CN107342787B - A kind of improved ultra-wideband frequency displacement Gaussian waveform pulse design method - Google Patents
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Abstract
Pulse Waveform Design for UWB Communication field of the present invention specifically discloses a kind of improved ultra-wideband frequency displacement Gaussian waveform pulse design method, 0~12GHz UWB spectrum is first divided into 4~6 sub-bands, determines centre frequency to each sub-band；Select a kind of Gaussian function as main pulse function；Main pulse function is multiplied to obtain several multipliers from the sinusoidal carrier with different sub-band centre frequencies respectively, being added after the optimal weighting coefficients that each multiplier makes ultra-wideband pulse power spectrum utilization rate optimal multiplied by one, obtains ultra-wideband pulse.When present invention ultra-short pulse generated is punched in applied to the Emission Mask as defined in Federal Communications Commission (FCC), power spectrum utilization rate is high, long transmission distance.
Description
Technical field
The invention belongs to Pulse Waveform Design for UWB Communication fields, are related to a kind of improved ultra-wideband frequency displacement Gaussian waveform pulse
Design method.
Background technique
Ultra wide band (Ultra-Wideband, UWB) wireless communication system using nanosecond ultrashort pulse as information carrier,
The digital information to be sent is carried by modulating to burst pulse.The technology is with message capacity is big, transmission power is low, anti-multipath
The advantages that interference performance is strong, structure is simple and good confidentiality.Currently, only available Emission Mask mark in UWB radio communication
Standard be by Federal Communications Commission (Federal Communication Commission, FCC) formulate [FCC,
2002].For indoor UWB system, masking limitation is the -10dB bandwidth being directed within the scope of 3.1~10.6GHz, and to outer spoke
Penetrating masking also has stringent limitation.Requirement according to FCC to radiation template, UWB pulse must occupy very wide frequency spectrum, to avoid to width
The interference of other interior communications facilitys of band, good burst pulse design are even more important.
Nowadays, the research method of ultra-wideband pulse can be divided into two classes: one kind is the design method from time domain to frequency domain,
The masking spectrum whether its frequency spectrum meets FCC is analyzed according to the time-domain expression of pulse, revises pulse according to its constraint condition
Parameter；Another kind of is to acquire pulse in turn in time domain in the constraint condition of frequency domain according to masking spectrum from frequency domain to time domain
Expression formula, the design philosophy of various filters belongs to this kind of methods.
Meet the superwide band pulse wave of FCC standard in order to obtain, domestic and international many scholars to the design of impulse waveform with
Optimization is studied.Win and Scholtz is proposed using the second dervative of Gaussian function as the impulse wave of pulsed radio system
Shape, it overcomes the disadvantage that Gaussian pulse contains DC component and radiation efficiency is not high；Hermite is used in Ghavami et al. proposition
Polynomial function reduces multiuser interference as ultra-wideband pulse, using the orthogonality of different rank multinomials；Sheng et al. is mentioned
A kind of selection best differential order of Gaussian pulse and the best formation factor are gone out and have been allowed to approach the algorithm of Emission Mask, but has used
Single pulse is difficult efficiently to approach masking standard；At the same time, Parr is by passing through Eigenvalues Decomposition number from frequency domain
The method of filter has acquired two pulses, i.e. Parr pulse, and the pulse energy of this method design is largely focused on 3.1~
Within the scope of 10.6GHz, better conforms to spectrum requirement and there is flexibility, the different corresponding different bandpass filterings of frequency spectrum limitation
Device；Zhang Honggang et al. proposes that the pulse for using approximate prolate spheroidal wave functions (PSWF) as DS~UWB, the pulse have orthogonal complete
For property and flexible spectrum control may be implemented；Rui Chen proposes to carry out linear combination using Rayleigh pulse and its all-order derivative
Method generate pulse；White intelligence congruence people proposes to use frequency displacement Gaussian waveform (spectrum shifted Gaussian
Waveforms, SSGW) method, ensure that the waveform of time domain impulse meets FCC spectrum masking from frequency domain, this method has
Significant flexibility, and be widely used；Zhendong Yin et al. proposes a kind of new wavelength-division multiplex super broad band radio communication system
System pulse waveform design, correlation and the bit error rate (BER) performance significantly improve, close to single user system.
