CN108988969B - Spectrum sensing method and device based on energy detection - Google Patents

Spectrum sensing method and device based on energy detection Download PDF

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CN108988969B
CN108988969B CN201810979658.XA CN201810979658A CN108988969B CN 108988969 B CN108988969 B CN 108988969B CN 201810979658 A CN201810979658 A CN 201810979658A CN 108988969 B CN108988969 B CN 108988969B
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CN108988969A (en
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景晓军
穆俊生
何元
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Beijing University of Posts and Telecommunications
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Abstract

The invention discloses a frequency spectrum sensing method and device based on energy detection. The method comprises the following steps: receiving a signal of a target frequency band to obtain a received signal; sampling the received signal to obtain a sampled signal; calculating an energy value of the sampled signal; expressing the optimization problem which gives consideration to the detection probability, the false alarm probability and the system throughput of the constraint condition into an objective function, and calculating a detection threshold under the optimal condition of the objective function; and judging the state of the target frequency band according to the relation between the energy value and the detection threshold value. The spectrum sensing method and the spectrum sensing device based on the energy detection adopt an energy detection means and comprehensively consider a plurality of influence factors for determining the sensing performance, thereby judging the state of the frequency band. Compared with the frequency spectrum sensing method for obtaining the optimal sensing performance at the cost of sacrificing system performance in other aspects in the prior art, the method can simultaneously guarantee the detection probability, the false alarm probability and the system throughput, and can be suitable for complex network environments.

Description

Spectrum sensing method and device based on energy detection
Technical Field
The invention relates to the technical field of cognitive radio, in particular to a frequency spectrum sensing method and device based on energy detection.
Background
Due to the important role in wireless communications, the radio spectrum is a precious resource that is tightly regulated. With the rapid development of wireless communication technology, the deep integration of new generation information technology represented by mobile internet, internet of things and cloud computing and the traditional industry, the application characteristics of broadband, ubiquitous and mobile radio technology become more obvious, explosive growth of spectrum demand is brought, and extreme shortage of spectrum resources is caused. The usage of the licensed radio spectrum is only about 30% as reported by the Federal Communications Commission (FCC). In addition, according to the 450MHz-5GHz band of interest spectrum resource assessment report issued by the national radio detection center and the global mobile communication system association in 7 months 2014, the spectrum usage rate of most bands of interest below 5GHz is far less than 10%. The frequency utilization efficiency is effectively improved, so that the problem of frequency spectrum scarcity is solved, and the objective requirements of mass business experience are enriched.
The concept of Cognitive Radio (CR) originated from the basic work of Joseph Mitola doctor 1999, and its core idea is to realize Dynamic Spectrum Allocation (DSA) and Spectrum Sharing (Spectrum Sharing) and limit and reduce the occurrence of collisions through Spectrum Sensing and intelligent learning capability of the system. As a key technology of cognitive radio, spectrum sensing plays a leading role in the whole cognitive network, and is the basis of spectrum allocation and spectrum sharing.
The target function of the spectrum sensing is combined with main factors influencing the spectrum sensing performance, is the optimization direction of the spectrum sensing performance, and plays a decisive role in the upper limit of the sensing performance. At present, most of objective functions used by mainstream spectrum sensing methods are local objective functions formed by collecting part of factors influencing spectrum sensing performance, so that the adaptability and robustness of a cognitive system are reduced, and the application and popularization of spectrum sensing in a complex network environment are not facilitated.
Disclosure of Invention
In view of this, an object of the embodiments of the present invention is to provide a method and an apparatus for spectrum sensing based on energy detection, which comprehensively consider main factors affecting spectrum sensing performance and effectively improve spectrum detection accuracy.
Based on the above object, an embodiment of the present invention provides a spectrum sensing method based on energy detection, including:
receiving a signal of a target frequency band to obtain a received signal;
sampling the received signal to obtain a sampled signal;
calculating an energy value of the sampled signal;
expressing an optimization problem which considers the detection probability, the false alarm probability and the system throughput of the constraint condition into an objective function, and calculating a detection threshold under the optimal condition of the objective function;
and judging the state of the target frequency band according to the relation between the energy value and the detection threshold value.
