CN109246044A - Frequency deviation estimating method and system for 32 ary quadrature amplitude-modulated signals - Google Patents
Frequency deviation estimating method and system for 32 ary quadrature amplitude-modulated signals Download PDFInfo
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- CN109246044A CN109246044A CN201811255107.5A CN201811255107A CN109246044A CN 109246044 A CN109246044 A CN 109246044A CN 201811255107 A CN201811255107 A CN 201811255107A CN 109246044 A CN109246044 A CN 109246044A
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L27/00—Modulated-carrier systems
- H04L27/26—Systems using multi-frequency codes
- H04L27/2601—Multicarrier modulation systems
- H04L27/2647—Arrangements specific to the receiver only
- H04L27/2655—Synchronisation arrangements
- H04L27/2657—Carrier synchronisation
- H04L27/2659—Coarse or integer frequency offset determination and synchronisation
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L27/00—Modulated-carrier systems
- H04L27/26—Systems using multi-frequency codes
- H04L27/2601—Multicarrier modulation systems
- H04L27/2647—Arrangements specific to the receiver only
- H04L27/2655—Synchronisation arrangements
- H04L27/2657—Carrier synchronisation
- H04L27/266—Fine or fractional frequency offset determination and synchronisation
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L27/00—Modulated-carrier systems
- H04L27/26—Systems using multi-frequency codes
- H04L27/2601—Multicarrier modulation systems
- H04L27/2647—Arrangements specific to the receiver only
- H04L27/2655—Synchronisation arrangements
- H04L27/2668—Details of algorithms
- H04L27/2669—Details of algorithms characterised by the domain of operation
- H04L27/2672—Frequency domain
Abstract
The present invention discloses a kind of frequency deviation estimating method and system for 32 ary quadrature amplitude-modulated signals.Frequency deviation estimating method provided by the invention and system, first by the 32 ary quadrature amplitude-modulated signal sequences received II class signal sequence and IV class signal sequence rotate in the same direction after formed rotating modulation signals sequence, then using making the maximum each amplification coefficient of peak-to-average power ratio amplify processing to rotating modulation signals sequence, amplification modulated signal sequences are obtained；Fast Fourier Transform (FFT) is carried out to the bipyramid of amplification modulated signal sequences on this basis, the corresponding frequency of peak value so as to obtain spectrum amplitude；The offset estimation value of 32 ary quadrature amplitude-modulated signal sequences is finally determined according to the corresponding frequency of the peak value of spectrum amplitude.Frequency deviation estimating method provided by the invention and system, frequency offset estimation accuracy is high, and snr threshold performance is good, practical, has a good application prospect.
Description
Technical field
The present invention relates to coherent optical communication system fields, are used for 32 ary quadrature amplitude-modulated signals more particularly to one kind
Frequency deviation estimating method and system.
Background technique
It is high that 32 ary quadrature amplitude modulation (32-QAM) coherent optical communication systems very likely become further generation data rate
Up to the optical communication system of 400Gb/s to 1Tb/s.This is primarily due to the system than quadrature phase shift keying (Quadrature before this
Phase Shift Keying, QPSK) and 16-QAM modulation format under Transmission system have higher spectrum efficiency and channel
Capacity.In digital coherent receiver, needed before carrier phase recovery using frequency deviation (FO) estimation method to transmission laser
Frequency deviation between device and local oscillator laser is estimated and is compensated.
Because of the particularity of 32-QAM system constellation figure, cause high performance frequency deviation estimating method few.It is traditional based on fast
The frequency deviation estimating method (FFT-FOE) of fast Fourier transformation (FFT) can not successfully be used at small data length (such as several hundred)
In the offset estimation of 32-QAM system.To find out its cause, still because the planisphere of 32-QAM is different from 16-QAM and 64-QAM, not
Stringent distributed rectangular causes spectrum peak in low signal-to-noise ratio region to be seriously impaired.
Summary of the invention
The object of the present invention is to provide a kind of frequency deviation estimating method and system for 32 ary quadrature amplitude-modulated signals,
Frequency offset estimation accuracy is high, and snr threshold performance is good.
