CN101834630A - A Joint Spectrum Detection Method Based on Energy-Cyclostationary Features - Google Patents

Abstract

The invention relates to a joint spectrum detection method based on energy-cyclostationary characteristic for improving the detection probability and reducing the complexity as soon as possible at the same time. The invention utilizes the characteristics of energy detection and cyclostationary characteristic detection, and realizes spectrum joint detection in cognitive radio systems by utilizing two thresholds. In the invention, an energy detection method of the two thresholds is utilized for crude detection, if the energy is at both ends of the two thresholds, the energy of a signal to be detected is calculated, the energy obtained from the calculation is compared with the two predetermined thresholds, if the energy is no less than the high threshold, a primary user signal is determined to exist; if the energy is no more than the low threshold, the primary user signal is determined to not exist; and if the energy is between the two thresholds, the cyclostationary characteristic is utilized for detection, and the value of a specific cycle frequency is calculated and is compared with the cycle detection threshold, if the value is no less than the threshold, the primary user signal is determined to exist, and the primary user signal is determined to not exist if the value is no more than the threshold.

Description

Translated fromChinese

一种基于能量-循环平稳特征的联合频谱检测方法A Joint Spectrum Detection Method Based on Energy-Cyclostationary Features

技术领域technical field

本发明涉及一种特别用于认知无线电系统中基于能量-循环平稳特征进行联合频谱检测的实现方案，属于通信技术领域。The invention relates to an implementation scheme for joint spectrum detection based on energy-cycling stationary features in a cognitive radio system, which belongs to the technical field of communication.

背景技术Background technique

随着无线通信业务需求的快速增长，可用频谱资源变得越来越稀缺。为了提高通信系统的频谱使用效率，以应对由国家统一管理、统一授权使用的固定频谱分配政策，缓解“频谱资源日益紧张”的局面。认知无线电(Cognitive Radio，CR)一经Mitola提出便引起了广泛的关注，CR是当授权用户未使用授权频带时，CR用户即可“插空”使用该频段进行通信，这样可以大大提高频谱利用率。当然使用的前提是不对授权用户产生干扰，这就需要CR用户对授权频谱的空穴能够进行非常准确的探测和识别。With the rapid growth of demand for wireless communication services, available spectrum resources are becoming increasingly scarce. In order to improve the spectrum utilization efficiency of the communication system, in response to the fixed spectrum allocation policy that is uniformly managed and authorized by the state, and alleviate the situation of "increasingly tight spectrum resources". Cognitive Radio (CR) has attracted widespread attention once it was proposed by Mitola. CR means that when licensed users do not use the licensed frequency band, CR users can "insert" the frequency band for communication, which can greatly improve spectrum utilization. Rate. Of course, the premise of using it is not to interfere with the licensed users, which requires the CR users to be able to detect and identify holes in the licensed spectrum very accurately.

认知无线电网络要求能够动态的感知频谱空穴，利用空闲频段来进行通信。认知用户要进行通信的首要条件就是检测出主用户的空闲频谱段(频谱空穴的检测)。因此，频谱感知问题从本质上来看，关键是一个信号检测问题。对频谱进行感知，就是要在给定的短时间内可靠地检测出主用户(PU)信号在这段频谱上是否存在，或者该段频谱中是否干扰足够小，可以允许CR用户接入，利用其进行通信。信号的可靠检测的重要性表现在以下两个方面：(1)可靠性，即准确的感知PU信号能确保认知无线电用户不会对PU造成干扰；(2)有效性，即及时有效的感知到空闲频谱，从而增加认知无线电网络的通信带宽。Cognitive radio networks require the ability to dynamically sense spectrum holes and use idle frequency bands for communication. The first condition for the cognitive user to communicate is to detect the idle spectrum segment of the primary user (spectrum hole detection). Therefore, the spectrum sensing problem is essentially a signal detection problem. Sensing the spectrum is to reliably detect whether the primary user (PU) signal exists on this spectrum in a given short period of time, or whether the interference in this spectrum is small enough to allow CR users to access, using It communicates. The importance of reliable detection of signals is manifested in the following two aspects: (1) reliability, that is, accurate perception of PU signals can ensure that cognitive radio users will not cause interference to PU; (2) effectiveness, that is, timely and effective perception To the free spectrum, thereby increasing the communication bandwidth of the cognitive radio network.

频谱感知是认知无线电的前提和关键技术，目前国内外提出的感知方法主要分为单用户感知和多用户协作感知。协作感知需要多个认知用户相互协作，以克服无线信道中的隐节点问题和深衰落的影响，提高认知无线电的感知性能，但是当网络中有大量的认知用户共存时，它们就需要占用大量的通信带宽来进行检测信息的传送。单用户感知不需要传送额外的感知信息，在系统中常常得到应用。常用的方法有基于能量检测的频谱感知方法和基于信号特征值的频谱感知方法。能量检测方法只需要知道被检测频段内信号的能量，为了测量接收信号的能量，需要对带通滤波器的输出信号进行平方运算并在观测时间段内进行积分，将积分器的输出和固定门限值相比较，得出检测结果。基于信号特征的频谱感知方法利用不同类型的调制信号具有不同频谱相关函数、信号均值、自相关函数具有周期平稳性、以及噪声和干扰之间相互独立性等特征进行检测。Spectrum sensing is the premise and key technology of cognitive radio. At present, the sensing methods proposed at home and abroad are mainly divided into single-user sensing and multi-user cooperative sensing. Cooperative sensing requires multiple cognitive users to cooperate with each other to overcome the hidden node problem and the influence of deep fading in the wireless channel, and improve the cognitive performance of cognitive radio, but when a large number of cognitive users coexist in the network, they need It takes up a large amount of communication bandwidth to transmit detection information. Single-user sensing does not need to transmit additional sensing information, and is often applied in the system. Commonly used methods include spectrum sensing based on energy detection and spectrum sensing based on signal eigenvalues. The energy detection method only needs to know the energy of the signal in the detected frequency band. In order to measure the energy of the received signal, the output signal of the band-pass filter needs to be squared and integrated within the observation period, and the output of the integrator and the fixed gate Compared with the limit value, the detection result is obtained. Spectrum sensing methods based on signal characteristics use different types of modulated signals to have different spectral correlation functions, signal mean value, autocorrelation function with cyclostationarity, and mutual independence between noise and interference for detection.

发明内容Contents of the invention

技术问题：本发明的目的是提供一种基于能量-循环平稳特征的联合频谱检测方法，该方法以提高检测概率同时尽量减少复杂度为目的，利用能量检测与循环平稳特征检测的特点，基于双门限实现了认知无线电系统中的频谱联合检测。Technical problem: the purpose of the present invention is to provide a joint spectrum detection method based on energy-cyclostationary features, which aims to improve the detection probability and reduce the complexity as much as possible, and utilizes the characteristics of energy detection and cyclostationary feature detection, based on dual Threshold implements spectrum joint detection in cognitive radio systems.

技术方案：本发明根据能量检测与循环平稳特征检测的特点，利用双门限的能量检测法进行粗检，若能量落在两门限的两端，则直接进行判断，若能量落在两门限之间，则利用循环平稳特征进行检测。Technical solution: According to the characteristics of energy detection and cyclostationary feature detection, the present invention uses the double-threshold energy detection method for rough detection. , the cyclostationary feature is used for detection.