Optionally, the received signal r (t) is:
r(t)＝h(t)s(t)+w(t)，
where s (t) is a signal from an authorized user, w (t) is noise, and s (t) has a variance of
Figure BDA0001778204960000027
Variance of w (t) is
Figure BDA0001778204960000028
h (t) is the channel gain, t is time.
Optionally, the sampling signal r (n) is:
Figure BDA0001778204960000021
wherein the sampling rate of sampling the received signal is fs，fsW is more than or equal to 2W and represents bandwidth H0Indicates that the target frequency band is idle, H1And indicating that the authorized user exists in the target frequency band, wherein n indicates the serial number of the sampling point.
Optionally, the objective function is:
Figure BDA0001778204960000022
wherein, PdThe probability of detection is indicated and indicated,
Figure BDA0001778204960000023
denotes the lowest detection probability, PfThe probability of a false alarm is represented,
Figure BDA0001778204960000024
representing the maximum false alarm probability.
Optionally, when γ is greater than or equal to 1.5, calculating the detection threshold under the optimal condition of the objective function as:
Figure BDA0001778204960000025
wherein the content of the first and second substances,
Figure BDA0001778204960000026
representing the signal-to-noise ratio of the CR receiver at its location.
Optionally, the determining the state of the target frequency band according to the relationship between the energy value and the detection threshold includes:
if the energy value is larger than the detection threshold value, determining that the target frequency band is in a busy state;
and if the energy value is smaller than the detection threshold, judging that the target frequency band is in an idle state.
The invention also provides a frequency spectrum sensing device based on energy detection, which comprises:
the signal receiving module is used for receiving the signal of the target frequency band to obtain a received signal;
the sampling module is used for sampling the received signal to obtain a sampling signal;
the energy calculation module is used for calculating the energy value of the sampling signal;
the detection threshold calculation module is used for expressing the optimization problem which considers the constraint condition detection probability, the false alarm probability and the system throughput into an objective function and calculating the detection threshold under the optimal condition of the objective function;
and the judging module is used for judging the state of the target frequency band according to the relation between the energy value and the detection threshold value.
Optionally, the received signal r (t) is:
r(t)＝h(t)s(t)+w(t)，
where s (t) is a signal from an authorized user, w (t) is noise, and s (t) has a variance of
Figure BDA0001778204960000031
Variance of w (t) is
Figure BDA0001778204960000032
h (t) is channel gain
Optionally, the sampling signal r (n) is:
Figure BDA0001778204960000033
wherein the sampling rate of sampling the received signal is fs，fsW is more than or equal to 2W and represents bandwidth H0Indicates that the target frequency band is idle, H1Indicating the existence of the authorized user in the target frequency band.
Optionally, the objective function is:
Figure BDA0001778204960000034
wherein, PdThe probability of detection is indicated and indicated,
Figure BDA0001778204960000035
denotes the lowest detection probability, PfThe probability of a false alarm is represented,
Figure BDA0001778204960000036
representing the maximum false alarm probability.
As can be seen from the above, the spectrum sensing method based on energy detection provided by the embodiment of the present invention adopts an energy detection means, and comprehensively considers a plurality of influence factors for determining the sensing performance, so as to determine the state of the frequency band. Compared with the frequency spectrum sensing method for obtaining the optimal sensing performance at the cost of sacrificing system performance in other aspects in the prior art, the method provided by the embodiment of the invention can simultaneously ensure the detection probability, the false alarm probability and the system throughput, and can be suitable for complex network environments.