To achieve the above object, the present invention provides following schemes:
A kind of frequency deviation estimating method for 32 ary quadrature amplitude-modulated signals, the frequency deviation estimating method include:
Obtain the 32 ary quadrature amplitude-modulated signal sequences received, wherein the 32 ary quadrature amplitude modulation letter
Number sequence includes: I class signal sequence, II class signal sequence, Group III signal sequence, IV class signal sequence and V class signal sequence；
The II class signal sequence and the IV class signal sequence are rotated in the same direction into π/4, obtain postrotational II
Class signal sequence and postrotational IV class signal sequence；
Determine rotating modulation signals sequence, the rotating modulation signals sequence be according to the I class signal sequence, rotation after
The II class signal sequence, the Group III signal sequence, the postrotational IV class signal sequence and the V class signal sequence
Arrange determining quadrature amplitude modulation signal sequence；
Acquisition makes the corresponding amplification coefficient of the maximum various types of signal sequence of peak-to-average power ratio, and is according to each amplification
It is several that processing is amplified to the rotating modulation signals sequence, obtain amplification modulated signal sequences；
Fast Fourier Transform (FFT) is carried out to the bipyramid of the amplification modulated signal sequences, obtains discrete spectrum；
The corresponding frequency of peak value of spectrum amplitude is determined according to the discrete spectrum；
The offset estimation value of the 32 ary quadrature amplitude-modulated signal sequence is determined according to the frequency.
Optionally, make the determination method packet of the corresponding amplification coefficient of the maximum various types of signal sequence of peak-to-average power ratio
It includes:
Obtain the peak-to-average power ratio calculation formula of the amplification modulated signal:Wherein,Indicate that peak is equal
Power ratio,Indicate the peak power of the frequency spectrum of I class signal sequence,Indicate the frequency spectrum of postrotational II class signal sequence
Peak power,Indicate the peak power of the frequency spectrum of Group III signal sequence,Indicate the frequency of postrotational IV class signal sequence
The peak power of spectrum,Indicate the peak power of the frequency spectrum of V class signal sequence, k1Indicate the amplification coefficient of I class signal sequence, k2
Indicate the amplification coefficient of postrotational II class signal sequence, k3Indicate the amplification coefficient of Group III signal sequence, k4After indicating rotation
IV class signal sequence amplification coefficient, k5Indicate the amplification coefficient of V class signal sequence,Indicate the frequency spectrum of I class signal sequence
Mean power,Indicate the mean power of the frequency spectrum of postrotational II class signal sequence,Indicate Group III signal sequence
The mean power of frequency spectrum,Indicate the mean power of the frequency spectrum of postrotational IV class signal sequence,Indicate V class signal sequence
Frequency spectrum mean power.
So that the peak-to-average power ratio calculation formula is equal to zero to the local derviation of each amplification coefficient respectively, obtains each described put
The scale relation of big coefficient:
Each amplification coefficient is determined according to the peak power of various types of signal sequence, mean power and the scale relation.
Optionally, the offset estimation that the 32 ary quadrature amplitude-modulated signal sequence is determined according to the frequency
Value, specifically includes:
According to formula:Determine the 32 ary quadrature amplitude-modulated signal
The offset estimation value of sequence, whereinIndicating offset estimation value, L indicates the length of 32 ary quadrature amplitude-modulated signal sequences,Indicate the nth elements in amplification modulated signal sequences, n indicates the serial number of amplification modulated signal sequences, and f indicates Fourier's frequency
The frequency of spectrum, T indicate the period of 32 ary quadrature amplitude-modulated signals.
Optionally, described that the II class signal sequence and the IV class signal sequence are rotated in the same direction into π/4, it obtains
Postrotational II class signal sequence and postrotational IV class signal sequence, specifically include:
The II class signal sequence is rotated counterclockwise into π/4, obtains postrotational II class signal sequence；
The IV class signal sequence is rotated counterclockwise into π/4, obtains postrotational IV class signal sequence.
