CN101848177B - Bistable optimal stochastic resonance single-frequency weak signal detection method based on frequency conversion - Google Patents

Bistable optimal stochastic resonance single-frequency weak signal detection method based on frequency conversion Download PDF

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CN101848177B
CN101848177B CN 201010154338 CN201010154338A CN101848177B CN 101848177 B CN101848177 B CN 101848177B CN 201010154338 CN201010154338 CN 201010154338 CN 201010154338 A CN201010154338 A CN 201010154338A CN 101848177 B CN101848177 B CN 101848177B
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frequency
signal
stochastic resonance
bistable
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CN101848177A (en
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何迪
何晨
蒋铃鸽
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上海交通大学
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Abstract

The invention relates to a bistable optimal stochastic resonance single-frequency weak signal detection method based on variable frequency in the technical field of signal processing. The method comprises the following steps of: multiplying a single-frequency received signal r(t) and a local signal cos([omega]st+2[pi][delta]f*t) to perform frequency conversion; performing weighted summation of the received signal r(t) cos([omega]st+2[pi][delta]f*t) after frequency conversion and a locally generated zero-mean unit power resonance white Gaussian noise nSR(t); inputting the weighted sum signal [k1r(t)cos([omega]st+2[pi][delta]f*t)+k2nSR(t)] into a bistable stochastic resonance system to obtain an output signal-to-noise ratio SNRo of the bistable stochastic resonance system at a frequency [delta]f; performing maximum likelihood optimization on a weighting coefficient to obtain an optimal weighting coefficient; bringing the optimal weighting coefficient into the bistable stochastic resonance system to obtain a state variable output sequence of the system, and inputting the output sequence into an energy detector to obtain the energy of an output signal; and judging that a signal to be detected exists when the energy of the output signal is greater than the set energy threshold,. The invention has advantages of low calculation complexity, good robustness, high detection accuracy andstrong feasibility and practicability.

Description

基于变频的双稳态最优随机共振单频微弱信号检测方法 Based on the optimal stochastic resonance frequency of the bi-stable single-frequency weak signal detection method

技术领域 FIELD

[0001] 本发明涉及的是一种信号处理技术领域的方法,具体是一种基于变频的双稳态最优随机共振单频微弱信号检测方法。 [0001] The present invention relates to a method of signal processing art, in particular based on the optimal stochastic resonance frequency of the bi-stable single-frequency weak signal detection.

背景技术 Background technique

[0002] 在通信系统和信号处理系统中,较低信噪比条件下单频微弱信号的检测是一个常见的问题,尤其是当信号谱线被背景噪声所淹没时,该检测问题变得更加困难。 [0002] In the communication system and signal processing system, a single frequency low SNR detection of weak signals is a common problem, especially when the signal line is overwhelmed by background noise, the detection problem becomes more difficult. 一些在高信噪比情况下常用的检测方法,如频谱分析、能量检测等,会随着信噪比的下降而严重影响其检测性能甚至无法使用。 Some common method of detection at high SNR, such as spectral analysis, energy detection, signal to noise ratio and with the decline will seriously affect the detection performance can not even use.

[0003] 经对现有文献检索发现,相关文献如下: [0003] been found that the prior document retrieval, the following literature:

[0004] I、最小平方法(O. Besson and P. Stoica, “Sinusoidal signals with randomamplitude :least_squares estimators and their statistical analysis (随机振巾畐正弦信号的最小平方估计器及其统计分析),” IEEE Trans. Signal Processing, vol. 43,no. 11,pp. 2733-2744,Nov. 1995.)是一种较为常见的基于二阶统计量的优化方法,主要利用优化理论中的最小平方统计量对信号进行检测。 [0004] I, a least squares method (O. Besson and P. Stoica, "Sinusoidal signals with randomamplitude: least_squares estimators and their statistical analysis (least squares estimator towels and Statistical Analysis of Random Vibration sinusoidal signal Bi)," IEEE Trans . signal Processing, vol. 43, no. 11, pp. 2733-2744, Nov. 1995.) is a more common optimization method based on second order statistics, statistics mainly using least squares optimization theory signal for testing. 这种方法在高信噪比条件下具有较好的检测效率,但在低信噪比条件下(如-IOdB以下的情况)其检测准确率很低,实用性不好。 This method has better detection efficiency at high SNR, but at low SNR (e.g., less -IOdB case) which detection accuracy is very low, not practical.