When the ultra-wideband pulse that current design method obtains is applied to the masking spectrum of FCC, power spectral density utilization rate
Low, transmission range is short.
Summary of the invention
It is an object of the invention to overcome the above-mentioned prior art, a kind of improved ultra-wideband frequency displacement high bass wave is provided
Shape pulse design method.
The purpose of the present invention is by the following technical programs to solve:
This improved ultra-wideband frequency displacement Gaussian waveform pulse design method, which comprises the following steps:
1) 0~12GHz UWB spectrum is divided into 4~6 sub-bands by, determines centre frequency to each sub-band；Selection one
Kind Gaussian function is as main pulse function；
2) main pulse function is multiplied to obtain several from the sinusoidal carrier with different sub-band centre frequencies by respectively multiplies
Formula is obtained being added after the optimal weighting coefficients that each multiplier makes ultra-wideband pulse power spectrum utilization rate optimal multiplied by one
Ultra-wideband pulse, the time-domain expression of the ultra-wideband pulse are as follows:
X (t)=p (t) { A1cos(2πfc1t)+A2cos(2πfc2t)+…+Ancos(2πfcjt)}
Wherein p (t) is main pulse function；A=[A1,A1,…,An] it is weighting coefficient, the corresponding coefficient of each sub-band
An；F=[fc1,fc1,…fcj] it is modulated sinusoidal carrier sub-band centre frequency；T is the time.
Further, 0~12GHz UWB spectrum is divided into 5 sub-bands, is respectively as follows: 0-0.96GHz, 0.96-
1.61GHz, 1.61-3.1GHz, 3.1-10.6GHz, 10.6-12GHz.
Further, the main pulse function is
Further, the determination method of the sub-band centre frequency is, if Fmax—Fmin< 2GHz, then center frequency
The quantity of rate is one, and FCenter=(Fmax+Fmin)/2；If Fmax—Fmin> 2GHz, then the quantity of centre frequency is greater than one
A, first value is FCenter=(Fmax+Fmin)/2；Other values are (Fmax+Fmin)/2+Z or (Fmax+FminThe Z of)/2-, and
(Fmax+Fmin)/2+Z and (Fmax+FminThe obtained frequency of the Z of)/2-all must be within the scope of the sub-band belonging to it；
Wherein FmaxFor a sub-band maximum frequency；FminFor a sub-band minimum frequency；FCenterFor sub-band center
Frequently；Z is positive integer, and 1≤Z≤12.
Further, the optimal weighting coefficient is obtained by RS algorithm, specific steps are as follows:
5.1) one group of weighting coefficient is generated with random function, is denoted as A；
5.2) examine whether the power spectral density of ultra-wideband pulse X (t) meets FCC spectrum limitation；
5.3) if conditions are not met, return step 5.1)；If it is satisfied, enabling S=A；
5.4) one group of new weighting coefficient A is reselected, examines whether the spectral density of new ultra-wideband pulse meets ratio
Weighting coefficient is the spectral density of the ultra-wideband pulse of S closer to spectral mask, if it is satisfied, enabling S=A；
5.5) if conditions are not met, judging whether the power spectral density of ultra-wideband pulse X (t) is optimal condition, if reached
To optimal conditions, then S is optimal weighting coefficients required by one group, if not being optimal condition, return step 5.4).
Further, the optimal weighting coefficient is obtained by LSE algorithm, specific steps are as follows:
6.1) one group of weighting coefficient is generated with random function, is denoted as A；
6.2) several groups weighting coefficient A is generated, objective function is substituted into:
The minimum dispersion degree e between composite pulse spectral density and FCC Emission Mask is found out, wherein m (t) is that FCC is formulated
Indoor UWB spectrum mask specification be converted to voltage masking, m (t) acquisition process be will by normalized radiation of power masking with
Free space impedance is divided by, its square root is taken, and is then carried out inverse Fourier transform and is obtained；P (t) is main pulse function,A=[A1,A1,…,An] it is weighting coefficient, the corresponding coefficient A of each sub-bandn；F=[fc1,
fc1,…fcj] it is modulated sinusoidal carrier sub-band centre frequency, fcjFor in j-th of sub-band within the scope of 0~12GHz UWB spectrum
Frequency of heart；
6.3) this group of weighting coefficient A when obtaining minimum dispersion degree e is denoted as S, S is optimal weighting coefficients at this time.