A kind of frequency deviation estimation system for 32 ary quadrature amplitude-modulated signals, the frequency deviation estimation system include:
Signal sequence obtains module, for obtaining the 32 ary quadrature amplitude-modulated signal sequences received, wherein described
32 ary quadrature amplitude-modulated signal sequences include: I class signal sequence, II class signal sequence, Group III signal sequence, IV class letter
Number sequence and V class signal sequence；
Rotation processing module, for by the II class signal sequence and the IV class signal sequence rotate in the same direction π/
4, obtain postrotational II class signal sequence and postrotational IV class signal sequence；
Rotating modulation signals determining module, for determining that rotating modulation signals sequence, the rotating modulation signals sequence be
According to the I class signal sequence, the postrotational II class signal sequence, the Group III signal sequence, the postrotational IV
The quadrature amplitude modulation signal sequence that class signal sequence and the V class signal sequence determine；
Enhanced processing module makes the corresponding amplification coefficient of the maximum various types of signal sequence of peak-to-average power ratio for obtaining, and
Processing is amplified to the rotating modulation signals sequence according to each amplification coefficient, obtains amplification modulated signal sequences；
Fourier transformation module carries out Fast Fourier Transform (FFT) for the bipyramid to the amplification modulated signal sequences,
Obtain discrete spectrum；
Frequency determining module, the corresponding frequency of peak value for determining spectrum amplitude according to the discrete spectrum；
Offset estimation value determining module, for determining the 32 ary quadrature amplitude-modulated signal sequence according to the frequency
Offset estimation value.
Optionally, the frequency deviation estimation system further includes amplification coefficient determining module, and the amplification coefficient determining module is used
Make the corresponding amplification coefficient of the maximum various types of signal sequence of peak-to-average power ratio, the amplification coefficient determining module packet in determination
It includes:
Peak-to-average power ratio acquiring unit obtains the peak-to-average power ratio calculation formula of the amplification modulated signal:Wherein,Indicate the equal function in peak
Rate ratio,Indicate the peak power of the frequency spectrum of I class signal sequence,Indicate the peak of the frequency spectrum of postrotational II class signal sequence
It is worth power,Indicate the peak power of the frequency spectrum of Group III signal sequence,Indicate the frequency spectrum of postrotational IV class signal sequence
Peak power,Indicate the peak power of the frequency spectrum of V class signal sequence, k1Indicate the amplification coefficient of I class signal sequence, k2Table
Show the amplification coefficient of postrotational II class signal sequence, k3Indicate the amplification coefficient of Group III signal sequence, k4Indicate postrotational
The amplification coefficient of IV class signal sequence, k5Indicate the amplification coefficient of V class signal sequence,Indicate the frequency spectrum of I class signal sequence
Mean power,Indicate the mean power of the frequency spectrum of postrotational II class signal sequence,Indicate the frequency of Group III signal sequence
The mean power of spectrum,Indicate the mean power of the frequency spectrum of postrotational IV class signal sequence,Indicate V class signal sequence
Frequency spectrum mean power；
Coefficient scale relation determination unit, for making the peak-to-average power ratio calculation formula respectively to each amplification coefficient
Local derviation be equal to zero, obtain the scale relation of each amplification coefficient:
Amplification coefficient determination unit, for being closed according to the peak power of various types of signal sequence, mean power and the ratio
It is that formula determines each amplification coefficient.
Optionally, the offset estimation value determining module is according to formula:
Determine the offset estimation value of the 32 ary quadrature amplitude-modulated signal sequence, whereinIndicate offset estimation value, L indicates 32
The length of ary quadrature amplitude-modulated signal sequence,Indicate the nth elements in amplification modulated signal sequences, n indicates amplification
The serial number of modulated signal sequences, f indicate the frequency of Fourier spectrum, and T indicates the period of 32 ary quadrature amplitude-modulated signals.
Optionally, the rotation processing module includes:
II class is counterclockwise rotary unit, for the II class signal sequence to be rotated counterclockwise π/4, after being rotated
II class signal sequence；
IV class is counterclockwise rotary unit, for the IV class signal sequence to be rotated counterclockwise π/4, after being rotated
IV class signal sequence.
The specific embodiment provided according to the present invention, the invention discloses following technical effects:
Provided by the present invention for the frequency deviation estimating method and system of 32 ary quadrature amplitude-modulated signals, will receive first
To 32 ary quadrature amplitude-modulated signal sequences in II class signal sequence and IV class signal sequence rotate in the same direction π/4
Rotating modulation signals sequence is formed afterwards, and then using makes the maximum each amplification coefficient of peak-to-average power ratio to rotating modulation signals sequence
Column amplify processing, obtain amplification modulated signal sequences；The bipyramid of amplification modulated signal sequences is carried out on this basis
Fast Fourier Transform (FFT), the corresponding frequency of peak value so as to obtain spectrum amplitude；Finally according to the peak value pair of spectrum amplitude
The frequency answered determines the offset estimation value of 32 ary quadrature amplitude-modulated signal sequences.Frequency deviation estimating method provided by the invention and
System, frequency offset estimation accuracy is high, and snr threshold performance is good, practical, has a good application prospect.