[0005] 2、高阶统计量法(KM Hock, “Narrowband weak signal detection byhigher orderspectrum(用高阶谱方法实现窄带微弱信号检测),” IEEE Trans. SignalProcessing, vol. 44, no. 4, pp. 874-879, Apr. 1996.)是另一类受到广泛关注的微弱信号检测方法,是一种建立在二阶以上谱估计理论方法上的检测技术,但是这类方法往往具有较高的计算复杂度,使得其应用范围受到很大程度的限制,特别是对信号的检测具有实时性的要求时,其弱点显得尤为突出。 [0005] 2, higher order statistics method (KM Hock, "Narrowband weak signal detection byhigher orderspectrum (higher-order spectral method implemented by the narrowband weak signal detection)," IEEE Trans. SignalProcessing, vol. 44, no. 4, pp. 874-879, Apr. 1996.) are another class of weak signal detection method by widespread concern, a second order or more based on the detection spectrum estimation theory, but such methods tend to have high computational complexity when degrees so that its application range is limited to a large extent, especially those with real-time requirements of detection signals, the weakness is particularly prominent.

[0006] 3、信号子空间法(A. Eriksson, P. Stoica and T. Soderstrom, ^Second-orderproperties ofMUSIC and ESPRIT estimates of sinusoidal frequencies in highSNR scenarios (高信噪比条件下正弦信号频率估计的MUSIC方法和ESPRIT方法二阶特性),,' IEE Proceedings Radar andSignal Processing, vol. 140, no. 4, pp. 266-272,Aug. 1993.)是一种利用信号和加性噪声的相互独立特性而应运而生的方法,结合接收信号的协方差矩阵特征值分解来对信号子空间进行估计,相比前两种方法具有更优的检测精度,但由于这类方法在其实施中一般都需要经过对信号进行特征值分解的过程,因此同样具有较高的运算复杂度,实用性受到一定的影响。 MUSIC Method [0006] 3, a signal subspace method (A. Eriksson, P. Stoica and T. Soderstrom, ^ Second-orderproperties ofMUSIC and ESPRIT estimates of sinusoidal frequencies in highSNR scenarios (Frequency Estimator high SNR conditions second-order characteristic and ESPRIT) ,, 'IEE Proceedings Radar andSignal Processing, vol. 140, no. 4, pp. 266-272, Aug. 1993.) utilizing characteristics are independent additive noise of the signal to be transported the method of the students, wherein the covariance matrix of the received signal combined value decomposition of the signal subspace estimation, compared to the previous two methods have better accuracy of detection, but these methods generally require for their implementation through signal eigenvalue decomposition process, and therefore also has a high computational complexity, subject to certain practical impact.

[0007] 4、能量检测方法(H. Urkowitz, “Energy detection of unknown deterministicsignals (未知特定信号的能量检测),"Proceedings of the IEEE, vol. 55, no. 4,pp. 523-531,April 1967.)由于其运算简单而且在高信噪比情况下具有较高的检测概率而受到普遍重视,其应用也十分广泛。 [0007] 4, an energy detection method (H. Urkowitz, "Energy detection of unknown deterministicsignals (specific energy detect signal is unknown)," Proceedings of the IEEE, vol. 55, no. 4, pp. 523-531, April 1967 .) Because of its simple operation and has a high probability of detection at high SNR and attracted universal attention, its application is very extensive. 该方法通过直接计算接收信号的能量来判断信号是否存在,简单易行。 The method by directly calculating the energy of the received signal to determine whether the signal is present, simple. 但是能量检测方法存在一个严重的问题,即在低信噪情况下(如-IOdB以下的情况)其检测概率很低,因此在通信系统的信道环境较差时检测效果也较差,也成为一直制约其应用的一个重要方面。 However, a method for detecting the presence of energy serious problem, i.e., (e.g. -IOdB following cases) which detects a low probability in low SNR conditions, it is also poor poor detection results channel environment in a communication system, it has also become an important aspect of restricting its application.

发明内容 SUMMARY

[0008] 本发明的目的在于克服现有技术的上述不足,提供一种基于变频的双稳态最优随机共振单频微弱信号检测方法。 [0008] The object of the present invention is to overcome the above disadvantages of the prior art, there is provided a frequency based on a bistable single optimal stochastic resonance frequency weak signal detection. 本发明用于检测具有加性高斯白噪声且较低信噪比条件下的微弱单频率目标信号,特别适用于无线通信系统中调制信号的检测和信号检测中对单频率目标信号的检测,能够在恒虚警概率的条件下有效提高单频微弱信号的检测概率,而且其计算复杂度与能量检测方法相当。 The present invention is used to detect additive white gaussian noise and a weak signal at a single frequency of the target SNR is low, especially for a wireless communication system modulation and detection of the detection signal of the single frequency of the target detection signal, can be under conditions effective to improve the CFAR detection probability of weak single-frequency signal, and its computational complexity and considerable energy detection method.