The present invention have it is following the utility model has the advantages that
0~12GHz UWB spectrum is divided into sub-band by the present invention, then determines centre frequency to each sub-band；Selection
A kind of Gaussian function is as main pulse function, with Gaussian pulse basic function multiplied by the sinusoidal carrier of a centre frequency multiplied by one
A weighting coefficient, then all multipliers are added to obtain the time-domain expression of ultra-wideband pulse function of the invention, the expression formula
When being applied to FCC spectrum masking, power spectrum utilization rate is high, long transmission distance for corresponding pulse.
Further, 0~12GHz UWB spectrum is divided into 5 sub-bands by the present invention, is respectively as follows: 0-0.96GHz,
0.96-1.61GHz, 1.61-3.1GHz, 3.1-10.6GHz, 10.6-12GHz；Such division mode meets FCC spectrum mask
Feature, so that the ultra-wideband pulse availability of frequency spectrum finally obtained is higher.
Further, main pulse is selected asThe corresponding pulse signal of this function can be answered preferably
For FCC spectrum mask.
Further, forThis basic function, corresponding optimal centre frequency spacing division mode and
The centre frequency of generation substitutes into ultra-wideband pulse and is able to generate optimal ultra-wideband pulse.
Further, optimal weighting coefficient is obtained by RS algorithm, so that selecting optimal weighting coefficient operation into super
The time-domain expression of wideband pulse, so that the availability of frequency spectrum of ultra-wideband pulse is more preferable.
Further, optimal weighting coefficient is obtained by LSE algorithm, so that selecting optimal weighting coefficient operation into super
The time-domain expression of wideband pulse, so that the availability of frequency spectrum of ultra-wideband pulse is more preferable.
Detailed description of the invention
Fig. 1 is that the present invention surpasses using produced by RS algorithm acquirement weighting coefficient optimal solution substitution wideband pulse time-domain expression
Wideband pulse time domain waveform；
Fig. 2 brings ultra-wideband pulse time-domain expression into using LSE algorithm acquirement weighting coefficient optimal solution by the present invention and is produced
Raw ultra-wideband pulse time domain waveform；
Fig. 3 is that the present invention uses RS and LSE algorithm acquirement weighting coefficient optimal solution to bring ultra-wideband pulse time-domain expression into
Figure compared with produced ultra-wideband pulse generates pulse power spectrum density with Gauss derived function combined method；
Fig. 4 is that the present invention uses RS and LSE algorithm acquirement weighting coefficient optimal solution to bring ultra-wideband pulse time-domain expression into
Produced ultra-wideband pulse improves frequency displacement Gaussian waveform method system link performance and Gauss derived function combined method, frequency displacement Gauss
Waveform display method compares figure；
Fig. 5 is the embodiment that ultra-wideband pulse of the present invention generates.
Wherein: RS-SSGW brings ultra-wideband pulse time-domain expression institute into obtain weighting coefficient optimal solution using RS algorithm
Generate ultra-wideband pulse；LSE-SSGW obtains weighting coefficient optimal solution for LSE algorithm and brings ultra-wideband pulse time-domain expression institute into
Generate ultra-wideband pulse；RS-Gaussian is the ultra-wideband pulse generated using RS algorithm Gauss derived function combined method；LSE-
Gaussian is the ultra-wideband pulse generated using LSE algorithm Gauss derived function combined method；SSGW is frequency displacement Gaussian waveform side
The ultra-wideband pulse that method generates.