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Fig. 1 is a flowchart of a spectrum sensing method based on energy detection according to an embodiment of the present invention;
fig. 2 is a structural diagram of a spectrum sensing apparatus based on energy detection according to an embodiment of the present invention;
FIG. 3a is a first comparison graph of the best performance of four objective functions at different SNR according to the present invention;
FIG. 3b is a second comparison graph of the best performance of four objective functions at different SNR according to the embodiment of the present invention;
FIG. 3c is a third comparison graph of the best performance of four objective functions at different SNR according to the embodiment of the present invention;
FIG. 4a is a first comparison graph of the optimal performance of two objective functions at different SNR according to an embodiment of the present invention;
FIG. 4b is a second comparison graph of the best performance of two objective functions at different SNR according to the embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to specific embodiments and the accompanying drawings.
It should be noted that all expressions using "first" and "second" in the embodiments of the present invention are used for distinguishing two entities with the same name but different names or different parameters, and it should be noted that "first" and "second" are merely for convenience of description and should not be construed as limitations of the embodiments of the present invention, and they are not described in any more detail in the following embodiments.
For a single-node spectrum sensing algorithm, four factors determine the sensing performance: false alarm probability, detection probability, sensing time and system throughput. A higher detection probability indicates that the CR has better ability to protect the PU (authorized user); a lower false alarm probability indicates that the CR has a stronger communication capability. In fact, the sensing time directly determines the sensing accuracy of the CR and the system throughput. Generally, the longer the sensing time, the better the accuracy and reliability of the detection; meanwhile, the smaller the system throughput of the CR. However, when various spectrum sensing algorithms are compared in performance, the sensing time is often a constant value. Therefore, the sensing time in the embodiment of the present invention is also fixed to a certain constant value.
Based on the above problems, the embodiments of the present invention provide a spectrum sensing method based on energy detection, which can comprehensively consider the constraint conditions including the detection probability, the false alarm probability, and the system throughput, and simultaneously satisfy the requirements of high detection probability, low false alarm probability, and large system throughput. Referring to fig. 1, the spectrum sensing method based on energy detection includes:
step 101, adjusting the frequency of the CR antenna, and receiving a signal of a target frequency band to obtain a received signal.
Step 102, sampling the received signal according to a specific frequency spectrum to obtain a sampled signal.
Step 103, calculating the energy value of the sampling signal.
And 104, expressing the optimization problem which gives consideration to the constraint condition detection probability, the false alarm probability and the system throughput into an objective function, and calculating a detection threshold value under the optimal condition of the objective function.
And 105, judging the state of the target frequency band according to the relation between the energy value and the detection threshold value.
Through the embodiment, the spectrum sensing method based on energy detection adopts an energy detection means, and comprehensively considers and determines a plurality of influence factors of sensing performance, so that the state of a frequency band is judged. Compared with the frequency spectrum sensing method for obtaining the optimal sensing performance at the cost of sacrificing system performance in other aspects in the prior art, the method provided by the embodiment of the invention can simultaneously ensure the detection probability, the false alarm probability and the system throughput, and can be suitable for complex network environments.
In other embodiments of the present invention, assuming that the received signal r (t) of CR is a superposition of the signal s (t) from PU and the noise w (t), the received signal r (t) is:
r(t)＝h(t)s(t)+w(t), (4-1)
wherein s (t) is a signal from an authorized user, w (t) is noise, s (t) is independent of w (t), s (t) and w (t) are both independent and identically distributed steady-state random processes, and the variance of s (t) is
Figure BDA0001778204960000051
Variance of w (t) is
Figure BDA0001778204960000052
w (t) obeys a gaussian distribution, h (t) is the channel gain, | h (t) | obeys a Nakagami-mi distribution. Where s (t) may be a superposition of multiple source signals from different PUs.
Considering the theory of binary hypothesis, the CR received signal has a sampling rate fs(fsNot less than 2W) samples are receivedThe sampled signal r (n) of (a) is:
Figure BDA0001778204960000053
wherein the sampling rate of sampling the received signal is fs，fsW is more than or equal to 2W and represents bandwidth H0Indicates that the target frequency band is idle, H1And indicating that the authorized user PU exists in the target frequency band.