该方法包括：根据待检测信号的能量大小不同而采用不同的检测方法，若能量落在两门限的两端，则采用能量检测法进行判断，若能量落在两门限之间，则利用循环平稳特征进行检测，该方法具体包括：The method includes: adopting different detection methods according to the energy of the signal to be detected. If the energy falls at both ends of the two thresholds, the energy detection method is used for judgment. If the energy falls between the two thresholds, the cyclostationary feature detection, the method specifically includes:

a.确定联合检测算法的双门限：确定高门限λ_H和低门限λ_L以及循环检测的门限；高门限

低门限

其中N为检测信号样本采样点数，为高斯白噪声的方差，P_f为虚警概率；Q^-1为a. Determine the double threshold of the joint detection algorithm: determine the threshold of the high threshold λ_H and the low threshold λ_L and the loop detection; the high threshold

low threshold

Among them, N is the number of sampling points of the detection signal sample, is the variance of Gaussian white noise, P_f is the false alarm probability; Q^-1 is

b.利用能量检测法进行粗检：计算待检测信号的能量，将计算所得的能量与事先确定的双门限进行比较，若能量大于等于λ_H则判为H₁，即主用户信号存在；若能量小于等于λ_L则判为H₀，即主用户信号不存在；若计算所得的能量处于λ_L与λ_H之间，表明能量检测法无法确定是否有主用户信号存在，则需用循环平稳特征作进一步检测；b. Use the energy detection method for rough detection: calculate the energy of the signal to be detected, and compare the calculated energy with the double threshold determined in advance. If the energy is greater than or equal to λ_H , it is judged as H₁ , that is, the primary user signal exists; if If the energy is less than or equal to λ_L , it is judged as H₀ , that is, the primary user signal does not exist; if the calculated energy is between λ_L and λ_H , it indicates that the energy detection method cannot determine whether there is a primary user signal, and the cyclostationary features for further testing;

c.利用循环平稳特征进行细检：对能量落在λ_L与λ_H之间的信号进行循环平稳特征检测，由于不同调制方式对应不同的循环谱特征，针对主用户信号的调制方式通过检测特定循环频率α处的值确定是否有主用户存在：c. Use cyclostationary features for detailed inspection: Cyclostationary feature detection is performed on signals whose energy falls between λ_L and λ_H. Since different modulation modes correspond to different cyclic spectrum features, the modulation mode of the primary user signal is specified by detection. The value at cycle frequency α determines whether a primary user is present:

c1.对输入的时间序列y(n)做N点的FFT，得到y(n)的谱密度函数X_T(k)，T为分段长度；K为c1. Perform N-point FFT on the input time series y(n) to obtain the spectral density function X_T (k) of y(n), where T is the segment length; K is

c2.对FFT的结果X_T(k)分别左右频移α/2，相应地得到x(n)移频信号的谱密度函数：X_T(k+α/2)和X_T(k-α/2)；c2. The results of FFT X_T (k) are shifted left and right by α/2 respectively, and the spectral density functions of the frequency-shifted signal of x(n) are obtained accordingly: X_T (k+α/2) and X_T (k-α /2);

c3.计算y(n)在频率(k+α/2)和(k-α/2)的谱分量之间的相关密度循环周期谱

c3. Calculate the correlation density cycle period spectrum of y(n) between the spectral components of frequency (k+α/2) and (k-α/2)

c4.对循环周期谱进行平滑得到输入信号的循环功率谱估计

c4. Smooth the cyclic period spectrum to obtain the cyclic power spectrum estimation of the input signal

C5.计算循环频率α处的值并与循环检测门限进行比较，若大于等于门限则判为H₁，即主用户信号存在，若小于等于门限则判为H₀，即主用户信号不存在。C5. Calculate the value at the cycle frequency α and compare it with the cycle detection threshold. If it is greater than or equal to the threshold, it is judged as H₁ , that is, the primary user signal exists; if it is less than or equal to the threshold, it is judged as H₀ , that is, the primary user signal does not exist.

有益效果：本发明提供一种认知无线电系统中基于双门限的能量-循环平稳特征联合频谱检测方法，该方法以提高检测概率同时尽量减少复杂度为目的，利用能量检测与循环平稳特征检测的特点，基于双门限实现了认知无线电系统中的频谱联合检测。若能量落在两门限的两端，则直接进行判断，若能量落在两门限之间，则利用循环平稳特征进行检测。与循环平稳特征检测相比，在保证检测性能下降不多的情况下，该方法大大降低了计算复杂度；与能量检测方法相比，该方法在复杂度增加不多的情况下，大大提高了检测性能。本发明简单实用，可以在认知无线电系统中得到广泛的应用。Beneficial effects: the present invention provides a dual-threshold based energy-cyclostationary feature joint spectrum detection method in a cognitive radio system. The method aims to improve the detection probability while minimizing complexity, and utilizes the energy detection and cyclostationary feature detection Based on the characteristics, the spectrum joint detection in the cognitive radio system is realized based on the double threshold. If the energy falls at both ends of the two thresholds, it is directly judged, and if the energy falls between the two thresholds, the cyclostationary feature is used for detection. Compared with the cyclostationary feature detection, this method greatly reduces the computational complexity while ensuring that the detection performance does not drop much; compared with the energy detection method, this method greatly improves the Detection performance. The invention is simple and practical, and can be widely used in cognitive radio systems.

附图说明Description of drawings

图1双门限判决示意图。Fig. 1 Schematic diagram of double-threshold judgment.

图2能量检测框图。Figure 2 Energy detection block diagram.

图3循环平稳特征检测结构图。Figure 3 Cyclostationary feature detection structure diagram.

图4能量检测阶段的不同情况下能量分布情况Figure 4 Energy distribution under different conditions in the energy detection stage

具体实施方式Detailed ways

能量检测法是一中比较简单的信号检测方法，属于信号的非相干检测，它的性能会受到不确定噪声能量的影响，例如会将比较微弱的信号排除在外，而将幅度较大的脉冲噪声或突发干扰检测为信号。而且能量检测不能区分信号类型，仅能判定信号的存在性。所以，能量检测并不适合检测意外情况下的信号。The energy detection method is a relatively simple signal detection method, which belongs to the non-coherent detection of signals. Its performance will be affected by the energy of uncertain noise. or burst interference is detected as a signal. Moreover, energy detection cannot distinguish signal types, but can only determine the existence of signals. Therefore, energy detection is not suitable for detecting signals in unexpected situations.

循环平稳特性检测最大的优点是可以将噪声能量与调制信号能量区分开。这是由于噪声是宽平稳信号、无相关性的，而调制信号由于信号周期的自冗余呈现循环平稳性。循环平稳特性检测不易受到不确定噪声功率的影响，所以在噪声环境中，它的检测性能要优于能量检测，但是其计算更为复杂，且需要足够长的监测时间。The biggest advantage of cyclostationary characteristic detection is that it can distinguish noise energy from modulation signal energy. This is because the noise is a broad stationary signal without correlation, while the modulated signal exhibits cyclostationarity due to the self-redundancy of the signal period. Cyclostationary characteristic detection is not easily affected by uncertain noise power, so its detection performance is better than energy detection in noisy environments, but its calculation is more complicated and requires a long enough monitoring time.

本发明为基于双门限的能量-循环平稳特征联合检测算法，它的目的是提高检测概率同时尽量减少复杂度。如图1所示，该方法利用双门限的能量检测法进行粗检，若能量落在两门限的两端，则直接进行判断，若能量落在两门限之间，则利用循环平稳特征进行检测，步骤如下：首先确定联合检测算法的双门限λ_H，λ_L；然后按能量检测法计算待检信号的能量，将计算所得的能量与图1中的双门限进行比较，若能量大于等于λ_H则判为H₁即存在主用户信号，小于等于λ_L则判为H₀即不存在主用户信号，次用户可暂时使用；若计算所得的能量处于λ_L与λ_H之间表明能量检测法无法确定是否有主用户信号存在，则需用循环平稳特征作进一步检测；对能量落在(λ_H，λ_L)之间的信号进行循环平稳特征检测，由于不同调制方式对应不同的循环谱特征，针对主用户信号的调制方式通过检测特定循环频率α处的能量确定是否有主用户存在。The invention is an energy-circular stationary feature joint detection algorithm based on double thresholds, and its purpose is to increase the detection probability and reduce the complexity as much as possible. As shown in Figure 1, this method uses the double-threshold energy detection method for rough detection. If the energy falls at both ends of the two thresholds, it will be directly judged. If the energy falls between the two thresholds, the cyclostationary feature will be used for detection. , the steps are as follows: first determine the double threshold λ_H , λ_L of the joint detection algorithm; then calculate the energy of the signal to be detected according to the energy detection method, compare the calculated energy with the double threshold in Figure 1, if the energy is greater than or equal to λ_H is judged as H₁ , that is, there is a primary user signal, and if it is less than or equal to λ_L , it is judged as H₀ , that is, there is no primary user signal, and the secondary user can temporarily use it; if the calculated energy is between λ_L and λ_H , it indicates energy detection If the method cannot determine whether there is a primary user signal, it is necessary to use the cyclostationary feature for further detection; the cyclostationary feature detection is performed on the signal whose energy falls between (λ_H , λ_L ), because different modulation methods correspond to different cyclic spectra Characteristically, for the modulation mode of the primary user signal, it is determined whether there is a primary user by detecting the energy at a specific cycle frequency α.

