CN107181548A - One kind compression frequency spectrum perception performance improvement method - Google Patents
One kind compression frequency spectrum perception performance improvement method Download PDFInfo
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- CN107181548A CN107181548A CN201710339578.3A CN201710339578A CN107181548A CN 107181548 A CN107181548 A CN 107181548A CN 201710339578 A CN201710339578 A CN 201710339578A CN 107181548 A CN107181548 A CN 107181548A
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
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- H04B17/00—Monitoring; Testing
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- H04B17/382—Monitoring; Testing of propagation channels for resource allocation, admission control or handover
Abstract
Frequency spectrum perception performance improvement method is compressed the invention discloses one kind, an embodiment of methods described includes：The spacing wireless electric signal received using wide-band modulation converter to antenna is compressed sampling, obtains compressed and multiplexed measurement sample；Pre- decision method is offseted using branch energy to determine to whether there is primary user's signal in the compression measurement sample；In response to determining that primary user's signal is not present, then full frequency band is available free frequency range, in response to there is primary user's signal, then completing support using orthogonal matching pursuit algorithm determines, the frequency range taken by primary user is found out, remaining unappropriated frequency range is available free frequency range.It is high that there is the embodiment support to reconstruct probability, computation complexity is low, there is robustness to noise uncertainty, the advantage of the non-openness influence to lack sampling frequency spectrum perception of broadband Gaussian white noise can be effectively reduced, during the broader frequency spectrum available for analog signal compression sampling is perceived.
Description
Technical field
The invention belongs to communication technical field, it is related to frequency spectrum perception technology, further relates to a kind of compression frequency spectrum perception
Performance improvement method, the broader frequency spectrum that this method can be used in cognitive radio is perceived.
Background technology
In recent years, the wireless device quantity and radio service type of Exponential growth, which are exacerbated, rationally applies limited spectrum
The pressure of resource.Current spectral management policy is distribution fixed frequency range to a wireless user, the frequency spectrum distribution political affairs of this fixation
Plan has been demonstrated the relatively low of the availability of frequency spectrum, is easily caused in some frequency range congestions, and not enough in other frequency range utilization rates.It is cognitive
Radio (Cognitive Radio, CR) allows secondary user's (Secondary Users, SU) to access to chance unused nothing
Line electricity frequency spectrum, i.e. blank frequency band, this is considered as the effective means solved the above problems.Frequency spectrum perception is used as cognitive radio system
The key technology of system, is the most basic ability of cognitive radio users, is also one of core technology of cognitive radio.Pass through frequency
Spectrum is perceived it is known that frequency range occupancy situation and primary user (Primary Users, SU) signal whether there is, so that dynamic land productivity
With the time and spatially frequency spectrum resource of temporary standby.In order to which using more idle frequency ranges, broader frequency spectrum has been perceived gradually
Receive significant attention, SU carries out frequency spectrum perception to search for more frequencies in very wide band limits in broader frequency spectrum cognition technology
Spectrum access chance.However, broader frequency spectrum is perceived often has certain technical bottleneck in Practical Project realization, for example, need width
Collection input front end, high sampling rate analog-to-digital conversion, Large Volume Data caching and the very high speed digital signal processor of analog bandwidth,
These defects constrain the popularization of broader frequency spectrum cognition technology to a certain extent.
Compression sampling theory needs only to the non-self-adapting linear measurement sample point of only a few, it is possible to pass through convex optimization
Method recovers analog signal sparse in time domain or other transform domains with great probability, with conventional Nyquist Sampling Frame
Frame, which is compared, can significantly reduce analog signal sampling rate.Signal from analog turning to information can be directly realized by according to this method
Change, be that reduction Analog-digital Converter speed and alleviation Digital Signal Processing pressure provide new theoretical foundation.In consideration of it, will
Compression sampling is perceived with broader frequency spectrum and is combined, and the sparse characteristic for treating perceived spectral is made full use of, to be adopted far below Nyquist
The analog-to-digital conversion rate of sample rate completes the information gathering of broader frequency spectrum, and real-time with extremely low Digital Signal Processing expense
Complete broader frequency spectrum to perceive, be to solve broadband analog signal collection and high-speed digital signal transmission, storage and processing bottleneck
One of effective way.