Detailed description of the invention
It in order to more clearly explain the embodiment of the invention or the technical proposal in the existing technology, below will be to institute in embodiment
Attached drawing to be used is needed to be briefly described, it should be apparent that, the accompanying drawings in the following description is only some implementations of the invention
Example, for those of ordinary skill in the art, without creative efforts, can also obtain according to these attached drawings
Obtain other attached drawings.
Fig. 1 is a kind of frequency deviation estimating method for 32 ary quadrature amplitude-modulated signals provided in an embodiment of the present invention
Flow chart；
Fig. 2 is a kind of frequency deviation estimation system for 32 ary quadrature amplitude-modulated signals provided in an embodiment of the present invention
Structural block diagram；
Fig. 3 is that the frequency deviation estimation system provided in an embodiment of the present invention for being used for 32 ary quadrature amplitude-modulated signals carries out frequency
The implementation flow chart estimated partially；
Fig. 4 is the 32-QAM planisphere of standard；
Fig. 5 is the planisphere provided in an embodiment of the present invention to after II class and IV class signal rotation；
Fig. 6 is mean power provided in an embodiment of the present invention and Between Signal To Noise Ratio figure；
Fig. 7 is peak power provided in an embodiment of the present invention and Between Signal To Noise Ratio figure；
Fig. 8 is optimal coefficient provided in an embodiment of the present invention and Between Signal To Noise Ratio figure；
Fig. 9 is PAPR provided in an embodiment of the present invention and Between Signal To Noise Ratio figure；
Figure 10 is error probability provided in an embodiment of the present invention and Between Signal To Noise Ratio figure；
Figure 11 is normalization variance provided in an embodiment of the present invention and Between Signal To Noise Ratio figure；
Figure 12 is the bit error rate provided in an embodiment of the present invention and Between Signal To Noise Ratio figure.
Specific embodiment
Following will be combined with the drawings in the embodiments of the present invention, and technical solution in the embodiment of the present invention carries out clear, complete
Site preparation description, it is clear that described embodiments are only a part of the embodiments of the present invention, instead of all the embodiments.It is based on
Embodiment in the present invention, it is obtained by those of ordinary skill in the art without making creative efforts every other
Embodiment shall fall within the protection scope of the present invention.
The object of the present invention is to provide a kind of frequency deviation estimating method and system for 32 ary quadrature amplitude-modulated signals,
Frequency offset estimation accuracy is high, and snr threshold performance is good.
In order to make the foregoing objectives, features and advantages of the present invention clearer and more comprehensible, with reference to the accompanying drawing and specific real
Applying mode, the present invention is described in further detail.
Fig. 1 is a kind of frequency deviation estimating method for 32 ary quadrature amplitude-modulated signals provided in an embodiment of the present invention
Flow chart.As shown in Figure 1, a kind of frequency deviation estimating method for 32 ary quadrature amplitude-modulated signals, the offset estimation side
Method includes:
Step 101: obtaining the 32 ary quadrature amplitude-modulated signal sequences received, wherein the 32 ary quadrature vibration
Amplitude modulating signal sequence includes: I class signal sequence, II class signal sequence, Group III signal sequence, IV class signal sequence and V class letter
Number sequence.
Step 102: the II class signal sequence and the IV class signal sequence being rotated in the same direction into π/4, revolved
II class signal sequence and postrotational IV class signal sequence after turning.
In the present embodiment, the II class signal sequence and the IV class signal sequence are rotated in the same direction into π/4, obtained
Postrotational II class signal sequence and postrotational IV class signal sequence, specifically include:
The II class signal sequence is rotated counterclockwise into π/4, obtains postrotational II class signal sequence；
The IV class signal sequence is rotated counterclockwise into π/4, obtains postrotational IV class signal sequence.