这里双门限的取值非常重要，高门限λ_H取值将影响虚警概率，取值越高虚警概率越低，但增大了能量落在双门限之间的概率从而增加算法的复杂度高门限；低门限λ_L的取值影响检测概率，取值越小检测概率越大，但同样也会增加算法的复杂度；而双门限值之差太大也会增加算法复杂度。因此，要综合考虑虚警概率、检测概率以及算法复杂度来确定双门限的取值。The value of the double threshold is very important here. The value of the high threshold λ_H will affect the probability of false alarm. The higher the value, the lower the probability of false alarm, but it increases the probability that the energy falls between the double thresholds and increases the complexity of the algorithm. The value of high threshold and low threshold λ_L affects the detection probability. The smaller the value, the greater the detection probability, but it will also increase the complexity of the algorithm; and the large difference between the two thresholds will also increase the complexity of the algorithm. Therefore, it is necessary to comprehensively consider the false alarm probability, detection probability and algorithm complexity to determine the value of the double threshold.

本发明根据能量检测与循环平稳特征检测的特点，基于双门限实现了能量-循环平稳特征的联合频谱检测方法。According to the characteristics of energy detection and cyclostationary feature detection, the invention realizes the joint frequency spectrum detection method of energy and cyclostationary feature based on double thresholds.

能量检测的方法根据接受信号功率大小的不同进行检测，它是一种对未知参数的确定性信号存在性检测的有效方法，其检测框图如图2所示。The method of energy detection detects according to the difference in the received signal power. It is an effective method for detecting the existence of deterministic signals with unknown parameters. The detection block diagram is shown in Figure 2.

AWGN信道下用能量检测法检测主用户信号就是区分下面两种假设：Using the energy detection method to detect the primary user signal in the AWGN channel is to distinguish the following two assumptions:

$\left\{\begin{array}{ccc}{\mathrm{<span><span>H</span>h</span>}}_{\mathrm{<span><span>0</span>0</span>}}<span><span>:</span>:</span>& \mathrm{<span><span>Y</span>Y</span>}<span><span>(</span>(</span>\mathrm{<span><span>n</span>no</span>}<span><span>)</span>)</span><span><span>=</span>=</span>\mathrm{<span><span>W</span>W</span>}<span><span>(</span>(</span>\mathrm{<span><span>n</span>no</span>}<span><span>)</span>)</span>& \mathrm{<span><span>n</span>no</span>}<span><span>=</span>=</span>\mathrm{<span><span>0</span>0</span>}<span><span>,</span>,</span><span><span>\&CenterDot;</span>\&CenterDot;</span><span><span>\&CenterDot;</span>\&CenterDot;</span><span><span>\&CenterDot;</span>\&CenterDot;</span><span><span>,</span>,</span>\mathrm{<span><span>N</span>N</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}\\ {\mathrm{<span><span>H</span>h</span>}}_{\mathrm{<span><span>1</span>1</span>}}<span><span>:</span>:</span>& \mathrm{<span><span>Y</span>Y</span>}<span><span>(</span>(</span>\mathrm{<span><span>n</span>no</span>}<span><span>)</span>)</span><span><span>=</span>=</span>\mathrm{<span><span>X</span>x</span>}<span><span>(</span>(</span>\mathrm{<span><span>n</span>no</span>}<span><span>)</span>)</span><span><span>+</span>+</span>\mathrm{<span><span>W</span>W</span>}<span><span>(</span>(</span>\mathrm{<span><span>n</span>no</span>}<span><span>)</span>)</span>& \mathrm{<span><span>n</span>no</span>}<span><span>=</span>=</span>\mathrm{<span><span>0</span>0</span>}<span><span>,</span>,</span><span><span>\&CenterDot;</span>\&Center\; Dot;</span><span><span>\&CenterDot;</span>\&CenterDot;</span><span><span>\&CenterDot;</span>\&Center\; Dot;</span><span><span>,</span>,</span>\mathrm{<span><span>N</span>N</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}\end{array}\right.$

其中：W(n)为零均值方差为

加性高斯白噪声，即

X(n)为被检测的主用户信号；Y(n)表示CR用户接收信号；N为检测信号采样点数；H₀和H₁分别表示主用户信号X(t)不存在和存在两种假设。该检测方法中我们将X(n)看成均值为零，方差为

的高斯随机过程，即

且X(n)与W(n)相互独立，则

Where: W(n) is zero mean and variance is

Additive white Gaussian noise, namely

X(n) is the detected primary user signal; Y(n) represents the signal received by the CR user; N is the number of sampling points of the detection signal; H₀ and H₁ represent the absence and existence of the primary user signal X(t) respectively . In this detection method, we regard X(n) as having a mean of zero and a variance of

Gaussian random process of

And X(n) and W(n) are independent of each other, then

采用数理统计的方法，根据Y(t)构造相应检验统计量V(Y)。依据V(Y)及判决规则：The method of mathematical statistics is used to construct the corresponding test statistic V(Y) according to Y(t). According to V(Y) and judgment rules:

$\mathrm{<span><span>V</span>V</span>}{<span><span>(</span>(</span>\mathrm{<span><span>Y</span>Y</span>}<span><span>)</span>)</span>}_{\stackrel{<span><span><</span><</span>}{{\mathrm{<span><span>H</span><figure-callout\; label="h"\; filenames="HSA00000115301800014.png"\; state="\{\{state\}\}">h</figure-callout></span>}}_{\mathrm{<span><span>0</span>0</span>}}}}^{\underset{<span><span>></span>></span>}{{\mathrm{<span><span>H</span>h</span>}}_{\mathrm{<span><span>1</span>1</span>}}}}\mathrm{<span><span>\&gamma;</span>\&gamma;</span>}$

其中γ为判决门限。Where γ is the decision threshold.

感知性能由两种概率来衡量：检测概率P_d和虚警概率P_f，分别如下式表示：Perceptual performance is measured by two probabilities: detection probability P_d and false alarm probability P_f , respectively expressed as follows:

P_d＝P(判为H₁|H₁)P_d ＝P (judged as H₁ |H₁ )

P_f＝P(判为H₁|H₀)P_f ＝P (judged as H₁ |H₀ )

其中检测概率P_d表示授权用户正在使用频谱同时认知用户也检测到授权用户的情况，其大小表明授权用户被保护而不受认知用户干扰的程度。虚警概率P_f表明认知用户检测到授权用户而实际上授权用户并不存在的情况。如果虚警概率较高，则认知用户对空闲信道的利用率降低，丧失接入无线网络的机会，相应的认知无线电网络的吞吐量也会降低。因为即使这时实际上没有授权用户存在，认知用户仍然会认为授权用户正在使用信道而让出信道。The detection probability_Pd represents the situation that licensed users are using the spectrum while cognitive users also detect licensed users, and its magnitude indicates the extent to which licensed users are protected from interference by cognitive users. The false alarm probability P_f indicates the situation where an authorized user is detected by a cognitive user when in fact the authorized user does not exist. If the probability of false alarm is high, cognitive users will reduce the utilization rate of idle channels, lose the opportunity to access wireless networks, and the throughput of the corresponding cognitive radio network will also decrease. Because even if no authorized user actually exists at this time, the cognitive user will still think that the authorized user is using the channel and give up the channel.