At present, the broader frequency spectrum cognitive method based on analog signal compression sampling is broadly divided into two categories below：
The first kind is to be based on analog information converter (Analog to Information Converter, AIC), and AIC is owed
Sampling frequency cognitive method is made up of two stages, in first stage, and original wideband signal is reconstructed from compression sampling sample
Or its power spectrum；In second stage, perform broader frequency spectrum and perceive to determine band occupancy position.The collection framework realizes letter
It is single, but when recovering continuous spectra signal in broadband, input signal model mismatch can be faced and produce great reconstructed error or defeated
Enter the predicament for the higher-dimension complex matrix computing that signal model accurate strips are come.
Equations of The Second Kind is the lack sampling based on wide-band modulation converter (Modulated Wideband Converter, MWC)
Frequency spectrum sensing method, MWC lack samplings framework is used as analog input signal mould using the limited union with translation invariant subspace
Type, by the way that input signal is multiplied on multiple branch roads with cycle random mark sequence ± 1, is then filtered with low pass filter,
Sampled finally by slow-type analog digital quantizer (Analog to Digital Converter, ADC).Constructed by framework
With the multiple measurement Vector Problems of solution, the corresponding support of occupied frequency range is obtained with orthogonal matching pursuit algorithm without complete
Signal recovers.Research can adapt to different types of letter it has been shown that the lack sampling broader frequency spectrum cognitive method based on MWC has
Number, fast signal supports the advantage of recovery and low computation complexity.
But the above method all assumes that PU signals are present in the frequency band of correlation, and it is sparse, but treats
The target frequency bands of monitoring are entirely possible to be existed without any primary user, and only ambient noise is present, such as in wideband satellite communication
In millimetre-wave attenuator.In this case, the directly above-mentioned lack sampling frequency spectrum sensing method of application is inappropriate, is easily drawn
Play following problem：
(1) when white Gaussian noise is only existed in the broadband frequency range perceived, the restructing algorithm of compressed sensing still can foundation
The openness occupancy situation provided in frequency band, this will cause serious false-alarm probability；
(2) process that signal reconstruction and support are determined is carried out using lack sampling sample, brings great calculation cost, and
These computings are insignificant.
The content of the invention
It is an object of the invention to overcome the above-mentioned deficiency based on wide-band modulation converter lack sampling frequency spectrum perception technology, carry
Go out a kind of compression frequency spectrum perception performance improvement method.This method determines that PU whether there is, and only exist before signal is supported to recover
Detected in associated frequency band with the presence of PU signals, signal support determining module is just actuated to perceive the position of band occupancy；It is no
Then, signal support determining module will be bypassed, and directly be judged full frequency band and be can use.It is necessary to note that this method not merely can use
In MWC sampling frames, extend also in other compression sampling frames.The inventive method can effectively reduce non-sparse broadband
Influence of the white Gaussian noise to lack sampling frequency spectrum perception performance, the lifting support reconstruct degree of accuracy, reduces calculation cost, improves frequency band
Utilization rate.
The present invention proposes a kind of compression frequency spectrum perception performance improvement method, and methods described includes：Converted using wide-band modulation
The spacing wireless electric signal that device is received to antenna is compressed sampling, obtains compressed and multiplexed measurement sample；Utilize branch energy
Pre- decision method is offseted to determine to whether there is primary user's signal in the compression measurement sample；In response to determining that primary user is not present
Signal, then full frequency band is available free frequency range, in response to there is primary user's signal, then completes branch using orthogonal matching pursuit algorithm
Collection is determined, finds out the frequency range taken by primary user, and remaining unappropriated frequency range is available free frequency range.
In certain embodiments, the spacing wireless electric signal received using wide-band modulation converter to antenna is carried out
Compression sampling, obtains compressed and multiplexed measurement sample, including：The space radio received using wide-band modulation converter to antenna
Signal x (t) is compressed sampling, obtains compressed and multiplexed measurement sample yi(n), i=1,2 ..., m, n=0,1 ..., N-1, its
In, m is compression sampling circuitry number, and N is sample points.
In certain embodiments, the utilization branch energy offsets pre- decision method and determines that described compress in measurement sample is
No have primary user's signal, including：
(a) time domain energy of the compression measurement sample of each branch road is calculated；
(b) test statistics is built using the time domain energy of each branch roadWherein,For jth branch road when
Domain energy,For the time domain energy of the branch road of jth+1, j=1,2 ..., m, definition
(c) the detection statistic r is calculatedjCumulative distribution function Pf,j：
Wherein, γjFor decision threshold, ρjIt isWithCoefficient correlation, value isΦ () function expression isRepresent variance, Cov
[] represents covariance；
(d) according to the cumulative distribution function of the test statistics, using CFAR criterion, decision threshold γ is calculatedj：
Wherein,For the false-alarm probability of each branch decision, PfaPre- judgement is offseted for branch energy
The default false-alarm probability of method, Φ-1() is the inverse function of Φ () function；
(e) the test statistics r for obtaining step (b)jThe judging threshold γ obtained with step (d)jCompare, if rj≥
γj, then it is 1 to set judgement matrix element C (j), otherwise C (j)=0, and final court verdict can be expressed as follows：
Wherein, if court verdict is H0, then it represents that primary user's signal is not present in the compression measurement sample, if sentenced
Certainly result is H1, then it represents that there is primary user's signal in the compression measurement sample.