Step 103: determining that rotating modulation signals sequence, the rotating modulation signals sequence are according to the I class signal sequence
Column, the postrotational II class signal sequence, the Group III signal sequence, the postrotational IV class signal sequence and the V
The quadrature amplitude modulation signal sequence that class signal sequence determines.
Step 104: acquisition makes the corresponding amplification coefficient of the maximum various types of signal sequence of peak-to-average power ratio, and according to each institute
It states amplification coefficient and processing is amplified to the rotating modulation signals sequence, obtain amplification modulated signal sequences, the amplification is adjusted
Signal sequence processed includes: I class amplified signal sequence, II class amplified signal sequence, Group III amplified signal sequence, IV class amplification letter
Number sequence and V class amplified signal sequence.
Step 105: Fast Fourier Transform (FFT) being carried out to the bipyramid of the amplification modulated signal sequences, obtains discrete frequency
Spectrum.
Step 106: the corresponding frequency of peak value of spectrum amplitude is determined according to the discrete spectrum.
Step 107: the offset estimation value of the 32 ary quadrature amplitude-modulated signal sequence is determined according to the frequency.Institute
The offset estimation value for determining the 32 ary quadrature amplitude-modulated signal sequence according to the frequency is stated, is specifically included:
According to formula:Determine the 32 ary quadrature amplitude-modulated signal
The offset estimation value of sequence, whereinIndicating offset estimation value, L indicates the length of 32 ary quadrature amplitude-modulated signal sequences,Indicate the nth elements in amplification modulated signal sequences, n indicates the serial number of amplification modulated signal sequences, and f indicates Fourier's frequency
The frequency of spectrum, T indicate the period of 32 ary quadrature amplitude-modulated signals.
In the present embodiment, make the determination method of the corresponding amplification coefficient of the maximum various types of signal sequence of peak-to-average power ratio
Include:
Obtain the peak-to-average power ratio calculation formula of the amplification modulated signal:
Wherein,It indicates
Peak-to-average power ratio,Indicate the peak power of the frequency spectrum of I class signal sequence,Indicate the frequency of postrotational II class signal sequence
The peak power of spectrum,Indicate the peak power of the frequency spectrum of Group III signal sequence,Indicate postrotational IV class signal sequence
Frequency spectrum peak power,Indicate the peak power of the frequency spectrum of V class signal sequence, k1Indicate the amplification system of I class signal sequence
Number, k2Indicate the amplification coefficient of postrotational II class signal sequence, k3Indicate the amplification coefficient of Group III signal sequence, k4Indicate rotation
The amplification coefficient of IV class signal sequence after turning, k5Indicate the amplification coefficient of V class signal sequence,Indicate I class signal sequence
The mean power of frequency spectrum,Indicate the mean power of the frequency spectrum of postrotational II class signal sequence,Indicate Group III signal sequence
The mean power of the frequency spectrum of column,Indicate the mean power of the frequency spectrum of postrotational IV class signal sequence,Indicate V class signal
The mean power of the frequency spectrum of sequence；
So that the peak-to-average power ratio calculation formula is equal to zero to the local derviation of each amplification coefficient respectively, obtains each described put
The scale relation of big coefficient:
Each amplification coefficient is determined according to the peak power of various types of signal sequence, mean power and the scale relation.
Fig. 2 is a kind of frequency deviation estimation system for 32 ary quadrature amplitude-modulated signals provided in an embodiment of the present invention
Structural block diagram.As shown in Fig. 2, a kind of frequency deviation estimation system for 32 ary quadrature amplitude-modulated signals, the offset estimation
System includes:
Signal sequence obtains module 201, for obtaining the 32 ary quadrature amplitude-modulated signal sequences received, wherein
The 32 ary quadrature amplitude-modulated signal sequence includes: I class signal sequence, II class signal sequence, Group III signal sequence, IV
Class signal sequence and V class signal sequence.
Rotation processing module 202, for revolving the II class signal sequence and the IV class signal sequence to same direction
Turn π/4, obtains postrotational II class signal sequence and postrotational IV class signal sequence.
Specifically, the embodiment of the present invention rotation processing module 202 includes:
II class is counterclockwise rotary unit, for the II class signal sequence to be rotated counterclockwise π/4, after being rotated
II class signal sequence；
IV class is counterclockwise rotary unit, for the IV class signal sequence to be rotated counterclockwise π/4, after being rotated
IV class signal sequence.