[0009] 本发明是通过以下技术方案实现的,本发明包括以下步骤: [0009] The present invention is achieved by the following technical solution, the present invention comprises the steps of:

[0010] 第一步,将目标角频率为的且有加性噪声的单频接收信号r(t)与本地信号cos(cost+2 3i Δ f · t)相乘进行变频,得到变频后的接收信号r(t)cos(cost+2 31 Af ·!:),其中:r(t) = Acosco st+n(t), A为单频接收信号r(t)的振幅,n(t)为加性噪声,ω3为单频接收信号Ht)的角频率,Af为设定的频率偏值。 [0010] The first step, the target angular frequency and single frequency plus noise received signal r (t) of the local signal cos (cost + 2 3i Δ f · t) for multiplying the frequency, the frequency obtained after received signal r (t) cos (cost + 2 31 Af · :), wherein:! r (t) = Acosco st + n (t), a is a single frequency amplitude of the received signal r (t) is, n (t) additive noise, ω3 Ht of the single frequency reception signal) of angular frequency, Af is the frequency offset value set. [0011] 第二步,将变频后的接收信号r (t) COS (ω st+2 π Λ f · t)和本地产生的零均值单位功率共振高斯白噪声nSK(t)进行加权求和,得到加权和信号[kir(t)cos(cost+2 3i Af · t)+k2nSK(t)],其中:nSK(t)为均值为O、方差为I的高斯白噪声,Ii1为信号1^)(:08((0』+2 31 Af * t)的加权系数,k2为信号nSK(t)的加权系数。 [0011] In a second step, the up-converted received signal r (t) COS (ω st + 2 π Λ f · t) with zero mean and unit power locally generated Gaussian white noise resonance nSK (t) weighted sum, to obtain a weighted signal [kir (t) cos (cost + 2 3i Af · t) + k2nSK (t)], where: nSK (t) is the average is O, variance I Gaussian white noise, Ii1 signal 1 ^ ) (: 08 ((0 "+2 31 Af * t) is a weighting coefficient, k2 is the signal nSK (t) is a weighting coefficient.

[0012] 第三步,将加权和信号[1^(1:)(308((0 3+2 31 Δ f · t) +k2nSE (t)]输入至一个双稳态随机共振系统中,得到该双稳态随机共振系统在频率Af处的输出信噪比SNR。。 [0012] The third step, and the weighted signal [1 ^ (1:) (308 ((0 3 + 2 31 Δ f · t) + k2nSE (t)] is input to a bistable stochastic resonance system to give the bistable system stochastic resonance frequency at the output SNR SNR Af ..

[0013] 所述的双稳态随机共振系统,具体是: [0013] The bistable stochastic resonance systems, in particular:

[0014] x^t + :)= 2x(t) - X3 ⑴ + A1 ■ r(t) cos(iy/ + rInAf ■ f) + k2 ■ nSR (t), [0014] x ^ t +:) = 2x (t) - X3 ⑴ + A1 ■ r (t) cos (iy / + rInAf ■ f) + k2 ■ nSR (t),

[0015] 其中:x(t)为系统的状态变量,At为系统的时间采样间隔。 [0015] where: x (t) of the system state variables, At is the sampling interval of the system time.

[0016] 所述的双稳态随机共振系统在频率Λ f处的输出信噪比SNR。 [0016] The bistable system stochastic resonance frequency of the output signal to noise ratio SNR f Λ at. ,具体是: ,specifically is:

__2 __2

SNR _ SNR _

[0017] ^κο - yz ' ye , [0017] ^ κο - yz 'ye,

+k2 +2 ^i2 c7^J + K2 +2 ^ i2 c7 ^ J

[0018] 其中:σ n2为单频接收信号r (t)中所包含的信道加性高斯白噪声的方差。 [0018] wherein: σ n2 is a channel additive white gaussian noise in the single-frequency received signal r (t) included in the variance.