In certain embodiments, it is described to calculate the detection statistic rjCumulative distribution function Pf,jIncluding：
(a) in the case of primary user's signal being not present in compression measurement sample, the spacing wireless electric signal x received
(t) frequency spectrum X (k) is that average is that 0, variance isDiscrete random variable, using X (k) average and variance, branch can be calculated
Road compression measurement sample spectra Yi(k) statistical property characteristic, wherein, the statistical property includes average, variance, covariance：
Wherein,Expression takes real part,Expression takes imaginary part, cilFor the sequence p of cycle pseudorandom ± 1i(t) cycle
Fourier expansion coefficient, k=0,1 ..., N-1；
(b) incite somebody to action | | Yi(k)||2Regard the quadratic sum of two independent Gaussian stochastic variables as, can calculate | | Yi(k)||2Statistics
Characteristic：
Wherein, p, q=1,2 ..., m, p ≠ q, k=0,1 ..., N-1,
In formula, cpm、cqmFor the cycle Fourier series expansion coefficient of the sequence of cycle pseudorandom ± 1；
(c) in the case of primary user's signal being not present in compression measurement sample, using principle of conservation of energy, N is worked as>20
When,Approximate Gaussian distributed, its average and variance are respectivelyWith WithCoefficient correlation be ρj, by
This can obtain test statistics rjCumulative distribution function Pf,j：
Wherein, γjFor decision threshold, H0Represent the non-existent situation of primary user's signal, ρjIt isWithPhase relation
Count, value isΦ () function expression is
The present invention has advantages below：
1st, the present invention measures sample just with a small amount of compression, passes through the openness of the spacing wireless electric signal to receiving
Judgement, effectively reduces influence of the broadband Gaussian white noise to lack sampling frequency spectrum perception performance in advance；
2nd, it is of the invention because its threshold value is unrelated with noise power size, so the shadow that perceptual performance is fluctuated by noise variance
Sound is smaller, it is adaptable to high dynamic background noise environment；
3rd, the compression frequency spectrum perception performance improvement method that the present invention is provided significantly is carried under the conditions of at a fairly low calculation cost
The correctness that signal support is determined during high lack sampling broader frequency spectrum is perceived.
Brief description of the drawings
By reading the detailed description made to non-limiting example made with reference to the following drawings, the application's is other
Feature, objects and advantages will become more apparent upon：
Fig. 1 is the flow chart of one embodiment of the present of invention；
Fig. 2 is another flow chart of one embodiment of the present of invention；
Fig. 3 is correct detection probability emulation of the present invention under different signal to noise ratio and under the conditions of different compression measured value
Figure；
Fig. 4 is false-alarm probability analogous diagram of the present invention in the case of different compression sampling numbers；
Fig. 5 is the receiver performance curve in the present invention；
Fig. 6 is support reconstruct accuracy comparison diagram when whetheing there is the inventive method.
Embodiment
The application is described in further detail with reference to the accompanying drawings and examples.It is understood that this place is retouched
The specific embodiment stated is used only for explaining related invention, rather than the restriction to the invention.It also should be noted that, in order to
Be easy to description, illustrate only in accompanying drawing to about the related part of invention.
The present invention is perceived for the lack sampling broader frequency spectrum of analog signal, perceives end and signal is received in each subchannel, and
The sampling of the docking collection of letters number is handled.Describe the application in detail below with reference to the accompanying drawings and in conjunction with the embodiments.
Reference picture 1, shows the flow chart 100 of one embodiment of the present of invention.Comprise the following steps：
Step 101, the spacing wireless electric signal received using wide-band modulation converter to antenna is compressed sampling, obtains
To compressed and multiplexed measurement sample.
Sampling is compressed to the spacing wireless electric signal x (t) that antenna is received using wide-band modulation converter, obtains many
Road sample yi(n), i=1,2 ..., m, n=0,1 ..., N-1, wherein, it is that m is compression sampling circuitry number, N is sample points；
Step 102, pre- decision method is offseted using branch energy to determine in compression measurement sample with the presence or absence of primary user's letter
Number.