Specific embodiment
The invention will be described in further detail with reference to the accompanying drawing:
Referring to Fig. 1-5, improved ultra-wideband frequency displacement Gaussian waveform pulse design method of the present invention, comprising the following steps:
1) 0~12GHz UWB spectrum is divided into 4~6 sub-bands, centre frequency is determined to each sub-band；Selection one
Kind Gaussian function is as main pulse function；
2) main pulse function is multiplied to obtain several from the sinusoidal carrier with different sub-band centre frequencies respectively and is multiplied
Formula is obtained being added after the optimal weighting coefficients that each multiplier makes ultra-wideband pulse power spectrum utilization rate optimal multiplied by one
Ultra-wideband pulse, the time-domain expression of the ultra-wideband pulse are as follows:
X (t)=p (t) { A1 cos(2πfc1t)+A2 cos(2πfc2t)+…+An cos(2πfcj t)}
Wherein p (t) is main pulse function；A=[A1,A1,…,An] it is weighting coefficient, the corresponding coefficient of each sub-band
An；F=[fc1,fc1,…fcj] it is modulated sinusoidal carrier sub-band centre frequency, fcjIndicate j-th of sub-band centre frequency；T is
Time.
0~12GHz UWB spectrum is divided into 5 sub-bands, is respectively as follows: 0-0.96GHz, 0.96-1.61GHz, 1.61-
3.1GHz, 3.1-10.6GHz, 10.6-12GHz.
The main pulse function is
The determination method of the sub-band centre frequency is, if Fmax—Fmin< 2GHz, then the quantity of centre frequency
It is one, and FCenter=(Fmax+Fmin)/2；If Fmax—Fmin> 2GHz, then the quantity of centre frequency is greater than one, first
A value is FCenter=(Fmax+Fmin)/2；Other values are (Fmax+Fmin)/2+Z or (Fmax+FminThe Z of)/2-, and (Fmax+Fmin)/
2+Z and (Fmax+FminThe obtained frequency of the Z of)/2-all must be within the scope of the sub-band belonging to it；
Wherein FmaxFor a sub-band maximum frequency；FminFor a sub-band minimum frequency；FCenterFor sub-band center
Frequently；Z is positive integer, and 1≤Z≤12.
It is for main pulse functionGaussian pulse, the spacing of adjacent center frequencies is 1GHz high
The power spectral density of this pulse is summed, and general power spectrum is maintained at a steady state value.Since UWB whole bandwidth is divided into 5
Sub-band, the frequency of sub-band are 0-0.96GHz, 0.96-1.61GHz, 1.61-3.1GHz, 3.1-10.6GHz, 10.6-
12GHz only need to be by simply taking middle-value calculating that each center frequency points, respectively f can be obtained for 1,2,3,5 partsc1=
0.48GHz, fc2=1.28GHz, fc3=2.35GHz, fc11=11.3GHz；And the 4th part, then its center frequency should be found first
Rate point fc4=6.85GHz (i.e. fc4=(3.1+10.6)/2), then being put using this as center 1GHz is spacing in 3.1-10.6GHz
It is interior to extend to both ends, obtain each center frequency points are as follows: fc5=5.85GHz, fc6=7.85GHz, fc7=4.85GHz, fc8=
8.85GHz fc9=3.85GHz, fc10=9.85GHz.
The optimal weighting coefficient is obtained by RS algorithm, and the RS algorithm is stochastic selection algorithm, specific steps are as follows:
5.1) one group of weighting coefficient is generated with random function, is denoted as A；
5.2) examine whether the power spectral density of ultra-wideband pulse X (t) meets FCC spectrum limitation；
5.3) if conditions are not met, return step 5.1)；If it is satisfied, enabling S=A；
5.4) one group of new weighting coefficient A is reselected, examines whether the spectral density of new ultra-wideband pulse meets ratio
Weighting coefficient is the spectral density of the ultra-wideband pulse of S closer to spectral mask, if it is satisfied, enabling S=A；
5.5) if conditions are not met, judging whether the power spectral density of ultra-wideband pulse X (t) is optimal condition, if reached
To optimal conditions, then S is optimal weighting coefficients required by one group, if not being optimal condition, return step 5.4).