能量检测法的判决统计量为：The decision statistic of the energy detection method is:

$\mathrm{<span><span>V</span>V</span>}<span><span>=</span>=</span>\underset{\mathrm{<span><span>N</span>N</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}{<span><span>(</span>(</span>\mathrm{<span><span>Y</span>Y</span>}<span><span>(</span>(</span>\mathrm{<span><span>n</span>no</span>}<span><span>)</span>)</span><span><span>)</span>)</span>}^{\mathrm{<span><span>2</span>2</span>}}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>1</span>1</span>}<span><span>)</span>)</span>$

每一对(P_d，P_f)对应一个判决统计量的比较门限γ：Each pair (P_d , P_f ) corresponds to a comparison threshold γ of a decision statistic:

V＞γ存在主用户，即H₁成立V>γ exists the main user, that is, H₁ is established

V＞γ不存在主用户，即H₀成立There is no primary user for V>γ, that is, H₀ holds

当主用户不存在时，判决统计量V服从自由度为N的中心卡方分布；当主用户存在时，判决统计量服从自由度为N的非中心卡方分布，非中心的参数λ为主用户信号能量与AWGN双边带功率谱密度之比，即：When the primary user does not exist, the decision statistic V follows the central chi-square distribution with N degrees of freedom; when the primary user exists, the decision statistic follows the non-central chi-square distribution with N degrees of freedom, and the non-central parameter λ is the primary user signal The ratio of energy to AWGN double sideband power spectral density, namely:

根据中心极限定理，当N远远大于1时，判决统计量V可近似为高斯随机过程，即：According to the central limit theorem, when N is far greater than 1, the decision statistic V can be approximated as a Gaussian random process, namely:

基于以上近似，可以推导出检测概率P_d和虚警概率P_f计算公式如(2)和(3)所示：Based on the above approximation, the calculation formulas of detection probability P_d and false alarm probability P_f can be deduced as shown in (2) and (3):

${\mathrm{<span><span>P</span>P</span>}}_{\mathrm{<span><span>d</span>d</span>}}<span><span>=</span>=</span>\mathrm{<span><span>Q</span>Q</span>}<span><span>(</span>(</span>\frac{\mathrm{<span><span>\&gamma;</span>\&gamma;</span>}<span><span>-</span>-</span>\mathrm{<span><span>N</span>N</span>}<span><span>(</span>(</span>{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}_{\mathrm{<span><span>w</span>w</span>}}^{\mathrm{<span><span>2</span>2</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}_{\mathrm{<span><span>x</span>x</span>}}^{\mathrm{<span><span>2</span>2</span>}}<span><span>)</span>)</span>}{\sqrt{\mathrm{<span><span>2</span>2</span>}\mathrm{<span><span>N</span>N</span>}{<span><span>(</span>(</span>{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}_{\mathrm{<span><span>w</span>w</span>}}^{\mathrm{<span><span>2</span>2</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}_{\mathrm{<span><span>x</span>x</span>}}^{\mathrm{<span><span>2</span>2</span>}}<span><span>)</span>)</span>}^{\mathrm{<span><span>2</span>2</span>}}}}<span><span>)</span>)</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>2</span>2</span>}<span><span>)</span>)</span>$

${\mathrm{<span><span>P</span>P</span>}}_{\mathrm{<span><span>f</span>f</span>}}<span><span>=</span>=</span>\mathrm{<span><span>Q</span>Q</span>}<span><span>(</span>(</span>\frac{\mathrm{<span><span>\&gamma;</span>\&gamma;</span>}<span><span>-</span>-</span>\mathrm{<span><span>N</span>N</span>}{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}_{\mathrm{<span><span>w</span>w</span>}}^{\mathrm{<span><span>2</span>2</span>}}}{\sqrt{\mathrm{<span><span>2</span>2</span>}\mathrm{<span><span>N</span>N</span>}{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}_{\mathrm{<span><span>w</span>w</span>}}^{\mathrm{<span><span>4</span>4</span>}}}}<span><span>)</span>)</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>3</span>3</span>}<span><span>)</span>)</span>$

如果对采样点数N的取值没有限制的话，理论上能量检测法能满足任意给定的检测概率P_d和虚警概率P_f。CR系统中，给定一组(P_d，P_f)后，采样点数N的最小取值与信噪比SNR有关，如(4)所示：If there is no limit to the value of the number of sampling points N, theoretically the energy detection method can satisfy any given detection probability P_d and false alarm probability P_f . In the CR system, after a set of (P_d , P_f ) is given, the minimum value of the number of sampling points N is related to the signal-to-noise ratio SNR, as shown in (4):

N＝2[(Q^-1(P_f)-Q^-1(P_d))SNR^-1-Q^-1(P_d)]²其中$\mathrm{SNR}={\mathrm{\&delta;}}_x^2/{\mathrm{\&delta;}}_w^2---\left(4\right)$N=2[(Q^-1 (P_f )-Q^-1 (P_d ))SNR^-1 -Q^-1 (P_d )]² where$\mathrm{SNR}={\mathrm{\&delta;}}_x^2/{\mathrm{\&delta;}}_w^2---\left(4\right)$

通常检测器的设计遵循给定虚警概率准则(CFAR Constant False AlarmRate)，基于该准则判决门限可由采样点数N和给定的虚警概率P_f表示如下式所示：Usually the design of the detector follows the given false alarm probability criterion (CFAR Constant False AlarmRate), based on this criterion, the decision threshold can be expressed by the number of sampling points N and the given false alarm probability P_f as shown in the following formula:

$\mathrm{<span><span>\&gamma;</span>\&gamma;</span>}<span><span>=</span>=</span>{\mathrm{<span><span>N\&delta;</span>N\&delta;</span>}}_{\mathrm{<span><span>w</span>w</span>}}^{\mathrm{<span><span>2</span>2</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>Q</span>Q</span>}}^{<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}}<span><span>(</span>(</span>{\mathrm{<span><span>P</span>P</span>}}_{\mathrm{<span><span>f</span>f</span>}}<span><span>)</span>)</span>\sqrt{\mathrm{<span><span>2</span>2</span>}\mathrm{<span><span>N</span>N</span>}{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}_{\mathrm{<span><span>w</span>w</span>}}^{\mathrm{<span><span>4</span>4</span>}}}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>5</span>5</span>}<span><span>)</span>)</span>$

影响能量检测法性能的一个主要因素是噪声的不确定性，它使得能量检测法在低信噪比下检测性能很差，甚至不可用。首先构建了一个简单的描述噪声不确定性数学模型，这个数学模型仅考虑噪声方差的估计值在某一个确定的范围内均匀分布，不考虑更复杂的情况。假设理想的高斯白噪声过程

那么综合考虑传输环境的影响和接收端估计误差的影响，可以假设接收端的高斯白噪声方差估计值满足在下式的范围内变化：A major factor affecting the performance of energy detection methods is the uncertainty of the noise, which makes the detection performance of energy detection methods poor or even unusable at low signal-to-noise ratios. First, a simple mathematical model describing the noise uncertainty is constructed, which only considers that the estimated value of the noise variance is within a certain range Uniform distribution, not considering more complicated cases. Assuming an ideal white Gaussian noise process

Then considering the influence of the transmission environment and the influence of the estimation error at the receiving end, it can be assumed that the estimated value of the Gaussian white noise variance at the receiving end is Satisfied varies within the range of the following formula:

$<span><span>(</span>(</span>\mathrm{<span><span>1</span>1</span>}<span><span>-</span>-</span>{\mathrm{<span><span>\&epsiv;</span>\&epsiv;</span>}}_{\mathrm{<span><span>1</span>1</span>}}<span><span>)</span>)</span>{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}_{\mathrm{<span><span>w</span>w</span>}}^{\mathrm{<span><span>2</span>2</span>}}<span><span>\&le;</span>\&le;</span>\stackrel{\mathrm{<span><span>\&Lambda;</span>\&Lambda;</span>}}{{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}_{\mathrm{<span><span>w</span>w</span>}}^{\mathrm{<span><span>2</span>2</span>}}}<span><span>\&le;</span>\&le;</span><span><span>(</span>(</span>\mathrm{<span><span>1</span>1</span>}<span><span>+</span>+</span>{\mathrm{<span><span>\&epsiv;</span>\&epsiv;</span>}}_{\mathrm{<span><span>2</span>2</span>}}<span><span>)</span>)</span>{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}_{\mathrm{<span><span>w</span><figure-callout\; label="w"\; filenames="HSA00000115301800014.png"\; state="\{\{state\}\}">w</figure-callout></span>}}^{\mathrm{<span><span>2</span>2</span>}}<span><span>,</span>,</span>\mathrm{<span><span>0</span>0</span>}<span><span>\&le;</span>\&le;</span>{\mathrm{<span><span>\&epsiv;</span>\&epsiv;</span>}}_{\mathrm{<span><span>1</span>1</span>}}<span><span><</span><</span>\mathrm{<span><span>1</span>1</span>}<span><span>;</span>;</span>{\mathrm{<span><span>\&epsiv;</span>\&epsiv;</span>}}_{\mathrm{<span><span>2</span>2</span>}}<span><span>\&GreaterEqual;</span>\&Greater\; Equal;</span>\mathrm{<span><span>0</span>0</span>}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>6</span>6</span>}<span><span>)</span>)</span>$

即

若噪声不确定度为x dB，则

假设感知用户接收到的主用户能量为P，若

感知用户将无法检测到主用户信号的存在，这就是能量检测法的信噪比界问题，即

考虑噪声不确定性后，能量检测法需检测以下两种假设：Right now

If the noise uncertainty is x dB, then

Assuming that the primary user energy received by the sensing user is P, if

The perception user will not be able to detect the existence of the primary user signal, which is the problem of the SNR bound of the energy detection method, namely

After accounting for noise uncertainty, the energy detection method needs to test the following two hypotheses:

与(2)，(3)式相对应的此时的检测概率P_d和虚警概率P_f如下：Corresponding to (2) and (3), the detection probability P_d and the false alarm probability P_f at this time are as follows:

${\mathrm{<span><span>P</span>P</span>}}_{\mathrm{<span><span>d</span>d</span>}}<span><span>=</span>=</span>\mathrm{<span><span>Q</span>Q</span>}<span><span>(</span>(</span>\frac{\mathrm{<span><span>\&gamma;</span>\&gamma;</span>}<span><span>-</span>-</span>\mathrm{<span><span>N</span>N</span>}<span><span>(</span>(</span>{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}_{\mathrm{<span><span>L</span>L</span>}}^{\mathrm{<span><span>2</span>2</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}_{\mathrm{<span><span>x</span>x</span>}}^{\mathrm{<span><span>2</span>2</span>}}<span><span>)</span>)</span>}{\sqrt{\mathrm{<span><span>2</span>2</span>}\mathrm{<span><span>N</span>N</span>}{<span><span>(</span>(</span>{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}_{\mathrm{<span><span>L</span>L</span>}}^{\mathrm{<span><span>2</span>2</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}_{\mathrm{<span><span>x</span>x</span>}}^{\mathrm{<span><span>2</span>2</span>}}<span><span>)</span>)</span>}^{\mathrm{<span><span>2</span>2</span>}}}}<span><span>)</span>)</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>8</span>8</span>}<span><span>)</span>)</span>$

${\mathrm{<span><span>P</span>P</span>}}_{\mathrm{<span><span>f</span>f</span>}}<span><span>=</span>=</span>\mathrm{<span><span>Q</span>Q</span>}<span><span>(</span>(</span>\frac{\mathrm{<span><span>\&gamma;</span>\&gamma;</span>}<span><span>-</span>-</span>\mathrm{<span><span>N</span>N</span>}{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}_{\mathrm{<span><span>H</span>h</span>}}^{\mathrm{<span><span>2</span>2</span>}}}{\sqrt{\mathrm{<span><span>2</span>2</span>}\mathrm{<span><span>N</span>N</span>}{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}_{\mathrm{<span><span>H</span>h</span>}}^{\mathrm{<span><span>4</span>4</span>}}}}<span><span>)</span>)</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>9</span>9</span>}<span><span>)</span>)</span>$

循环平稳信号理论是由Gardner创立的，他指出循环平稳信号x(t)的特定阶统计特性(均值和自相关函数)呈现周期性。循环谱相关函数就是根据此特性得到信号的循环谱特征，其最主要优点是能够把噪声能量和已调信号的能量区分开来。因此，循环平稳探测法具有很强的抗噪声干扰的能力。The cyclostationary signal theory was founded by Gardner, who pointed out that the specific order statistical characteristics (mean value and autocorrelation function) of the cyclostationary signal x(t) are periodic. The cyclic spectrum correlation function is to obtain the cyclic spectrum feature of the signal according to this characteristic, and its main advantage is that it can distinguish the noise energy from the energy of the modulated signal. Therefore, the cyclostationary detection method has a strong ability to resist noise interference.

Gardner循环平稳信号理论告诉我们，循环平稳过程有周期性的自相关函数，即：Gardner's cyclostationary signal theory tells us that the cyclostationary process has a periodic autocorrelation function, namely:

R_x(t，τ)＝R_x(t+T₀，τ)    (10)R_x (t, τ) = R_x (t+T₀ , τ) (10)

其中T₀为周期。对于周期函数可以对其进行傅立叶级数展开，上述循环平稳过程的周期自相关函数进行傅立叶级数展开后的傅立叶系数如下式所示：Where T₀ is the period. For periodic functions, Fourier series expansion can be performed on them. The Fourier coefficients of the periodic autocorrelation function of the above cyclostationary process after Fourier series expansion are shown in the following formula:

${\mathrm{<span><span>R</span>R</span>}}_{\mathrm{<span><span>x</span>x</span>}}^{\mathrm{<span><span>\&alpha;</span>\&alpha;</span>}}<span><span>(</span>(</span>\mathrm{<span><span>\&tau;</span>\&tau;</span>}<span><span>)</span>)</span><span><span>=</span>=</span>\underset{\mathrm{<span><span>T</span>T</span>}<span><span>\&RightArrow;</span>\&Right\; Arrow;</span><span><span>\&infin;</span>\&infin;</span>}{\mathrm{<span><span>lim</span>lim</span>}}\frac{\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>T</span>T</span>}}\underset{\mathrm{<span><span>T</span>T</span>}}{<span><span>\&Integral;</span>\&Integral;</span>}\mathrm{<span><span>x</span>x</span>}<span><span>(</span>(</span>\mathrm{<span><span>t</span>t</span>}<span><span>+</span>+</span>\frac{\mathrm{<span><span>\&tau;</span>\&tau;</span>}}{\mathrm{<span><span>2</span>2</span>}}<span><span>)</span>)</span>\mathrm{<span><span>x</span>x</span>}{<span><span>(</span>(</span>\mathrm{<span><span>t</span>t</span>}<span><span>-</span>-</span>\frac{\mathrm{<span><span>\&tau;</span>\&tau;</span>}}{\mathrm{<span><span>2</span>2</span>}}<span><span>)</span>)</span>}^{<span><span>*</span>*</span>}{\mathrm{<span><span>e</span>e</span>}}^{<span><span>-</span>-</span>\mathrm{<span><span>j</span>j</span>}\mathrm{<span><span>2</span>2</span>}\mathrm{<span><span>\&pi;\&alpha;</span>\&pi;\&alpha;</span>}\mathrm{<span><span>1</span>1</span>}}\mathrm{<span><span>dt</span>dt</span>}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>11</span>11</span>}<span><span>)</span>)</span>$

上式也称为循环平稳过程的循环自相关函数(CAF Cycle AutocorrelationFunction)。The above formula is also called the circular autocorrelation function (CAF Cycle AutocorrelationFunction) of the cyclostationary process.