(a) time domain energy of the compression measurement sample of each branch road is calculated, the i-th branch road can be estimated according to equation below
Time domain energy
(b) test statistics is built using the time domain energy of each branch roadWherein,For jth branch road when
Domain energy,For the time domain energy of the branch road of jth+1, j=1,2 ..., m, definition
(c) test statistics r is calculatedjCumulative distribution function Pf,j：
(c1) in the case of primary user's signal being not present in compression measurement sample, input signal x (t) frequency spectrum X (k) is
Average is that 0, variance isDiscrete random variable, using X (k) average and variance, branch road sample spectra can be calculatedThe statistical property such as average, variance, covariance and correlation, wherein, cil
For the sequence p of cycle pseudorandom ± 1i(t) cycle Fourier series expansion coefficient, l is in complete expression input signal x (t) Fu
Subspace number required for leaf transformation X (j Ω)：
Wherein,Expression takes real part,Expression takes imaginary part, k=0,1 ..., N-1；
(c2) incite somebody to action | | Yi(k)||2Regard the quadratic sum of two independent Gaussian stochastic variables as, can calculate | | Yi(k)||2System
Count characteristic：
Wherein p, q=1,2 ..., m, p ≠ q, k=0,1 ..., N-1,
In formula, cpm、cqmFor the cycle Fourier series expansion coefficient of the sequence of cycle pseudorandom ± 1.
(c3) in the case of primary user's signal being not present in compression measurement sample, using principle of conservation of energy, N is worked as>20
When,Approximate Gaussian distributed, its average and variance are respectivelyWith WithCoefficient correlation be ρj,
It can thus be concluded that test statistics rjCumulative distribution function Pf,j：
Wherein, γjFor decision threshold, H0Represent the non-existent situation of primary user's signal, ρjIt isWithPhase relation
Count, value isΦ () function expression is
(d) according to the cumulative distribution letter in compression measurement sample in the absence of the test statistics in the case of primary user's signal
Number, using CFAR criterion, calculates decision threshold γj：
Wherein, Pf0=1- (1-Pfa)1/mFor the false-alarm probability of each branch decision, PfaPre- judgement side is offseted for branch energy
The default false-alarm probability of method, Φ-1() is the inverse function of Φ () function.
(e) the test statistics r for obtaining step (b)jThe judging threshold γ obtained with step (d)jCompare, if rj≥
γj, then it is 1 to set judgement matrix element C (j), otherwise C (j)=0.Final court verdict can be expressed as follows：
Wherein, if court verdict is H0, then it represents that primary user's signal is not present in the compression measurement sample, if sentenced
Certainly result is H1, then it represents that there is primary user's signal in the compression measurement sample.
Step 103, in response to determining that primary user's signal is not present, then full frequency band is available free frequency range, in response to existing
Primary user's signal, then complete support using orthogonal matching pursuit algorithm and determine, find out the frequency range taken by primary user, it is remaining not by
The frequency range of occupancy is available free frequency range.
With continued reference to Fig. 2, Fig. 2 is another flow chart of one embodiment of the present of invention, and the flow chart mainly uses symbol
The flow of embodiment is represented with formula, as shown in Figure 2, first, the space received to antenna using wide-band modulation converter without
Line electric signal x (t) and the sequence p of cycle pseudorandom ± 1i(t) it is multiplied；Then, LPF is carried out by LPF and ADC is pressed
Contracting sampling, obtains compressed and multiplexed measurement sample yi(n), i=1,2 ..., m, n=0,1 ..., N-1, wherein, m is compression sampling branch
Way, N is sample points；Afterwards, offset pre- decision method using branch energy and determine whether deposited in the compression measurement sample
In primary user's signal, if being judged to the presence of primary user's signal, by compression measurement sample by short time data memory cell and in short-term
Data reconstruction unit obtains signal support S, further can obtain and recovers primary signal by compression measurement sample.
The effect of the present invention can be further illustrated by following emulation：
A, simulated conditions
The equivalent sampling speed for the wide-band modulation converter that analogue system is used is fNYQ=600MHz, collection circuitry number is m
=20, the cycle of the sequence of random mark ± 1 is Tp=75ns, frequency are fp=1/Tp, equivalent random chip number in a cycle
For L=45, LPF cut-off frequency used in each passage is fs/ 2, single channel sampling rate is fs=fp；Primary user's transmission letter
Number be made up of three digital modulation signals (altogether take six frequency bands), the chip rate of each signal is sr=1.024MBaud,
The carrier frequency of each signal is in [- fNYQ/2,fNYQ/ 2] uniformly random selection in the range of.The power of three signals is identical,
And the power used in simulations isWherein P is the general power of three primary user's signals.Factor ρ is defined as making an uproar
Sound variance is randomly dispersed in gapWhen noise uncertainty, wherein ρ >=1.According to invariable false alerting criterion,
P is setf=0.01.Following simulation result is all the average value under 10000 Monte-Carlo Simulations.