The classical spectrum sensing objective function mainly comprises the following three types:
Figure BDA0001778204960000061
Figure BDA0001778204960000062
min F＝Pf+Pm, (4-5)
wherein P isfThe probability of a false alarm is represented,
Figure BDA0001778204960000063
represents the maximum false alarm probability that the CR can tolerate; pdThe probability of detection is indicated and indicated,
Figure BDA0001778204960000064
represents the lowest detection probability that the CR should have; pm＝1-PdAnd (4) representing the probability of missed detection, wherein R is the throughput of the CR system, tau is the sensing time and is a detection threshold.
In one embodiment, for the objective function (4-3), when γ,
Figure BDA0001778204960000065
tau and fsWhen the pressure is fixed to a certain constant value,
Figure BDA0001778204960000066
wherein
Figure BDA0001778204960000067
τ denotes sensing time, Q-1An inverse function representing a standard normal distribution complementary cumulative distribution function represents the detection threshold.
The following can be obtained by calculation:
Figure BDA0001778204960000068
Figure BDA0001778204960000069
as can be seen from the above formula, since
Figure BDA00017782049600000610
And
Figure BDA00017782049600000611
Pdand PfMonotonically decreasing with respect to the detection threshold. However, when
Figure BDA00017782049600000612
When is, PdA maximum value is reached. At this point, the maximum detection probability comes at the expense of a higher false alarm probability. This results in a lower system throughput when the detection probability is maximal. Therefore, the objective function (4-3) is not the optimal choice if system throughput is considered.
In another embodiment, for the objective function (4-4), C is given0，P(H0) τ and T, when
Figure BDA00017782049600000613
The average system throughput of the CR is highest. Wherein, C0Representing the amount of information transmitted in CR units of time, P (H)0) Indicating the probability that the target channel is free and T indicating the sensing period.
The following can be obtained by calculation:
Figure BDA0001778204960000071
therefore, the temperature of the molten metal is controlled,
Figure BDA0001778204960000072
as can be seen from the above formula, when
Figure BDA0001778204960000073
The system throughput is maximized while the detection probability of CR is at a lower level.
In another embodiment, for the objective function (4-5), given
Figure BDA0001778204960000074
And fsWhen is coming into contact with
Figure BDA0001778204960000075
When, γ represents the signal-to-noise ratio, and F takes a minimum value.
The following can be obtained by calculation:
Figure BDA0001778204960000076
Figure BDA0001778204960000077
Figure BDA0001778204960000078
due to the fact that
Figure BDA0001778204960000079
Then
Figure BDA00017782049600000710
Figure BDA00017782049600000711
Figure BDA0001778204960000081
Thus, the number of the first and second electrodes,
Figure BDA0001778204960000082
at this time, it is possible to obtain,
Figure BDA0001778204960000083
thus, F in the interval ∈ [ alpha ]0, + ∞) monotonically increases, and in the interval ∈ (-infinity,0) Monotonically decreasing. That is to say when
Figure BDA0001778204960000084
When F is smaller, F takes the minimum value.
The objective function (4-5) is a compromise considering the detection probability and the false alarm probability, compared to the objective functions (4-3) and (4-4). That is, the objective function (4-5) has a strong ability to protect the PU, while also ensuring a high system throughput.
The following table shows the performance comparison of three classical spectrum sensing objective functions based on energy detection.
Figure BDA0001778204960000085
From the above table, some important conclusions can be drawn. Firstly, an objective function determines the performance of spectrum sensing; different objective functions correspond to different perceptual performances, which implies the importance of exploring the spectrum sensing objective function. Secondly, the first two objective functions obtain the best perception performance at the cost of sacrificing system performance in other aspects, and the objective function (4-5) is a compromise scheme and gives consideration to detection probability, false alarm probability and system throughput. Therefore, in some specific scenarios, it is very important to select a suitable objective function. Moreover, further exploring the spectrum sensing objective function is beneficial to popularization of a spectrum sensing algorithm and robustness of the spectrum sensing algorithm. The more effective spectrum sensing objective function is beneficial to providing more optimization directions and further improving the sensing performance under a specific scene.