Wiener定理告诉我们自相关函数与功率谱密度函数互为傅氏变换对，将Wiener定理应用于循环平稳过程，对循环自相关函数进行傅氏变换得：The Wiener theorem tells us that the autocorrelation function and the power spectral density function are Fourier transform pairs. Applying the Wiener theorem to the cyclostationary process, the Fourier transform of the circular autocorrelation function is:

${\mathrm{<span><span>S</span>S</span>}}_{\mathrm{<span><span>x</span>x</span>}}^{\mathrm{<span><span>\&alpha;</span>\&alpha;</span>}}<span><span>(</span>(</span>\mathrm{<span><span>f</span>f</span>}<span><span>)</span>)</span><span><span>=</span>=</span>\mathrm{<span><span>F</span>f</span>}<span><span>\{</span>\{</span>{\mathrm{<span><span>R</span>R</span>}}_{\mathrm{<span><span>x</span>x</span>}}^{\mathrm{<span><span>\&alpha;</span>\&alpha;</span>}}<span><span>(</span>(</span>\mathrm{<span><span>\&tau;</span>\&tau;</span>}<span><span>)</span>)</span><span><span>\}</span>\}</span><span><span>=</span>=</span>\underset{<span><span>-</span>-</span><span><span>\&infin;</span>\&infin;</span>}{\overset{<span><span>\&infin;</span>\&infin;</span>}{<span><span>\&Integral;</span>\&Integral;</span>}}{\mathrm{<span><span>R</span>R</span>}}_{\mathrm{<span><span>x</span>x</span>}}^{\mathrm{<span><span>\&alpha;</span>\&alpha;</span>}}<span><span>(</span>(</span>\mathrm{<span><span>\&tau;</span>\&tau;</span>}<span><span>)</span>)</span>{\mathrm{<span><span>e</span>e</span>}}^{<span><span>-</span>-</span>\mathrm{<span><span>j</span>j</span>}\mathrm{<span><span>2</span>2</span>}\mathrm{<span><span>\&pi;f\&tau;</span>\&pi;f\&tau;</span>}}\mathrm{<span><span>d\&tau;</span>d\&tau;</span>}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>12</span>12</span>}<span><span>)</span>)</span>$

将(11)代入(12)得：Substitute (11) into (12) to get:

${\mathrm{<span><span>S</span>S</span>}}_{\mathrm{<span><span>x</span>x</span>}}^{\mathrm{<span><span>\&alpha;</span>\&alpha;</span>}}<span><span>(</span>(</span>\mathrm{<span><span>f</span>f</span>}<span><span>)</span>)</span><span><span>=</span>=</span>\underset{\mathrm{<span><span>\&Delta;t</span>\&Delta;t</span>}<span><span>\&RightArrow;</span>\&Right\; Arrow;</span><span><span>\&infin;</span>\&infin;</span>}{\mathrm{<span><span>lim</span>lim</span>}}\underset{\mathrm{<span><span>T</span>T</span>}<span><span>\&RightArrow;</span>\&Right\; Arrow;</span><span><span>\&infin;</span>\&infin;</span>}{\mathrm{<span><span>lim</span>lim</span>}}\frac{\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>\&Delta;t</span>\&Delta;t</span>}}\frac{\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>T</span>T</span>}}\underset{<span><span>-</span>-</span>\mathrm{<span><span>\&Delta;t</span>\&Delta;t</span>}<span><span>/</span>/</span>\mathrm{<span><span>2</span>2</span>}}{\overset{\mathrm{<span><span>\&Delta;t</span>\&Delta;t</span>}<span><span>/</span>/</span>\mathrm{<span><span>2</span>2</span>}}{<span><span>\&Integral;</span>\&Integral;</span>}}{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>T</span>T</span>}}<span><span>(</span>(</span>\mathrm{<span><span>t</span>t</span>}<span><span>,</span>,</span>\mathrm{<span><span>f</span>f</span>}<span><span>+</span>+</span>\frac{\mathrm{<span><span>\&alpha;</span>\&alpha;</span>}}{\mathrm{<span><span>2</span>2</span>}}<span><span>)</span>)</span>{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>T</span>T</span>}}^{<span><span>*</span>*</span>}<span><span>(</span>(</span>\mathrm{<span><span>t</span>t</span>}<span><span>,</span>,</span>\mathrm{<span><span>f</span>f</span>}<span><span>-</span>-</span>\frac{\mathrm{<span><span>\&alpha;</span>\&alpha;</span>}}{\mathrm{<span><span>2</span>2</span>}}<span><span>)</span>)</span>\mathrm{<span><span>dt</span>dt</span>}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>13</span>13</span>}<span><span>)</span>)</span>$

上式称为循环平稳过程的谱相关函数(SCF Spectral Correlation Function)，其中α称为循环频率；

是带宽为1/T的信号x(t)在频率f处的谱分量。循环平稳特征检测的结构图如图3所示。The above formula is called the spectral correlation function (SCF Spectral Correlation Function) of the cyclostationary process, where α is called the cyclic frequency;

is the spectral component of a signal x(t) at frequency f with a bandwidth of 1/T. The structure diagram of cyclostationary feature detection is shown in Fig.3.

在实际应用中须注意以下几点：In practical application, the following points should be paid attention to:

a)采样频率：为了检测循环频率α处的特征，采样频率F_s须满足：Fs＞2max{α，B}，B为信号带宽，即对于

有个支持集合范围为：-Fs/2＜f，α＜Fs/2；a) Sampling frequency: In order to detect the characteristics at the cycle frequency α, the sampling frequency F_s must satisfy: Fs>2max{α, B}, B is the signal bandwidth, that is, for

There is a support set range: -Fs/2<f, α<Fs/2;

b)分辨率：要进行所需的特征检测，要求频率f和循环频率α有一定的分辨率，频率f的分辨率Δf＝1/T；循环频率α的分辨率Δα＝1/Δt，其中必须满足Δt＞＞T(Δt为信号整个观察区间，T为分段长度。)b) Resolution: To perform required feature detection, frequency f and cycle frequency α are required to have a certain resolution, frequency f resolution Δf=1/T; cycle frequency α resolution Δα=1/Δt, where Δt>>T must be satisfied (Δt is the entire observation interval of the signal, and T is the segment length.)