Rotating modulation signals determining module 203, for determining rotating modulation signals sequence, the rotating modulation signals sequence
For according to the I class signal sequence, the postrotational II class signal sequence, the Group III signal sequence, postrotational described
The quadrature amplitude modulation signal sequence that IV class signal sequence and the V class signal sequence determine.
Enhanced processing module 204 makes the corresponding amplification coefficient of the maximum various types of signal sequence of peak-to-average power ratio for obtaining,
And processing is amplified to the rotating modulation signals sequence according to each amplification coefficient, obtain amplification modulated signal sequence
Column.
Fourier transformation module 205 carries out fast Fourier change for the bipyramid to the amplification modulated signal sequences
It changes, obtains discrete spectrum.
Frequency determining module 206, the corresponding frequency of peak value for determining spectrum amplitude according to the discrete spectrum.
Offset estimation value determining module 207, for determining the 32 ary quadrature amplitude-modulated signal according to the frequency
The offset estimation value of sequence.
In the present embodiment, the offset estimation value determining module 207 is according to formula:Determine the offset estimation value of the 32 ary quadrature amplitude-modulated signal sequence,
Wherein,Indicating offset estimation value, L indicates the length of 32 ary quadrature amplitude-modulated signal sequences,Indicate amplification modulation letter
Nth elements in number sequence, n indicate the serial number of amplification modulated signal sequences, and f indicates the frequency of Fourier spectrum, and T indicates 32
The period of ary quadrature amplitude-modulated signal.
Further, the frequency deviation estimation system further includes amplification coefficient determining module, the amplification coefficient determining module
Make the corresponding amplification coefficient of the maximum various types of signal sequence of peak-to-average power ratio, the amplification coefficient determining module for determination
Include:
Peak-to-average power ratio acquiring unit, for obtaining the peak-to-average power ratio calculation formula of the amplification modulated signal:Wherein,Indicate the equal function in peak
Rate ratio,Indicate the peak power of the frequency spectrum of I class signal sequence,Indicate the peak of the frequency spectrum of postrotational II class signal sequence
It is worth power,Indicate the peak power of the frequency spectrum of Group III signal sequence,Indicate the frequency spectrum of postrotational IV class signal sequence
Peak power,Indicate the peak power of the frequency spectrum of V class signal sequence, k1Indicate the amplification coefficient of I class signal sequence, k2Table
Show the amplification coefficient of postrotational II class signal sequence, k3Indicate the amplification coefficient of Group III signal sequence, k4Indicate postrotational
The amplification coefficient of IV class signal sequence, k5Indicate the amplification coefficient of V class signal sequence,Indicate the frequency spectrum of I class signal sequence
Mean power,Indicate the mean power of the frequency spectrum of postrotational II class signal sequence,Indicate the frequency of Group III signal sequence
The mean power of spectrum,Indicate the mean power of the frequency spectrum of postrotational IV class signal sequence,Indicate V class signal sequence
The mean power of frequency spectrum；
Coefficient scale relation determination unit, for making the peak-to-average power ratio calculation formula respectively to each amplification coefficient
Local derviation be equal to zero, obtain the scale relation of each amplification coefficient:
Amplification coefficient determination unit, for being closed according to the peak power of various types of signal sequence, mean power and the ratio
It is that formula determines each amplification coefficient.
Fig. 3 is to carry out frequency deviation using the frequency deviation estimation system provided by the present invention for 32 ary quadrature amplitude-modulated signals
The implementation flow chart of estimation.As shown in figure 3, provided by the present invention for the offset estimation system of 32 ary quadrature amplitude-modulated signals
The implementing procedure that system carries out offset estimation is as follows:
(1) the 32 ary quadrature amplitude-modulated signal sequences received are obtained.
The 32-QAM signal sequence that n-th is received indicates are as follows:
Wherein, CnFor transmitted 32-QAM signal, as shown in Figure 4, L is 32 ary quadrature amplitude-modulated signals to planisphere
The length of sequence, n=0,1 ..., L-1, φl,nFor the phase noise that Wiener-Hopf equation description can be used, fdFor frequency deviation, T 32-
QAM signal period, NnSpontaneous radiation (ASE) noise for the amplification generated in description optical communication link, is mathematically modeled as multiple
Number additive white Gaussian noise.