B, emulation content and result
Emulation 1：Correct inspection under the conditions of signal to noise ratio is -20dB~-10dB and different sample points N to the present invention
Survey probability to be emulated, N value is respectively chosen as 200,400 and 800, and emulation is as shown in Figure 3.
In Fig. 3, abscissa SNR represents signal to noise ratio, ordinate PdRepresent detection probability, Theory representation theory curves, Sim
Simulation curve is represented, N represents sample points, and ρ represents noise uncertainty, Pd, Theory representation theory detection probability curves, Pd、
Sim represents to emulate detection probability curve, Pd, detection probability curve when Sim, ρ represent to have noise uncertainty.Can by Fig. 3
See, the present invention only can realize preferably pre- judgement property in the case where signal to noise ratio snr is relatively low with 200 compression samples
Can, performance can be detected with significant improve by increasing sample size.And whether there is incorrect noise, simulation result
Correct detection probability keep constant, illustrate influence that can effectively to antinoise uncertainty of the invention.
Emulation 2：It is -20dB~-10dB and default false-alarm probability P in signal to noise ratiofaUnder conditions of=0.01, to the present invention
False-alarm probability emulated, emulation is as shown in Figure 4.
In Fig. 4, abscissa Times represents time, ordinate PfFalse-alarm probability is represented, from fig. 4, it can be seen that false-alarm probability is imitative
True end value is slightly fluctuated near preset value, and this illustrates the reasonability of false-alarm probability and detection probability expression formula.Total score
Fig. 3 and 4 is analysed, it is known that the present invention can ensure relatively low false-alarm probability P in big SNR rangefIn the case of obtain
Higher detection probability Pd。
Emulation 3：False-alarm probability PfValue 10-3With 10-1Between change, during SNR=-16dB, in different sample points N
The receiver performance curve ROCs of the present invention is emulated in the case of respectively 350,300,200, simulation result such as Fig. 5 institutes
Show.
As seen from Figure 5, when there is noise uncertainty, in the case of different sample points N, receiver of the invention
Performance curve is also basically unchanged, and theoretical curve is essentially coincided with simulation curve, illustrates that the present invention has robust to noise uncertainty
Property.
Emulation 4：Compare support when whetheing there is pre- decision method and reconstruct correct percentage.During using pre- judgement, in compression
Sampling and support increase pre- decision method module between recovering, and and if only if show the broadband frequency in reception in pre- decision method
Support will be just performed when there is PU signals in section to recover.To maximum band occupancy number KmaxThree kinds of situations of=[4,6] are imitated
Very.In each case, emulate 1000 times, once provide Kmax, then band occupancy number is even number (including 0), and belongs to interval
[0, Kmax], of equal value in simulations will occur.Simulation result is as shown in Figure 6.
In Fig. 6, PcsrCorrect monitoring probability is represented, CEC represents the pre- decision method module of the present invention.Without CEC tables
Show the correct monitoring probability curve without pre- decision method, With CEC indicate that the correct monitoring probability of pre- decision method is bent
Line.As seen from Figure 6, it is general that the correct monitoring probability that the present invention has pre- decision method is higher than the correct monitoring without pre- decision method
Rate, average performance advantage determines by the probability for occurring without PU, and these performance advantages come from pre- decision method can be with
Accurate to judge whether received broadband signal only exists non-openness white noise, this prevents support to recover and prevent in time
The generation of mistake support.So, pre- judgement can improve the probability of support reconstruct with a fairly low calculating cost.
Summary analysis of simulation result, the present invention can be first in not any primary user in Gaussian white noise channel
In the case of testing knowledge, the pre- judgement performance got well in big SNR range with the false-alarm probability of very little.The present invention can compared with
Under the conditions of small false-alarm probability and relatively low signal to noise ratio, more superior perceptual performance is obtained, when there is noise uncertainty,
Perceptual performance is basically unchanged, and illustrates that the present invention can effectively antagonize noise uncertainty.Importantly, pre- decision algorithm is with extremely low
Calculation cost improve support recover probability, make broader frequency spectrum perceive it is more practical.