[0019] 第四步,根据双稳态随机共振系统在频率Λ f处的输出信噪比SNR。 [0019] The fourth step, according to Λ bistable stochastic resonance system signal to noise ratio SNR f the frequency at the output. 对加权系数Ii1和k2进行最大似然优化,得到最优加权系数k1(_)和k2(()pt),使得双稳态随机共振系统输出信号的信噪比在最优加权系数k1(_)和k2(()pt)下达到最大。 And k2 are weighting coefficients Ii1 maximum likelihood optimization, the optimal weighting coefficients K1 (_) and k2 (() Pt), so that the bistable stochastic resonance system output signal to noise ratio at the optimal weighting coefficients K1 (_ under) and k2 (() pt) maximum.

[0020] 所述的最大似然优化是:双稳态随机共振系统的输出信噪比SNR。 [0020] The maximum likelihood optimization is: SNR of the output bistable stochastic resonance system. 对加权系数匕一阶求导为零时的h取值即是最优加权系数k1(_),双稳态随机共振系统的输出信噪比SNR。 Weighting coefficients h dagger at a zero-order derivative value that is optimal weighting coefficients k1 (_), the output of the SNR bistable stochastic resonance system. 对加权系数k2 —阶求导为零时的k2取值即是最优加权系数k2(_)。 Weighting coefficient k2 - k2 value of the first derivation is zero, i.e., optimal weighting coefficients k2 (_).

[0021] 第五步,将最优加权系数k1(_)和k2(_)带入双稳态随机共振系统中,从而得到双稳态随机共振系统的状态变量输出序列lx(l),x(2),...,x(N)},再将该输出序列输入能量检测器中,得到输出信号的能量Tx。 [0021] The fifth step, the optimal weighting coefficients K1 (_) and K2 (_) into a bistable stochastic resonance system, thereby obtaining a bistable system stochastic resonance state variable output sequence lx (l), x (2), ..., x (N)}, then the output energy input energy detector sequence to obtain the output signal Tx.

[0022] 所述的输出信号的能量Tx是:[0023] [0022] The energy output of the Tx signal is: [0023]

Figure CN101848177BD00061

[0024] 其中:x⑴是第i个状态变量,I彡i彡N,N是采样序列的长度。 [0024] wherein: x⑴ is the i-th state variable, I i San San N, N being the length of the sequence of samples.

[0025] 第六步,当输出信号的能量Tx大于设定的能量阈值λ时,判定待检测信号存在;否则,判定待检测信号不存在。 [0025] The sixth step, when the energy of the output signal Tx is greater than the set energy threshold [lambda], a detection signal is determined to be present; otherwise, it is determined to be the detection signal is not present.

[0026] 所述的能量阈值λ,是: [0026] The energy threshold λ, is:

[0027] [0027]

Figure CN101848177BD00062

[0028] 其中:Pfa为设定的恒虚警概率,2g(_)为自由度为N的卡方分布右尾概率密度逆函数。 [0028] wherein: Pfa CFAR is set, 2g (_) N degree of freedom chi-squared inverse of the right tail probability density function.

[0029] 与现有技术相比,本发明的有益效果是:运算复杂度低,本发明的运算复杂度与最小平方法和能量检测法处于同一数量级,比高阶统计量法和信号子空间法的运算复杂度要低,鲁棒性好,不易受环境影响,且检测的准确率高,具有较好的可行性和实用性。 [0029] Compared with the prior art, the beneficial effects of the present invention are: low computational complexity and the computational complexity of the present invention and the method of least squares and an energy detection in the same order of magnitude, than the higher-order statistics method and the signal subspace method computational complexity is lower, robust, and not influenced by the environment, and high accuracy detection with better feasibility and practicability.

附图说明 BRIEF DESCRIPTION

[0030] 图I是实施例在信噪比为-15dB条件下的检测性能曲线图; [0030] Figure I is an embodiment of the detection SNR is -15dB performance curve under condition;

[0031] 图2是实施例在信噪比为_20dB条件下的检测性能曲线图。 [0031] FIG. 2 is a graph showing the detection performance under the conditions of Example _20dB SNR embodiment.

具体实施方式 Detailed ways

[0032] 下面结合附图对本发明的实施例作详细说明:本实施例在以本发明技术方案为前提下进行实施,给出了详细的实施方式和具体的操作过程,但本发明的保护范围不限于下述的实施例。 [0032] The following embodiments in conjunction with the accompanying drawings of embodiments of the present invention will be described in detail: In the present embodiments of the present invention is a technical premise, given the specific operation and detailed embodiments, but the scope of the present invention It is not limited to the following examples.