The optimal conditions of the RS algorithm refers to when the quantity for choosing A is enough, that is, the number of iterations of A is sufficiently large
When, a convergent state as a result can be presented, it is higher more optimal than convergence numerical requirements according to the selection of practical convergent one
Condition value, this completes the selected of convergence numerical value.
And the setting of optimal conditions value determines the runing time of program and the accuracy of result in RS algorithm, with one kind
Simplified form replaces optimal conditions value, and a number of iterations is arranged, and the number of iterations is number between 100~200.
The optimal weighting coefficient is obtained by LSE algorithm, and the LSE algorithm is Least Square Error calculation
Method, specific steps are as follows:
6.1) one group of weighting coefficient is generated with random function, is denoted as A；
6.2) several groups weighting coefficient A is generated, objective function is substituted into:
The minimum dispersion degree e between composite pulse spectral density and FCC Emission Mask is found out, wherein m (t) is that FCC is formulated
Indoor UWB spectrum mask specification be converted to voltage masking, m (t) acquisition process be will by normalized radiation of power masking with
Free space impedance is divided by, its square root is taken, and is then carried out inverse Fourier transform and is obtained；P (t) is main pulse function, A=[A1,A1,…,An] it is weighting coefficient, the corresponding coefficient An of each sub-band；F=[fc1,
fc1,…fcj] it is modulated sinusoidal carrier sub-band centre frequency, fcjFor in j-th of sub-band within the scope of 0~12GHz UWB spectrum
Frequency of heart；
6.3) this group of weighting coefficient A when obtaining minimum dispersion degree e is denoted as S, S is optimal weighting coefficients at this time.
The deformation that optimal decentralized degree e this formula is lsqlin function is sought, lsqlin function inherently solves target
Functional minimum value, so lsqlin function finds out optimal decentralized degree；
Prior art Gaussian pulse seeks weighting coefficient adjustment process and calculates complexity, and error is excessive, will lead to when serious
Ultra-wideband pulse out is not able to satisfy the masking spectrum requirement of FCC.
5 subdivided centre frequencies of sub-band, the time domain expression of ultra-wideband pulse will be divided to 0~12GHz UWB spectrum
Formula can specifically describe are as follows:
As seen from Figure 3, when the present invention brings ultra-wideband pulse into using RS and LSE algorithm acquirement weighting coefficient optimal solution
Ultra-wideband pulse RS-SSGW and LSE-SSGW produced by the expression formula of domain generates pulse RS- than Gauss derived function combined method
Gaussian and LSE-Gaussian, power spectral density utilization rate is higher, is more in line with FCC spectrum mask, wherein in frequency height
When 4GHz, the power spectral density that the present invention generates pulse is more nearly mask specification, has the higher availability of frequency spectrum.
As seen from Figure 4, when the present invention brings ultra-wideband pulse into using RS and LSE algorithm acquirement weighting coefficient optimal solution
Ultra-wideband pulse RS-SSGW and LSE-SSGW produced by the expression formula of domain is improving frequency displacement Gaussian waveform method system link performance
On, than produced by the RS-Gaussian and LSE-Gaussian of Gauss derived function combined method, frequency displacement Gaussian waveform method SSGW
Ultra-wideband pulse improvement frequency displacement Gaussian waveform method system link performance is strong, and effect of the invention is more excellent.Especially when transmission number
When being 40Mb/s according to rate, weighting coefficient optimal solution is obtained using RS of the present invention and LSE algorithm and brings ultra-wideband pulse time domain into
Pulse produced by expression formula is compared with the Gauss derived function combined method for equally using above two algorithm, in terms of transmission range
About 8 meters and 6 meters are increased separately, the effect of acquirement is more preferable.