Based on the above purpose, when γ is greater than or equal to 1.5, the embodiment of the present invention provides an optimal spectrum sensing objective function under the condition of considering detection probability, false alarm probability and system throughput. Wherein the objective function is:
Figure BDA0001778204960000091
wherein, PdThe probability of detection is indicated and indicated,
Figure BDA0001778204960000092
denotes the lowest detection probability, PfThe probability of a false alarm is represented,
Figure BDA0001778204960000093
representing the maximum false alarm probability.
In the above-described embodiment, at a given γ,
Figure BDA0001778204960000094
τ, can be obtained by calculation
Figure BDA0001778204960000095
Figure BDA0001778204960000096
Figure BDA0001778204960000097
Figure BDA0001778204960000098
Then
Figure BDA0001778204960000099
Thus when detecting the threshold
Figure BDA00017782049600000910
Then, G takes the maximum value, i.e. G is optimal.
The objective functions (4-5) and (4-16) were compared, and their main differences are as follows
Figure BDA0001778204960000101
Figure BDA0001778204960000102
Wherein0A detection threshold calculated for the objective function (4-5),1a detection threshold calculated for the objective function (4-16).
When coming from0To1When varied, the amount of change in CR performance can be approximated as
Figure BDA0001778204960000103
ΔPd＝Pd|＝1-Pd|＝0＞0, (4-26)
ΔPf＝Pf|＝1-Pf|＝0＞0, (4-27)
Figure BDA0001778204960000104
It should be noted that (4-25) holds based on the detection probability, the false alarm probability and the contribution of the system throughput to the CR. More specifically, an increase in the false alarm probability and a decrease in the system throughput degrade the system performance of the CR and an increase in the detection probability increases the system performance.
Alternatively, equations (4-25) can be further simplified to
Figure BDA0001778204960000105
Consider that (4-26) and (4-27), (4-29) can be further expressed as
Figure BDA0001778204960000106
Δ＝1-0. (4-30)
Due to the fact that
Figure BDA0001778204960000111
Then
Figure BDA0001778204960000112
Due to Pf|＝0→0&&ΔPfIf greater than 0, then
Figure BDA0001778204960000114
Namely: when gamma is more than or equal to 1.5, G is P in the objective function (4-16)d/PfIs better than the objective function (4-5).
In summary, considering the detection probability, the false alarm probability and the system throughput, when gamma is larger than or equal to 1.5, the objective function (4-16) is better than the objective function (4-5). It should be noted that if the number of samples is sufficiently large (τ f)s＞20)，
Figure BDA0001778204960000113
The objective function (4-16) and the objective function (4-5) have the best detection performance together under the condition of considering the detection probability, the false alarm probability and the system throughput.
Optionally, the determining the state of the target frequency band according to the relationship between the energy value and the detection threshold in step 105 includes: if the energy value is larger than the detection threshold value, the target frequency band is in a busy state; and if the energy value is smaller than the detection threshold value, the target frequency band is in an idle state.
Fig. 3a-3c show the comparison of the objective function proposed by the present invention with the false alarm probability, detection probability and throughput performance of the objective functions shown in formulas (4-3), (4-4) and (4-5), respectively. It should be noted that the detection performances of fig. 3a-3c (and fig. 4a-4b later) are obtained when the optimal solution is obtained for each objective function. In addition, the sampling points N in fig. 3a to 3c are 100, and the sampling points in fig. 4a to 4b are 20. 3a-3c, the false alarm probability of the objective function (4-3) is significantly higher under the same conditions, indicating that the higher detection probability of the objective function (4-3) comes at the expense of the false alarm probability; the detection probability of the objective function (4-4) is obviously lower, which shows that the higher throughput of the objective function (4-4) is at the cost of reducing the detection probability. Obviously, the objective function (4-3) and the objective function (4-4) are sub-optimal schemes under the condition of considering the detection probability, the false alarm probability and the system throughput. In comparison, the objective function (4-5) and the objective function (4-16) in the embodiment of the invention give consideration to the detection probability, the false alarm probability and the system throughput, and have better technical effects.