[0033] 实施例 [0033] Example

[0034] 本实施例是QPSK系统,载波频率为IO5Hz,则角频率cos = 6. 28X 105rad/s,时域 [0034] The present embodiment is a QPSK system, the carrier frequency is IO5Hz, the angular frequency cos = 6. 28X 105rad / s, the time-domain

「TT λTT 7τγΊ "TT λTT 7τγΊ

信号采用余弦表示形式,信号相位炉H,信道中的加性噪声为均值为零的高斯白噪声。 Cosine signal represented in the form of white Gaussian noise, signal phase furnace H, plus channel noise of zero mean.

[0035] 本实施例包括以下步骤: [0035] In the present embodiment includes the following steps:

[0036] 第一步,将目标角频率为的且有加性噪声的单频接收信号r(t)与本地信号cos(cost+2 3i Δ f · t)相乘进行变频,得到变频后的接收信号r(t)cos(cost+2 31 Af ·!:),其中:r(t) = Acoscost+n(t) ,A为单频接收信号r(t)的振幅,n(t)为一均值为O、方差为σ n2的加性噪声,《3为单频接收信号r(t)的角频率,Af为设定的频率偏值。 [0036] The first step, the target angular frequency and single frequency plus noise received signal r (t) of the local signal cos (cost + 2 3i Δ f · t) for multiplying the frequency, the frequency obtained after received signal r (t) cos (cost + 2 31 Af · :), wherein:! r (t) = Acoscost + amplitude n (t), a is a single-frequency received signal r (t) is, n (t) is a mean is O, additive noise variance σ n2, a "3 is the angular frequency reception signal r (t) of a single frequency, the frequency of Af set bias value.

[0037]本实施例中 A=I, Af = O. 2Hz。 [0037] In this example A = I, Af = O. 2Hz embodiment.

[0038] 第二步,将变频后的接收信号r (t) cos ( ω st+2 π Λ f · t)和本地产生的零均值单位功率共振高斯白噪声nSK(t)进行加权求和,得到加权和信号[kir(t)cos(cost+2 3i Af · t)+k2nSK(t)],其中:nSK(t)为均值为O、方差为I的高斯白噪声,Ii1为信号1^)(:08((0』+2 31 Af * t)的加权系数,k2为信号nSK(t)的加权系数。 [0038] The second step, the up-converted received signal r (t) cos (ω st + 2 π Λ f · t) with zero mean and unit power locally generated Gaussian white noise resonance nSK (t) weighted sum, to obtain a weighted signal [kir (t) cos (cost + 2 3i Af · t) + k2nSK (t)], where: nSK (t) is the average is O, variance I Gaussian white noise, Ii1 signal 1 ^ ) (: 08 ((0 "+2 31 Af * t) is a weighting coefficient, k2 is the signal nSK (t) is a weighting coefficient.

[0039] 第三步,将加权和信号IXr (t) cos (ω st+2 η Δ f · t) +k2nSE (t)]输入至一个双稳态随机共振系统中,得到该双稳态随机共振系统在频率Af处的输出信噪比SNR。 [0039] The third step, and the weighted signals IXr (t) cos (ω st + 2 η Δ f · t) + k2nSE (t)] is input to a bistable stochastic resonance system, to obtain the bistable random resonant frequency of the system at the output SNR SNR Af. .

[0040] 所述的双稳态随机共振系统,具体是:[0041 ] x^t + :)= 2x(t) - X3 ⑴ + k' ■ r(t) cos(iy/ + rInAf ■ f) + k2 ■ nSR (t), [0040] The bistable stochastic resonance systems, in particular: [0041] x ^ t +:) = 2x (t) - X3 ⑴ + k '■ r (t) cos (iy / + rInAf ■ f) + k2 ■ nSR (t),

[0042] 其中:x(t)为系统的状态变量,At为系统的时间采样间隔。 [0042] where: x (t) of the system state variables, At is the sampling interval of the system time.

[0043] 本实施例中At = O. 005秒。 [0043] In the present embodiment, At = O. 005 seconds.

[0044]根据文献(B. McNamara and K. Wilesenfeld,“Theory of stochasticresonance (随机共振理论),”Phys. Rev. A,vol. 39,no. 9,pp. 4854-4869,May 1989.)中的 [0044] Document (B. McNamara and K. Wilesenfeld, "Theory of stochasticresonance (SR theory)," Phys. Rev. A, vol. 39, no. 9, pp. 4854-4869, May 1989.) according to of

结果,共振系统状态变量x(t)在频率Af处的输出信噪比可近似为: As a result, the resonant system state variables x (t) at the output at the frequency Af SNR can be approximated as:

2 2

SNR -_^i2_e Χ,ν: SNR -_ ^ i2_e Χ, ν:

_5] snrO-(5 2 2 I 2 2γ6 , _5] snrO- (5 2 2 I 2 2γ6,

+々2 +2 σ« J + 々2 +2 σ «J

[0046] 其中:σ η2为接收信号r (t)中所包含的信道加性高斯白噪声的方差。 [0046] wherein: σ η2 is a channel additive white gaussian noise in the received signal r (t) included in the variance.