基于双门限的能量-循环平稳特征联合检测算法，利用双门限的能量检测法进行粗检，若能量落在两门限的两端，则直接进行判断，若能量落在两门限之间，则利用循环平稳特征进行检测，具体步骤如下：Based on the double-threshold energy-cyclostationary feature joint detection algorithm, the double-threshold energy detection method is used for rough detection. If the energy falls at both ends of the two thresholds, it will be directly judged. The cyclostationary feature is detected, and the specific steps are as follows:

1确定联合检测算法的双门限λ_H和λ_L：高门限

低门限${\mathrm{\&lambda;}}_L=N*{\mathrm{\&delta;}}_w^2;$1 Determine the double thresholds λ_H and λ_L of the joint detection algorithm: high threshold

low threshold${\mathrm{\&lambda;}}_L=N*{\mathrm{\&delta;}}_w^2;$

2基于能量检测法计算待检信号的能量，将计算所得的能量与步骤(a)中的双门限比较如图1所示，若能量大于等于λ_H判为H₁即存在主用户信号，小于等于λ_L判为H₀即不存在主用户信号，此用户可暂时使用，算法结束；若计算所得的能量处于λ_L与λ_H之间表明能量检测法无法确定是否有主用户信号存在，则需转入步骤(c)用循环平稳特征作进一步检测；2 Calculate the energy of the signal to be detected based on the energy detection method, and compare the calculated energy with the double threshold in step (a) as shown in Figure 1, if the energy is greater than or equal to λ_H , it is judged as H₁ that is, there is a primary user signal, less than It is equal to λ_L and judged as H₀ , that is, there is no primary user signal, this user can be used temporarily, and the algorithm ends; if the calculated energy is between λ_L and λ_H , it means that the energy detection method cannot determine whether there is a primary user signal, then Need to transfer to step (c) for further detection with cyclostationary features;

3对能量落在(λ_H，λ_L)之间的信号进行循环平稳特征检测，由于不同调制方式对应不同的循环谱特征，针对主用户信号的调制方式通过检测特定循环频率处α处的能量确定是否有主用户存在，具体如下：3. Cyclostationary feature detection is performed on signals whose energy falls between (λ_H , λ_L ). Since different modulation methods correspond to different cyclic spectrum characteristics, the modulation method of the primary user signal is detected by detecting the energy at α at a specific cyclic frequency Determine whether a primary user exists, as follows:

(1)产生谱相关函数(SCF)(1) Generate spectral correlation function (SCF)

SCF的计算有以下两种方法：The calculation of SCF has the following two methods:

·用FFT直接计算· Direct calculation with FFT

(i)采集信号并进行A/D变换，得到信号序列x(n)，序列长为N；令循环自相关函数的滞后量τ＝0；(i) collect signal and carry out A/D conversion, obtain signal sequence x (n), sequence length is N; Make the hysteresis τ=0 of circular autocorrelation function;

(ii)循环自相关函数的离散形式的计算公式(ii) Calculation formula of discrete form of circular autocorrelation function

${\mathrm{<span><span>R</span>R</span>}}_{\mathrm{<span><span>x</span>x</span>}}^{\mathrm{<span><span>\&alpha;</span>\&alpha;</span>}}<span><span>(</span>(</span>\mathrm{<span><span>\&tau;</span>\&tau;</span>}<span><span>)</span>)</span><span><span>=</span>=</span>\frac{\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>N</span>N</span>}}\underset{\mathrm{<span><span>n</span>no</span>}<span><span>=</span>=</span>\mathrm{<span><span>0</span>0</span>}}{\overset{\mathrm{<span><span>N</span>N</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}\mathrm{<span><span>x</span>x</span>}<span><span>(</span>(</span>\mathrm{<span><span>n</span>no</span>}<span><span>+</span>+</span>\mathrm{<span><span>\&tau;</span>\&tau;</span>}<span><span>/</span>/</span>\mathrm{<span><span>2</span>2</span>}<span><span>)</span>)</span>{\mathrm{<span><span>x</span>x</span>}}^{<span><span>*</span>*</span>}<span><span>(</span>(</span>\mathrm{<span><span>n</span>no</span>}<span><span>-</span>-</span>\mathrm{<span><span>\&tau;</span>\&tau;</span>}<span><span>/</span>/</span>\mathrm{<span><span>2</span>2</span>}<span><span>)</span>)</span>\mathrm{<span><span>exp</span>exp</span>}<span><span>(</span>(</span>\mathrm{<span><span>j</span>j</span>}\mathrm{<span><span>2</span>2</span>}\mathrm{<span><span>\&pi;\&alpha;n</span>\&pi;\&alpha;n</span>}<span><span>/</span>/</span>\mathrm{<span><span>N</span>N</span>}<span><span>)</span>)</span><span><span>;</span>;</span>$

(iii)τ＝τ+2；(iii)τ=τ+2;

(iv)若τ＜N，返回(ii)，继续计算否则，按下式计算信号谱相关函数(iv) If τ<N, return to (ii) and continue to calculate Otherwise, calculate the signal spectral correlation function as follows

${\mathrm{<span><span>S</span>S</span>}}_{\mathrm{<span><span>x</span>x</span>}}^{\mathrm{<span><span>\&alpha;</span>\&alpha;</span>}}<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span><span><span>=</span>=</span>\underset{\mathrm{<span><span>\&tau;</span>\&tau;</span>}<span><span>=</span>=</span>\mathrm{<span><span>0</span>0</span>}}{\overset{\mathrm{<span><span>N</span>N</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}{\mathrm{<span><span>R</span>R</span>}}_{\mathrm{<span><span>x</span>x</span>}}^{\mathrm{<span><span>\&alpha;</span>\&alpha;</span>}}<span><span>(</span>(</span>\mathrm{<span><span>\&tau;</span>\&tau;</span>}<span><span>)</span>)</span>\mathrm{<span><span>exp</span>exp</span>}<span><span>(</span>(</span>\mathrm{<span><span>j</span>j</span>}\mathrm{<span><span>2</span>2</span>}\mathrm{<span><span>\&pi;k\&tau;</span>\&pi;k\&tau;</span>}<span><span>/</span>/</span>\mathrm{<span><span>N</span>N</span>}<span><span>)</span>)</span><span><span>;</span>;</span>$

·通过平滑法计算· Calculated by smoothing method

谱相关函数

实际表示的是x(t)在频率(f+α/2)和(f-α/2)的谱分量之间的相关密度，如下式：spectral correlation function

What is actually expressed is the correlation density between the spectral components of x(t) at frequencies (f+α/2) and (f-α/2), as follows:

${\mathrm{<span><span>S</span>S</span>}}_{\mathrm{<span><span>x</span>x</span>}}^{\mathrm{<span><span>\&alpha;</span>\&alpha;</span>}}<span><span>(</span>(</span>\mathrm{<span><span>f</span>f</span>}<span><span>)</span>)</span><span><span>=</span>=</span>\frac{\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>2</span>2</span>}\mathrm{<span><span>T</span>T</span>}}\mathrm{<span><span>X</span>x</span>}<span><span>(</span>(</span>\mathrm{<span><span>f</span>f</span>}<span><span>+</span>+</span>\frac{\mathrm{<span><span>\&alpha;</span>\&alpha;</span>}}{\mathrm{<span><span>2</span>2</span>}}<span><span>)</span>)</span>{\mathrm{<span><span>X</span>x</span>}}^{<span><span>*</span>*</span>}<span><span>(</span>(</span>\mathrm{<span><span>f</span>f</span>}<span><span>-</span>-</span>\frac{\mathrm{<span><span>\&alpha;</span>\&alpha;</span>}}{\mathrm{<span><span>2</span>2</span>}}<span><span>)</span>)</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>14</span>14</span>}<span><span>)</span>)</span>$

其中，

下面给出基于式(14)的计算过程：in,

The calculation process based on formula (14) is given below:

(i)计算x(n)的时间长度为T＝NT_s的N点频谱(i) The time length of calculating x(n) is the N-point spectrum of T=NT_s

${\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>T</span>T</span>}}<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span><span><span>=</span>=</span>\underset{\mathrm{<span><span>n</span>no</span>}<span><span>=</span>=</span>\mathrm{<span><span>0</span>0</span>}}{\overset{\mathrm{<span><span>N</span>N</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}\mathrm{<span><span>x</span>x</span>}<span><span>(</span>(</span>\mathrm{<span><span>n</span>no</span>}<span><span>)</span>)</span>\mathrm{<span><span>exp</span>exp</span>}<span><span>(</span>(</span><span><span>-</span>-</span>\mathrm{<span><span>j</span>j</span>}\mathrm{<span><span>2</span>2</span>}\mathrm{<span><span>\&pi;nk</span>\&pi;nk</span>}<span><span>/</span>/</span>\mathrm{<span><span>N</span>N</span>}<span><span>)</span>)</span>$

