=4,B=1时,Pd=86.31%,PD=84.19%;A=4,B=2时,Pd=86.28%,PD=97.48%;A=12,B=1时,Pd=99.30%,PD=99.29%;A=12,B=2时,Pd=99.27%,PD=99.99%.这时,计数器值增加并到达A的概率较大,且不同B值下的单次检测概率较为接近,则初始位置越接近A,平均滞留次数越小.随着A的增加,不同B值下的平均滞留次数之差趋于定值,即计数器初始位置之差,例如,B=1和B=2两种情况下的平均滞留次数之差随着A的增加趋于1.

 A B (s/n)/dB 6 7 8 9 10 4 1 2.93 3.34 3.40 3.26 3.12 4 2 4.00 3.80 3.21 2.62 2.25 6 1 6.04 5.69 5.36 5.15 5.05 6 2 6.81 5.62 4.79 4.32 4.10 8 1 8.05 7.59 7.28 7.10 7.03 8 2 8.44 7.28 6.58 6.21 6.06 10 1 10.00 9.53 9.23 9.08 9.02 10 2 10.22 9.13 8.49 8.17 8.04 12 1 11.98 11.50 11.21 11.07 11.02 12 2 12.13 11.06 10.44 10.15 10.04

Tong算法的主要可调参数是AB.通过以上分析可知,当信号较强(即s/n较大)时,AB的值不需要取很大就能满足检测概率的需求.对于串行搜索,检测多数情况下在噪声单元中进行,适当增大A、减小B可以在保证检测概率的前提下,减小噪声单元中的平均滞留次数,例如可选A=8,B=1;对于并行搜索,信号单元滞留次数影响较大,可以适当减小A、增大B,这样可以在保证检测概率的前提下,减小信号单元中的平均滞留次数,缩短捕获时间,例如可选A=6,B=2.

1) 在涅曼-皮尔逊准则下,增加计数器上限A和初值B能使Tong检测算法的总检测概率提高,增加B的效果尤为明显.

2) 增加AB的值会使检测噪声单元的平均滞留次数增加,增加B的效果更为明显.

3) 信号单元的平均滞留次数远大于噪声单元的平均滞留次数,增大A会使信号单元的平均滞留次数增加.若预检测信噪比s/n较低,则B较小时,平均滞留次数也较小,B较大时,平均滞留次数也较大;若s/n较高,则B较小时,平均滞留次数较大,B较大时,平均滞留次数较小.

4) AB一定时,一般情况下信号单元平均滞留次数随着s/n的提高而减小.若AB均较小,则信号单元平均滞留次数随着s/n的提高先增大而后减小.

5) AB的选择需依据信号强弱和搜索方式,并且要折衷考虑对检测概率与平均滞留次数的影响.

6) 最大滞留次数可依据信号单元滞留次数的均值和方差,采用3西格玛原则确定.

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#### 文章信息

ZHU Yunlong, CHOU Wusheng, YANG Dongkai
Tong检测算法性能分析及参数设置
Performance analysis and parameter setting for Tong detection algorithm

Journal of Beijing University of Aeronautics and Astronsutics, 2015, 41(3): 418-423.
http://dx.doi.org/10.13700/j.bh.1001-5965.2014.0181