[0047] 在信噪比小于-IOdB的条件下,σ n2可用单频接收信号r (t)的方差σ /来对其进行估计,即: [0047] -IOdB at the SNR is less than, σ n2 variance available single-frequency signal received r (t) of σ / to be estimated, namely:

[0048] σ2η = G2r =^-Σ£[Γ(0-^[Κ0]]2, [0048] σ2η = G2r = ^ - Σ £ [Γ (0 - ^ [Κ0]] 2,

N /二I N / I two

[0049] 其中:N为采样序列的长度,本实施例中N = ΙΟ6,#为σ n2对单频接收信号r(t)的估计,E代表期望值。 [0049] where: N is the length of the sampling sequence, the present embodiment N = ΙΟ6, # is a single-frequency estimate σ received signal r (t) of the pair of n2, E representing expected value.

[0050] 第四步,根据双稳态随机共振系统在频率Λ f处的输出信噪比SNR。 [0050] The fourth step, according to Λ bistable stochastic resonance system signal to noise ratio SNR f the frequency at the output. 对加权系数Ii1和k2进行最大似然优化,得到最优加权系数k1(_)和k2(()pt),使得双稳态随机共振系统输出信号的信噪比在最优加权系数k1(_)和k2(()pt)下达到最大。 And k2 are weighting coefficients Ii1 maximum likelihood optimization, the optimal weighting coefficients K1 (_) and k2 (() Pt), so that the bistable stochastic resonance system output signal to noise ratio at the optimal weighting coefficients K1 (_ under) and k2 (() pt) maximum.

[0051] 所述的最大似然优化是:双稳态随机共振系统的输出信噪比SNR。 [0051] The maximum likelihood optimization is: SNR of the output bistable stochastic resonance system. 对加权系数匕一阶求导为零时的h取值即是最优加权系数k1(_),双稳态随机共振系统的输出信噪比SNR。 Weighting coefficients h dagger at a zero-order derivative value that is optimal weighting coefficients k1 (_), the output of the SNR bistable stochastic resonance system. 对加权系数k2 —阶求导为零时的k2取值即是最优加权系数k2(_)。 Weighting coefficient k2 - k2 value of the first derivation is zero, i.e., optimal weighting coefficients k2 (_).

[0052] 第五步,将最优加权系数k1(_)和k2(_)带入双稳态随机共振系统中,从而得到双稳态随机共振系统的状态变量输出序列lx(l),x(2),...,x(N)},再将该输出序列输入能量检测器中,得到输出信号的能量Tx。 [0052] The fifth step, the optimal weighting coefficients K1 (_) and K2 (_) into a bistable stochastic resonance system, thereby obtaining a bistable system stochastic resonance state variable output sequence lx (l), x (2), ..., x (N)}, then the output energy input energy detector sequence to obtain the output signal Tx.

[0053] 所述的输出信号的能量Tx是: [0053] Tx power of the output signal is:

[0054] Τχ=^-Υ^χ2{ί), [0054] Τχ = ^ - Υ ^ χ2 {ί),

^ / 二I ^ / II I

[0055] 其中:x(i)是第i个状态变量,I彡i彡N,N是采样序列的长度,本实施例中N =106。 [0055] where: x (i) is the i th state variable, the I San i San N, N being the length of the sequence of samples, in this embodiment N = 106.

[0056] 第六步,根据大数定律和中心极限定理,所得的信号能量在正确检测和误检测的情况下均服从卡方分布,因此当输出信号的能量Tx大于设定的能量阈值λ时,判定待检测信号存在;否则,判定待检测信号不存在。 [0056] The sixth step, according to the law of large numbers and the central limit theorem, the resulting signal energy in the case of correct detection and false detection obey a chi-square distribution, and therefore the output signal when the energy is greater than the energy threshold value Tx set when λ , the detection signal is determined to be present; otherwise, it is determined to be the detection signal is not present.