FIGS. 4a-4b show a comparison of the performance of the objective function (4-16) and the objective function (4-5) according to an embodiment of the present invention. Under the same condition, the detection probability and the false alarm probability of the target function (4-16) are obviously higher than those of the target function (4-5), which shows that the target function (4-16) of the embodiment of the invention increases the capability of protecting the normal work of the master user and reduces the information transmission capability of the CR user to a certain extent. According to the theoretical derivation, the overall performance of the objective function (4-16) of the embodiment of the invention is better than that of the objective function (4-5) when the environmental signal-to-noise ratio is larger than 1.5.
An embodiment of the present invention further provides a spectrum sensing device based on energy detection, and as shown in fig. 2, the device includes:
the signal receiving module 11 is configured to receive a signal of a target frequency band to obtain a received signal;
a sampling module 12, configured to sample the received signal to obtain a sampled signal;
an energy calculation module 13 for calculating an energy value of the sampled signal;
a detection threshold calculation module 14, configured to express an optimization problem that considers constraint detection probability, false alarm probability, and system throughput as an objective function, and calculate a detection threshold under the optimal condition of the objective function;
and the judging module 15 is configured to judge the state of the target frequency band according to the relationship between the energy value and the detection threshold.
Optionally, the received signal r (t) is:
r(t)＝h(t)s(t)+w(t)，
where s (t) is a signal from an authorized user, w (t) is noise, and s (t) has a variance of
Figure BDA0001778204960000125
Variance of w (t) is
Figure BDA0001778204960000126
h (t) is channel gain
Optionally, the sampling signal r (n) is:
Figure BDA0001778204960000121
wherein the sampling rate of sampling the received signal is fs，fsW is more than or equal to 2W and represents bandwidth H0Indicates that the target frequency band is idle, H1Indicating the existence of the authorized user in the target frequency band.
Optionally, the objective function is:
Figure BDA0001778204960000122
wherein, PdThe probability of detection is indicated and indicated,
Figure BDA0001778204960000123
denotes the lowest detection probability, PfThe probability of a false alarm is represented,
Figure BDA0001778204960000124
representing the maximum false alarm probability.
Optionally, when γ is greater than or equal to 1.5, calculating the detection threshold under the optimal condition of the objective function as:
Figure BDA0001778204960000131
where γ represents the signal-to-noise ratio.
Optionally, the determining module 15 is further configured to implement: if the energy value is larger than the detection threshold value, determining that the target frequency band is in a busy state; and if the energy value is smaller than the detection threshold, judging that the target frequency band is in an idle state.
Those of ordinary skill in the art will understand that: the discussion of any embodiment above is meant to be exemplary only, and is not intended to intimate that the scope of the disclosure, including the claims, is limited to these examples; within the idea of the invention, also features in the above embodiments or in different embodiments may be combined, steps may be implemented in any order, and there are many other variations of the different aspects of the invention as described above, which are not provided in detail for the sake of brevity.
In addition, well known power/ground connections to Integrated Circuit (IC) chips and other components may or may not be shown within the provided figures for simplicity of illustration and discussion, and so as not to obscure the invention. Furthermore, devices may be shown in block diagram form in order to avoid obscuring the invention, and also in view of the fact that specifics with respect to implementation of such block diagram devices are highly dependent upon the platform within which the present invention is to be implemented (i.e., specifics should be well within purview of one skilled in the art). Where specific details (e.g., circuits) are set forth in order to describe example embodiments of the invention, it should be apparent to one skilled in the art that the invention can be practiced without, or with variation of, these specific details. Accordingly, the description is to be regarded as illustrative instead of restrictive.
While the present invention has been described in conjunction with specific embodiments thereof, many alternatives, modifications, and variations of these embodiments will be apparent to those of ordinary skill in the art in light of the foregoing description. For example, other memory architectures (e.g., dynamic ram (dram)) may use the discussed embodiments.