Claims (4)
1. one kind compression frequency spectrum perception performance improvement method, it is characterised in that methods described includes：
The spacing wireless electric signal received using wide-band modulation converter to antenna is compressed sampling, obtains compressed and multiplexed survey
Measure sample；
Pre- decision method is offseted using branch energy to determine to whether there is primary user's signal in the compression measurement sample；
In response to determining that primary user's signal is not present, then full frequency band is available free frequency range, in response to there is primary user's signal, then
Support is completed using orthogonal matching pursuit algorithm to determine, finds out the frequency range taken by primary user, remaining unappropriated frequency range is
Available free frequency range.
2. compression frequency spectrum perception performance improvement method according to claim 1, it is characterised in that the utilization wide-band modulation
The spacing wireless electric signal that converter is received to antenna is compressed sampling, obtains compressed and multiplexed measurement sample, including：
Sampling is compressed to the spacing wireless electric signal x (t) that antenna is received using wide-band modulation converter, multichannel pressure is obtained
Contracting measurement sample yi(n), i=1,2 ..., m, n=0,1 ..., N-1, wherein, m is compression sampling circuitry number, and N is sample points.
3. compression frequency spectrum perception performance improvement method according to claim 2, it is characterised in that offseted using branch energy
Pre- decision method determines that the compression is measured with the presence or absence of primary user's signal in sample, including：
(a) time domain energy of the compression measurement sample of each branch road is calculated；
(b) test statistics is built using the time domain energy of each branch roadWherein,For the time domain energy of jth branch road
Amount,For the time domain energy of the branch road of jth+1, j=1,2 ..., m, definition
(c) the detection statistic r is calculatedjCumulative distribution function Pf,j：
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Wherein, Pf0=1- (1-Pfa)1/mFor the false-alarm probability of each branch decision, PfaPre- decision method is offseted for branch energy
Default false-alarm probability, Φ-1() is the inverse function of Φ () function；
(e) the test statistics r for obtaining step (b)jThe judging threshold γ obtained with step (d)jCompare, if rj≥γj, then
It is 1 to set judgement matrix element C (j), otherwise C (j)=0, and final court verdict can be expressed as follows：
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>j</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>m</mi>
</munderover>
<mi>C</mi>
<mrow>
<mo>(</mo>
<mi>j</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>0</mn>
<mo>,</mo>
</mrow>
</mtd>
<mtd>
<msub>
<mi>H</mi>
<mn>0</mn>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>j</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>m</mi>
</munderover>
<mi>C</mi>
<mrow>
<mo>(</mo>
<mi>j</mi>
<mo>)</mo>
</mrow>
<mo>&GreaterEqual;</mo>
<mn>1</mn>
<mo>,</mo>
</mrow>
</mtd>
<mtd>
<msub>
<mi>H</mi>
<mn>1</mn>
</msub>
</mtd>
</mtr>
</mtable>
</mfenced>
Wherein, if court verdict is H0, then it represents that primary user's signal is not present in the compression measurement sample, if judgement knot