[0057] 所述的能量阈值λ,是: [0057] The energy threshold λ, is:

[0058] ^ = σ2„-QzI(Pfa) ^ [0058] ^ = σ2 "-QzI (Pfa) ^

[0059] 其中:Pfa为设定的恒虚警概率,2=(_)为自由度为N的卡方分布右尾概率密度逆函数。 [0059] wherein: Pfa CFAR is set = 2 (_) N degree of freedom chi-squared inverse of the right tail probability density function. [0060] 图I是本实施例在信噪比为-15dB条件下,分别采用能量检测法和本实施例方法得到的检测性能曲线图;图2是本实施例在信噪比为_20dB条件下,分别采用能量检测法和本实施例方法得到的检测性能曲线图。 [0060] Figure I embodiment in that the present embodiment is -15dB SNR conditions, were used to detect the performance graph and an energy detection method of the present embodiment obtained in Example; FIG. 2 is a condition of this embodiment _20dB SNR lower, respectively Characteristic curve detected energy detection method and the method according to the present embodiment is obtained. 由图I和图2可见:本实施例方法在相同的虚警概率下能够获得必能量检测法更高的检测概率。 2 and seen from Figure I: Example of the present embodiment can obtain a higher energy detection will be detected at the same probability of false alarm probability. 同时,由于本实施例方法的计算复杂度和能量检测法的计算复杂度在同一数量级范围,因此,本实施例方法对低信噪比的单频目标信号具有很好的检测性能,能够有效解决通信系统和信号处理系统中的相关问题。 Meanwhile, since the computational complexity of calculating the present embodiment of the method of the complexity and energy detection in the same order of magnitude, therefore, the present embodiment of the method of low SNR signals of a single frequency having a good target detection performance can be effectively solved problems associated communication system and a signal processing system.

Claims (5)