Claims (6)
1. a kind of improved ultra-wideband frequency displacement Gaussian waveform pulse design method, which comprises the following steps:
1) 0~12GHz UWB spectrum is divided into 4~6 sub-bands by, determines centre frequency to each sub-band；It selects a kind of high
This function is as main pulse function；
2) main pulse function is multiplied to obtain several multipliers by from the sinusoidal carrier with different sub-band centre frequencies respectively,
Being added after the optimal weighting coefficients that each multiplier makes ultra-wideband pulse power spectrum utilization rate optimal multiplied by one, ultra-wide is obtained
Tape pulse, the time-domain expression of the ultra-wideband pulse are as follows:
X (t)=p (t) { A1cos(2πfc1t)+A2cos(2πfc2t)+…+Ancos(2πfcjt)}
Wherein p (t) is main pulse function；A=[A1,A1,…,An] it is weighting coefficient, the corresponding coefficient A of each sub-bandn；F
=[fc1,fc2,…fcj] it is modulated sinusoidal carrier sub-band centre frequency；fcjFor j-th of son within the scope of 0~12GHz UWB spectrum
Mid-band frequency, t are the time.
2. improved ultra-wideband frequency displacement Gaussian waveform pulse design method according to claim 1, which is characterized in that by 0
~12GHz UWB spectrum is divided into 5 sub-bands, is respectively as follows: 0-0.96GHz, 0.96-1.61GHz, 1.61-3.1GHz, 3.1-
10.6GHz 10.6-12GHz.
3. improved ultra-wideband frequency displacement Gaussian waveform pulse design method according to claim 1, which is characterized in that described
Main pulse function is
4. improved ultra-wideband frequency displacement Gaussian waveform pulse design method according to claim 3, which is characterized in that described
The determination method of sub-band centre frequency is, if Fmax—Fmin< 2GHz, then the quantity of centre frequency is one, and FCenter
=(Fmax+Fmin)/2；If Fmax—Fmin> 2GHz, then the quantity of centre frequency is greater than one, first value is FCenter=
(Fmax+Fmin)/2；Other values are (Fmax+Fmin)/2+Z or (Fmax+FminThe Z of)/2-, and (Fmax+Fmin)/2+Z or (Fmax+
FminThe obtained frequency of Z of)/2-is all in (Fmax+Fmin)/2+Z or (Fmax+FminWithin the scope of sub-band belonging to the Z of)/2-；
Wherein FmaxFor a sub-band maximum frequency；FminFor a sub-band minimum frequency；FCenterFor sub-band centre frequency；Z
For positive integer, and 1≤Z≤12.
5. improved ultra-wideband frequency displacement Gaussian waveform pulse design method according to claim 1, which is characterized in that described
Optimal weighting coefficients are obtained by RS algorithm, specific steps are as follows:
5.1) one group of weighting coefficient is generated with random function, is denoted as A；
5.2) examine whether the power spectral density of ultra-wideband pulse X (t) meets FCC spectrum limitation；
5.3) if conditions are not met, return step 5.1)；If it is satisfied, enabling S=A；
5.4) one group of new weighting coefficient A is reselected, examines whether the spectral density of new ultra-wideband pulse meets than weighting
Coefficient is the spectral density of the ultra-wideband pulse of S closer to spectral mask, if it is satisfied, enabling S=A；
5.5) if conditions are not met, judging whether the power spectral density of ultra-wideband pulse X (t) is optimal condition, if reached most
Excellent condition, then S is optimal weighting coefficients required by one group, if not being optimal condition, return step 5.4).
6. improved ultra-wideband frequency displacement Gaussian waveform pulse design method according to claim 1, which is characterized in that described
Optimal weighting coefficients are obtained by LSE algorithm, specific steps are as follows:
6.1) one group of weighting coefficient is generated with random function, is denoted as A；
6.2) several groups weighting coefficient A is generated, objective function is substituted into:
The minimum dispersion degree e between composite pulse spectral density and FCC Emission Mask is found out, wherein m (t) is that FCC formulates interior
UWB spectrum mask specification be converted to voltage masking, m (t) acquisition process be will by normalized radiation of power masking with freely
Space impedance is divided by, and takes its square root, then carries out inverse Fourier transform and obtains；P (t) is main pulse function, A=[A1,
A1,…,An] it is weighting coefficient, the corresponding coefficient A of each sub-bandn；F=[fc1,fc2,…fcj] it is modulated sinusoidal carrier
Mid-band frequency；
6.3) this group of weighting coefficient A when obtaining minimum dispersion degree e is denoted as S, S is optimal weighting coefficients at this time.
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