(ii)计算谱相关(ii) Calculation of spectral correlation

${\mathrm{<span><span>S</span>S</span>}}_{{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>T</span>T</span>}}}^{\mathrm{<span><span>\&alpha;</span>\&alpha;</span>}}<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span><span><span>=</span>=</span>\frac{\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>N</span>N</span>}}{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>T</span>T</span>}}<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>+</span>+</span>\mathrm{<span><span>\&alpha;</span>\&alpha;</span>}<span><span>/</span>/</span>\mathrm{<span><span>2</span>2</span>}<span><span>)</span>)</span>{{\mathrm{<span><span>X</span>x</span>}}^{<span><span>*</span>*</span>}}_{\mathrm{<span><span>T</span>T</span>}}<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>-</span>-</span>\mathrm{<span><span>\&alpha;</span>\&alpha;</span>}<span><span>/</span>/</span>\mathrm{<span><span>2</span>2</span>}<span><span>)</span>)</span>$

(iii)谱平滑(iii) Spectral smoothing

${\mathrm{<span><span>S</span>S</span>}}_{{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>T</span>T</span>}}}^{\mathrm{<span><span>\&alpha;</span>\&alpha;</span>}}{<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span>}_{\mathrm{<span><span>\&Delta;f</span>\&Delta;\; f</span>}}<span><span>=</span>=</span>\frac{\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>M</span>m</span>}<span><span>+</span>+</span>\mathrm{<span><span>1</span>1</span>}}\underset{\mathrm{<span><span>m</span>m</span>}<span><span>=</span>=</span><span><span>-</span>-</span>\mathrm{<span><span>M</span>m</span>}<span><span>/</span>/</span>\mathrm{<span><span>2</span>2</span>}}{\overset{\mathrm{<span><span>M</span>m</span>}<span><span>/</span>/</span>\mathrm{<span><span>2</span>2</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}{\mathrm{<span><span>S</span>S</span>}}_{{\mathrm{<span><span>X</span>x</span>}}_{\mathrm{<span><span>T</span>T</span>}}}^{\mathrm{<span><span>\&alpha;</span>\&alpha;</span>}}<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>+</span>+</span>\mathrm{<span><span>m</span>m</span>}<span><span>)</span>)</span>$

本文采用的第二种方法——通过平滑计算谱相关，图3中的检测结构图也是基于此方法进行的。The second method used in this paper—calculating spectral correlation by smoothing, the detection structure diagram in Figure 3 is also based on this method.

(2)搜寻唯一的循环频率(2) Search for a unique cycle frequency

使用已经产生的谱相关函数来搜寻循环频率，就是在谱相关函数上寻找峰值，谱相关函数只有在相应的循环频率和零循环频率处有峰值。Using the generated spectral correlation function to search for the cycle frequency is to search for a peak on the spectral correlation function, and the spectral correlation function has peaks only at the corresponding cycle frequency and zero cycle frequency.

(3)进行判决(3) Judgment

因为噪声是没有循环平稳特征的，所以利用第二步得到的峰值结果与一门限值比较，可以得到该频段上是否有主用户存在。Because the noise does not have cyclostationary characteristics, comparing the peak result obtained in the second step with a threshold value can determine whether there is a primary user in the frequency band.

图4是在虚警概率P_f＝0.04分别在噪声确定和不确定度为3dB时统计的在能量检测初检阶段能量的分布情况，每种情况统计2000次。由统计结果可以看出：Fig. 4 shows the statistics of energy distribution in the initial stage of energy detection when the false alarm probability P_f =0.04 and the noise is determined and the uncertainty is 3dB, respectively, and the statistics are 2000 times in each case. It can be seen from the statistical results that:

1)在低噪比时，信号的能量有50％-70％的落在(λ_H，λ_L)之间，即50％-70％的信号需要循环平稳特征进一步检测，这也表示在低信噪比时联合检测法比单用能量检测法复杂度要高50％-70％左右，比单用循环平稳特征检测低30％-50％左右；1) When the noise ratio is low, 50%-70% of the energy of the signal falls between (λ_H , λ_L ), that is, 50%-70% of the signal needs further detection of cyclostationary features, which also means that at low When the signal-to-noise ratio is used, the joint detection method is about 50%-70% more complex than the single-use energy detection method, and is about 30%-50% lower than the single-use cyclostationary feature detection;

2)在高信噪比时，落在(λ_H，λ_L)之间的概率接近0，说明高信噪比时联合检测法的复杂度与能量检测法相当；2) When the signal-to-noise ratio is high, the probability of falling between (λ_H , λ_L ) is close to 0, indicating that the complexity of the joint detection method is equivalent to that of the energy detection method when the signal-to-noise ratio is high;

3)在低信噪比时，噪声确定情况下的复杂度高于不确定情况；高信噪比时噪声不确定情况下复杂度高，但在信噪比高到一定程度时(如5dB)两者复杂度相同，皆为能量检测的复杂度，因为此时二者皆不需要循环平稳特征作进一步检测。3) When the SNR is low, the complexity in the case of definite noise is higher than that in the case of uncertainty; in the case of high SNR, the complexity is high in the case of uncertain noise, but when the SNR reaches a certain level (such as 5dB) Both have the same complexity, which is the complexity of energy detection, because neither of them need cyclostationary features for further detection at this time.

Claims (1)

1. A joint spectrum detection method based on energy-cyclostationary features is characterized by comprising the following steps: adopting different detection methods according to different energy of the signals to be detected, judging by adopting an energy detection method if the energy falls at two ends of two thresholds, and detecting by utilizing a cyclostationarity characteristic if the energy falls between the two thresholds, wherein the method specifically comprises the following steps:

a. determining a double threshold of a joint detection algorithm: determining a high threshold λ_HAnd a low threshold λ_LAnd a threshold for cycle detection; high thresholdLow threshold

Wherein N is the number of sampling points of the detection signal sample,

is the variance of Gaussian white noise, P_fIs the false alarm probability; q^-1Is composed of

b. Performing rough detection by using an energy detection method: calculating the energy of the signal to be detected, comparing the calculated energy with a predetermined double threshold, and if the energy is more than or equal to lambda_HThen it is judged as H₁I.e. a primary user signal is present; if the energy is less than or equal to λ_LThen it is judged as H₀I.e. the primary user signal is absent; if the calculated energy is at λ_LAnd λ_HIf the energy detection method cannot determine whether a main user signal exists, the cyclostationary feature is required to be used for further detection;

c. fine inspection is carried out by utilizing the cyclostationarity characteristic: for energy falling in lambda_LAnd λ_HThe signal between them is subjected to cyclostationary feature detection, and because different modulation modes correspond to different cyclic spectrum features, whether a main user exists is determined by detecting the value at a specific cyclic frequency alpha aiming at the modulation mode of the main user signal:

c1. performing FFT on N points of the input time sequence y (N) to obtain a spectral density function X of y (N)_T(k) T is the segment length; k is

c2. For result X of FFT_T(k) Left and right frequency shifts are respectively alpha/2, and accordingly, the spectrum density function of the x (n) frequency shift signal is obtained: x_T(k + α/2) and X_T(k-α/2)；

c3. Calculating a correlation density cyclic period spectrum between spectral components at frequencies (k + α/2) and (k- α/2)

c4. To circulationSmoothing the periodic spectrum to obtain a cyclic power spectrum estimate of the input signal

C5. Calculating the value of the circulation frequency alpha and comparing the value with a circulation detection threshold, and judging the value as H if the value is more than or equal to the threshold₁That is, the main user signal exists, if the main user signal is less than or equal to the threshold, the main user signal is judged to be H₀I.e. the main user signal is not present.

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