Fruit is H1, then it represents that there is primary user's signal in the compression measurement sample.
4. compression frequency spectrum perception performance improvement method according to claim 3, it is characterised in that the calculating detection
Statistic rjCumulative distribution function Pf,jIncluding：
(a) in the case of primary user's signal being not present in compression measurement sample, the spacing wireless electric signal x's (t) received
Frequency spectrum X (k) is that average is that 0, variance isDiscrete random variable, using X (k) average and variance, branch road pressure can be calculated
Contracting measurement sample spectra Yi(k) statistical property characteristic, wherein, the statistical property includes average, variance, covariance：
<mrow>
<mi>E</mi>
<mo>&lsqb;</mo>
<msub>
<mi>Y</mi>
<mi>i</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>)</mo>
</mrow>
<mo>&rsqb;</mo>
<mo>=</mo>
<mn>0</mn>
<mo>,</mo>
<mi>D</mi>
<mo>&lsqb;</mo>
<msub>
<mi>Y</mi>
<mi>i</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>)</mo>
</mrow>
<mo>&rsqb;</mo>
<mo>=</mo>
<msubsup>
<mi>N&sigma;</mi>
<mi>&omega;</mi>
<mn>2</mn>
</msubsup>
<mo>,</mo>
</mrow>
Wherein,Expression takes real part,Expression takes imaginary part, cilFor the sequence p of cycle pseudorandom ± 1i(t) in cycle Fu
Leaf-size class number expansion coefficient, k=0,1 ..., N-1；
(b) incite somebody to action | | Yi(k)||2Regard the quadratic sum of two independent Gaussian stochastic variables as, can calculate | | Yi(k)||2Statistical property：
<mrow>
<mi>E</mi>
<mo>&lsqb;</mo>
<mo>|</mo>
<mo>|</mo>
<msub>
<mi>Y</mi>
<mi>i</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>)</mo>
</mrow>
<mo>|</mo>
<msup>
<mo>|</mo>
<mn>2</mn>
</msup>
<mo>&rsqb;</mo>
<mo>=</mo>
<msubsup>
<mi>N&sigma;</mi>
<mi>&omega;</mi>
<mn>2</mn>
</msubsup>
<mo>,</mo>
<mi>D</mi>
<mo>&lsqb;</mo>
<mo>|</mo>
<mo>|</mo>
<msub>
<mi>Y</mi>
<mi>i</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>)</mo>
</mrow>
<mo>|</mo>
<msup>
<mo>|</mo>
<mn>2</mn>
</msup>
<mo>&rsqb;</mo>
<mo>=</mo>
<msup>
<mi>N</mi>
<mn>2</mn>
</msup>
<msubsup>
<mi>&sigma;</mi>
<mi>&omega;</mi>
<mn>4</mn>
</msubsup>
<mo>;</mo>
</mrow>
<mrow>
<mi>cov</mi>
<mo>&lsqb;</mo>
<mo>|</mo>
<mo>|</mo>
<msub>
<mi>Y</mi>
<mi>p</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>)</mo>
</mrow>
<mo>|</mo>
<msup>
<mo>|</mo>
<mn>2</mn>
</msup>
<mo>,</mo>
<mo>|</mo>
<mo>|</mo>
<msub>
<mi>Y</mi>
<mi>q</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>)</mo>
</mrow>
<mo>|</mo>
<msup>
<mo>|</mo>
<mn>2</mn>
</msup>
<mo>&rsqb;</mo>
<mo>=</mo>
<mfrac>
<mrow>
<msubsup>
<mi>&sigma;</mi>
<mi>w</mi>
<mn>4</mn>
</msubsup>
<mrow>
<mo>(</mo>
<msubsup>
<mi>&rho;</mi>
<mn>0</mn>
<mn>2</mn>
</msubsup>
<mo>+</mo>
<msubsup>
<mi>&rho;</mi>
<mn>1</mn>
<mn>2</mn>
</msubsup>
<mo>+</mo>
<msubsup>
<mi>&rho;</mi>
<mn>2</mn>
<mn>2</mn>
</msubsup>
<mo>+</mo>
<msubsup>
<mi>&rho;</mi>
<mn>3</mn>
<mn>2</mn>
</msubsup>
<mo>)</mo>
</mrow>
</mrow>
<mn>2</mn>
</mfrac>
<mo>,</mo>
</mrow>
Wherein, p, q=1,2 ..., m, p ≠ q, k=0,1 ..., N-1,
In formula, cpm、cqmFor the cycle Fourier series expansion coefficient of the sequence of cycle pseudorandom ± 1；
(c) in the case of primary user's signal being not present in compression measurement sample, using principle of conservation of energy, N is worked as>When 20, Ti td
Approximate Gaussian distributed, its average and variance are respectivelyWith WithCoefficient correlation be ρj, it can thus be concluded that
Test statistics rjCumulative distribution function Pf,j：