1. 一种基于变频的双稳态最优随机共振单频微弱信号检测方法,其特征在于,包括如下具体步骤: 第一步,将目标角频率为的且有加性噪声的单频接收信号Ht)与本地信号cos(wst+2 n A f • t)相乘进行变频,得到变频后的接收信号r(t) cos O st+2 31 Af •!:),其中:r(t) = Acos wst+n(t), A为单频接收信号r(t)的振幅,n(t)为加性噪声,为单频接收信号Ht)的角频率,Af为设定的频率偏值; 第二步,将变频后的接收信号r(t)C0S(«st+2 Ji Af • t)和本地产生的零均值单位功率共振高斯白噪声nSK(t)进行加权求和,得到加权和信号[kir(t)cos(wst+2 n Af • t)+k2nSK(t)],其中:nSK(t)为均值为O、方差为I的高斯白噪声,k:为信号r (t) cos (o st+2 A f * t)的加权系数,k2为信号nSK (t)的加权系数; 第三步,将加权和信号IXHOcosOst+Z 31 A f • t) +k2nSE (t)]输入至一个双稳态随机共振系统中,得到该双稳态随机共振 A single optimal stochastic resonance frequency weak signal detection method, wherein the frequency conversion based on bistable, comprising the following specific steps: first, the target angular frequency and single frequency of the received signal plus noise HT) and the local signal cos (wst + 2 n a f • t) for multiplying the frequency, the received signal r (t) obtained after the frequency conversion cos O st + 2 31 Af • :), wherein:! r (t) = Acos wst + n (t), a is a single frequency amplitude of the received signal r (t) is, n (t) is additive noise, single frequency Ht of the received signal) of angular frequency, the frequency of Af set bias value; a second step, the received signal r (t) after frequency conversion C0S ( «st + 2 Ji Af • t) and the zero-mean unit power locally generated Gaussian white noise resonance nSK (t) weighted sum, to obtain a weighted signal and [kir (t) cos (wst + 2 n Af • t) + k2nSK (t)], where: nSK (t) is the average is O, variance I Gaussian white noise, k: a signal r (t) cos (o st + 2 a f * t) is a weighting coefficient, k2 is the signal nSK (t) is a weighting coefficient; a third step, and the weighted signals IXHOcosOst + Z 31 a f • t) + k2nSE (t)] is input to a bistable stochastic resonance system, to obtain the bistable stochastic resonance 统在频率Af处的输出信噪比SNR。 In the system frequency at the output SNR SNR Af. ; 第四步,根据双稳态随机共振系统在频率△ f处的输出信噪比SNR。 ; Fourth step, according to the SNR of the output bistable stochastic resonance system at the frequency △ f. 对加权系数Ic1和k2进行最大似然优化,得到最优加权系数k1(_)和k2(_),使得双稳态随机共振系统输出信号的噪比在最优加权系数k1(_)和k2(()pt)下达到最大; 第五步,将最优加权系数k1(_)和k2(_)带入双稳态随机共振系统中,从而得到双稳态随机共振系统的状态变量输出序列lx(l),x(2),...,x(N)},再将该输出序列输入能量检测器中,得到输出信号的能量Tx; 第六步,当输出信号的能量Tx大于设定的能量阈值\时,判定待检测信号存在;否则,判定待检测信号不存在; 所述的双稳态随机共振系统,具体是: x(/ + A/)—£(0 _ 2x(t) — X3 (/) + k, ■ r{t) cos(a) t + 2M/ -t) + k^- nSR (t),At " 其中:x(t)为系统的状态变量,At为系统的时间采样间隔。 Ic1 and k2 are weighting coefficients maximum likelihood optimization, the optimal weighting coefficients k1 (_) and k2 (_), such that a bistable system stochastic resonance noise ratio of the output signal k1 optimal weighting coefficients (_) and k2 reaches the lower (() Pt) maximum; a fifth step, the optimal weighting coefficients K1 (_) and K2 (_) into a bistable stochastic resonance system, thereby obtaining a bistable system stochastic resonance state variables output sequence lx (l), x (2), ..., x (N)}, then the output sequence detector input energy, the energy of an output signal Tx; a sixth step, when the energy of the output signal is greater than Tx provided \ when a predetermined energy threshold, a detection signal is determined to be present; otherwise, the detection signal is determined to be absent; said bistable stochastic resonance system, in particular: x (/ + a /) - £ (0 _ 2x (t ) - X3 (/) + k, ■ r {t) cos (a) t + 2M / -t) + k ^ - nSR (t), At "wherein: x (t) of the system state variables, At is time sampling interval of the system.
2.根据权利要求I所述的基于变频的双稳态最优随机共振单频微弱信号检测方法,其特征是,所述的双稳态随机共振系统在频率Af•处的输出信噪比,具体是: SNR0 =--7e 僉?+傘, 其中为单频接收信号Ht)中所包含的信道加性高斯白噪声的方差。 According to claim I based on the optimal stochastic resonance frequency of the bi-stable single-frequency weak signal detection method, wherein said bistable system stochastic resonance frequency of the output signal to noise ratio at the Af •, specifically: SNR0 = - 7e + umbrella Qian, wherein Ht of the received signal is a single frequency) channel variance contained in the additive white Gaussian noise?.
3.根据权利要求I所述的基于变频的双稳态最优随机共振单频微弱信号检测方法,其特征是,所述的最大似然优化是:双稳态随机共振系统的输出信噪比SNR。 According to claim I based on the optimal stochastic resonance frequency of the bi-stable single-frequency weak signal detection method, characterized in that the maximum likelihood optimization is: output SNR bistable stochastic resonance system SNR. 对加权系数Ic1 一阶求导为零时的h取值即是最优加权系数k1(_),双稳态随机共振系统的输出信噪比SNR。 Of weighting coefficients h Ic1 when a first derivation is zero value that is optimal weighting coefficients k1 (_), the output of the SNR bistable stochastic resonance system. 对加权系数k2 —阶求导为零时的k2取值即是最优加权系数k2(_)。 Weighting coefficient k2 - k2 value of the first derivation is zero, i.e., optimal weighting coefficients k2 (_).
4.根据权利要求I所述的基于变频的双稳态最优随机共振单频微弱信号检测方法,其特征是,所述的输出信号的能量Tx是: I -V Tx=-Tx2(I), Nj^其中:x(i)是第i个状态变量,I < i SN,N是采样序列的长度。 The downconverted I based on the bistable single optimal stochastic resonance frequency weak signal detection method, wherein, said energy output signals are Tx claim: I -V Tx = -Tx2 (I) , Nj ^ where: x (i) is the i th state variable, I <i SN, N is the length of the sequence of samples.
5.根据权利要求I所述的基于变频的双稳态最优随机共振单频微弱信号检测方法,其特征是,所述的能量阈值入,是: According to claim I based on the optimal stochastic resonance frequency of the bi-stable single-frequency weak signal detection method, characterized in that the said energy threshold, is:
Figure CN101848177BC00031
其中:Pfa为设定的恒虚警概率, Wherein: Pfa CFAR is set,
Figure CN101848177BC00032
为自由度为N的卡方分布右尾概率密度逆函数,<为单频接收信号Ht)中所包含的信道加性高斯白噪声的方差。 The variance of the additive white Gaussian channel noise right tail probability density function of the inverse of the degree of freedom chi-square N, <Ht single frequency reception signal) contained.
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