The embodiments of the invention are intended to embrace all such alternatives, modifications and variances that fall within the broad scope of the appended claims. Therefore, any omissions, modifications, substitutions, improvements and the like that may be made without departing from the spirit and principles of the invention are intended to be included within the scope of the invention.

Claims (7)

1. A spectrum sensing method based on energy detection is characterized by comprising the following steps:
receiving a signal of a target frequency band to obtain a received signal;
sampling the received signal to obtain a sampled signal;
calculating an energy value of the sampled signal;
expressing an optimization problem which considers the detection probability, the false alarm probability and the system throughput of the constraint condition into an objective function, and calculating a detection threshold under the optimal condition of the objective function; the objective function is:
Figure FDA0002427935680000011
wherein, PdThe probability of detection is indicated and indicated,
Figure FDA0002427935680000012
denotes the lowest detection probability, PfThe probability of a false alarm is represented,
Figure FDA0002427935680000013
representing a maximum false alarm probability; when gamma is larger than or equal to 1.5, calculating the detection threshold under the optimal condition of the target function as follows:
Figure FDA0002427935680000014
wherein γ represents the signal-to-noise ratio;
and judging the state of the target frequency band according to the relation between the energy value and the detection threshold value.
2. The method for spectrum sensing based on energy detection according to claim 1, wherein the received signal r (t) is:
r(t)＝h(t)s(t)+w(t)，
where s (t) is a signal from an authorized user, w (t) is noise, and s (t) has a variance of
Figure FDA0002427935680000015
Variance of w (t) is
Figure FDA0002427935680000016
h (t) is the channel gain, t is time.
3. The method for sensing spectrum based on energy detection according to claim 2, wherein the sampled signal r (n) is:
Figure FDA0002427935680000017
wherein the sampling rate of sampling the received signal is fs，fsW is more than or equal to 2W and represents bandwidth H0Indicates that the target frequency band is idle, H1And indicating that the authorized user exists in the target frequency band, wherein n indicates the serial number of the sampling point.
4. The method for sensing frequency spectrum based on energy detection according to claim 1, wherein said determining the state of the target frequency band according to the relation between the energy value and the detection threshold comprises:
if the energy value is larger than the detection threshold value, determining that the target frequency band is in a busy state;
and if the energy value is smaller than the detection threshold, judging that the target frequency band is in an idle state.
5. An apparatus for spectrum sensing based on energy detection, comprising:
the signal receiving module is used for receiving the signal of the target frequency band to obtain a received signal;
the sampling module is used for sampling the received signal to obtain a sampling signal;
the energy calculation module is used for calculating the energy value of the sampling signal;
the detection threshold calculation module is used for expressing the optimization problem which considers the constraint condition detection probability, the false alarm probability and the system throughput into an objective function and calculating the detection threshold under the optimal condition of the objective function; the objective function is:
Figure FDA0002427935680000021
wherein, PdThe probability of detection is indicated and indicated,
Figure FDA0002427935680000022
denotes the lowest detection probability, PfThe probability of a false alarm is represented,
Figure FDA0002427935680000023
representing a maximum false alarm probability; when gamma is larger than or equal to 1.5, calculating the detection threshold under the optimal condition of the target function as follows:
Figure FDA0002427935680000024
wherein γ represents the signal-to-noise ratio;
and the judging module is used for judging the state of the target frequency band according to the relation between the energy value and the detection threshold value.
6. The energy detection-based spectrum sensing apparatus according to claim 5,
the received signal r (t) is:
r(t)＝h(t)s(t)+w(t)，
where s (t) is a signal from an authorized user, w (t) is noise, and s (t) has a variance of
Figure FDA0002427935680000025
Variance of w (t) is
Figure FDA0002427935680000026
h (t) is the channel gain.
7. The energy detection-based spectrum sensing apparatus according to claim 5, wherein the sampled signal r (n) is:
Figure FDA0002427935680000027
wherein the sampling rate of sampling the received signal is fs，fsW is more than or equal to 2W and represents bandwidth H0Indicates that the target frequency band is idle, H1Indicating the existence of the authorized user in the target frequency band.
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