<mfenced open = "" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<msub>
<mi>P</mi>
<mrow>
<mi>f</mi>
<mo>,</mo>
<mi>j</mi>
</mrow>
</msub>
<mo>=</mo>
<mi>P</mi>
<mrow>
<mo>(</mo>
<mfrac>
<msubsup>
<mi>T</mi>
<mi>j</mi>
<mrow>
<mi>t</mi>
<mi>d</mi>
</mrow>
</msubsup>
<msubsup>
<mi>T</mi>
<mrow>
<mi>j</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
<mrow>
<mi>t</mi>
<mi>d</mi>
</mrow>
</msubsup>
</mfrac>
<mo>&GreaterEqual;</mo>
<msub>
<mi>&gamma;</mi>
<mi>j</mi>
</msub>
<mo>|</mo>
<msub>
<mi>H</mi>
<mn>0</mn>
</msub>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>1</mn>
<mo>-</mo>
<mi>P</mi>
<mrow>
<mo>(</mo>
<mfrac>
<msubsup>
<mi>T</mi>
<mi>j</mi>
<mrow>
<mi>t</mi>
<mi>d</mi>
</mrow>
</msubsup>
<msubsup>
<mi>T</mi>
<mrow>
<mi>j</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
<mrow>
<mi>t</mi>
<mi>d</mi>
</mrow>
</msubsup>
</mfrac>
<mo><</mo>
<msub>
<mi>&gamma;</mi>
<mi>j</mi>
</msub>
<mo>|</mo>
<msub>
<mi>H</mi>
<mn>0</mn>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>=</mo>
<mn>1</mn>
<mo>-</mo>
<mi>&Phi;</mi>
<mrow>
<mo>(</mo>
<mfrac>
<mrow>
<msub>
<mi>&gamma;</mi>
<mi>j</mi>
</msub>
<mi>E</mi>
<mo>&lsqb;</mo>
<msubsup>
<mi>T</mi>
<mrow>
<mi>j</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
<mrow>
<mi>t</mi>
<mi>d</mi>
</mrow>
</msubsup>
<mo>|</mo>
<msub>
<mi>H</mi>
<mn>0</mn>
</msub>
<mo>&rsqb;</mo>
<mo>-</mo>
<mi>E</mi>
<mo>&lsqb;</mo>
<msubsup>
<mi>T</mi>
<mi>j</mi>
<mrow>
<mi>t</mi>
<mi>d</mi>
</mrow>
</msubsup>
<mo>|</mo>
<msub>
<mi>H</mi>
<mn>0</mn>
</msub>
<mo>&rsqb;</mo>
</mrow>
<msqrt>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mi>D</mi>
<mo>&lsqb;</mo>
<msubsup>
<mi>T</mi>
<mi>j</mi>
<mrow>
<mi>t</mi>
<mi>d</mi>
</mrow>
</msubsup>
<mo>|</mo>
<msub>
<mi>H</mi>
<mn>0</mn>
</msub>
<mo>&rsqb;</mo>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>-</mo>
<mn>2</mn>
<msub>
<mi>&gamma;</mi>
<mi>j</mi>
</msub>
<msub>
<mi>&rho;</mi>
<mi>j</mi>
</msub>
<msqrt>
<mrow>
<mi>D</mi>
<mo>&lsqb;</mo>
<msubsup>
<mi>T</mi>
<mi>j</mi>
<mrow>
<mi>t</mi>
<mi>d</mi>
</mrow>
</msubsup>
<mo>|</mo>
<msub>
<mi>H</mi>
<mn>0</mn>
</msub>
<mo>&rsqb;</mo>
<mi>D</mi>
<mo>&lsqb;</mo>
<msubsup>
<mi>T</mi>
<mrow>
<mi>j</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
<mrow>
<mi>t</mi>
<mi>d</mi>
</mrow>
</msubsup>
<mo>|</mo>
<msub>
<mi>H</mi>
<mn>0</mn>
</msub>
<mo>&rsqb;</mo>
</mrow>
</msqrt>
<mo>+</mo>
<msup>
<msub>
<mi>&gamma;</mi>
<mi>j</mi>
</msub>
<mn>2</mn>
</msup>
<msup>
<mrow>
<mo>(</mo>
<mi>D</mi>
<mo>&lsqb;</mo>
<msubsup>
<mi>T</mi>
<mrow>
<mi>j</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
<mrow>
<mi>t</mi>
<mi>d</mi>
</mrow>
</msubsup>
<mo>|</mo>
<msub>
<mi>H</mi>
<mn>0</mn>
</msub>
<mo>&rsqb;</mo>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</msqrt>
</mfrac>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>=</mo>
<mn>1</mn>
<mo>-</mo>
<mi>&Phi;</mi>
<mrow>
<mo>(</mo>
<mfrac>
<mrow>
<msqrt>
<mi>N</mi>
</msqrt>
<msub>
<mi>&gamma;</mi>
<mi>j</mi>
</msub>
<mo>-</mo>
<msqrt>
<mi>N</mi>
</msqrt>
</mrow>
<msqrt>
<mrow>
<mn>1</mn>
<mo>-</mo>
<mn>2</mn>
<msub>
<mi>&gamma;</mi>
<mi>j</mi>
</msub>
<msub>
<mi>&rho;</mi>
<mi>j</mi>
</msub>
<mo>+</mo>
<msup>
<msub>
<mi>&gamma;</mi>
<mi>j</mi>
</msub>
<mn>2</mn>
</msup>
</mrow>
</msqrt>
</mfrac>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
Wherein, γjFor decision threshold, H0Represent the non-existent situation of primary user's signal, ρjIt isWithCoefficient correlation, take
It is worth and isΦ () function expression is
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