As shown in figure 4,32 different constellation points are shared in 32-QAM, and on the ring of 5 different amplitudes, amplitude difference
It isFour threshold values are the average value of the amplitude of adjacent ring, to distinguish affiliated class
Not.Wherein
Threshold value R is utilized according to the ascending sequence of amplitude1、R2、R3And R432-QAM signal can be divided into I, II, III, IV, V this
Five classes.The signal sequence received can be expressed as row vector S=[S0 S1 … SL-1].Similarly, the signal of the i-th class is defined
Sequence isWherein i ∈ { I, II, III, IV, V }.
(2) the II class signal sequence and the IV class signal sequence are rotated in the same direction into π/4, obtained postrotational
II class signal sequence and postrotational IV class signal sequence, and according to I class signal sequence, postrotational II class signal sequence, III
The postrotational quadrature amplitude modulation signal sequence that class signal sequence, postrotational IV class signal sequence and V class signal sequence determine
Column.
Work as SnWhen ∈ i class,OtherwiseN=0,1 ..., L-1.Due between all kinds of without intersection, i.e., it is each
Signal is only possible to belong to certain one kind, so S=SI+SII+SIII+SIV+SVAnd 5 × L matrix [(SI)T (SII)T (SIII)T (SIV)T
(SV)T]TIn any one column, there must be a certain element equal to the signal in same row in S, and remaining element is all in the column
Zero, ()TRepresent transposition operation.The I class and Group III signal of standard constitute two quadrature phase shift keying with different amplitudes
(Quadrature Phase Shift Keying, QPSK) constellation, this makes data phase ± π/4 and ± 3 π/4 can be by 4 times
Power operation all removes.But II class, IV class and V class are different.If by the angle of II class and IV class signal rotation π/4,
So all constellation points all will accumulate in around diagonal line of two slopes equal to ± 1, and existing error can be considered noise, rotation
Planisphere after turning is as shown in Figure 5.Therefore, after rotation processing, all signals are using 4 power operations substantially by modulation
Data phase removes.
Selection II class and IV class signal are simultaneously rotated π/4, can be respectively indicated after rotation are as follows:
With
Define postrotational signal sequence are as follows:
(3) enhanced processing is done to various types of signal using five amplification coefficients, makes gained frequency spectrum in next step that there is maximum
Peak-to-average power ratio (peak to average power ratio, PAPR), this group of amplification coefficient is optimal coefficient.Definition
Amplified signal sequence are as follows:
(4) to signal sequenceBipyramid do FFT operation, pass through search spectrum peak obtain frequency deviation estimated value
In formula,For signal sequenceIn element.
By formula (4) as it can be seen that the estimated value of frequency deviation is calculated by the corresponding frequency of peak value of spectrum amplitude.In frequency domain,
PAPR may be defined as:
In formula, P and A are respectively the peak power and mean power of frequency spectrum.
Relationship between the mean power of each signal is as follows:
WithWithIt respectively indicatesSI、SIII、And SV
In each element do the row vector obtained after bipyramid operation.Obviously,And 5 × L matrixIn any one column, there must be a certain element and be equal toElement in middle same row, and remaining element all zero in the column.Therefore, in the time domain, signalMean power
Equal to signal (SI)4、(SIII)4、(SV)4The sum of mean power.Frequency domain is transformed to, which still sets up,
It may be expressed as:
In formula, AxIt indicates (x)4Frequency spectrum mean power.
Relationship between each signal peak power is as follows:
If not considering phase noise and ASE, mean value the E [(S of each time domain random signalI)4]、E
[(SIII)4]、With E [(SV)4] be negative real number, wherein E [x] represents the mathematic expectaion of x.Again because of the mean value of time domain
(be located at frequency is 4f to peak value in corresponding spectrumdPlace), so the peak value of the plural form of their frequency spectrums is same phase.Further according to
FFT linear behavio(u)r can obtain, and the amplitude of total peak value is equal to the sum of the amplitude of single peak value.Therefore, theoretically peak power it
Between relationship may be expressed as:
Wherein, PxIt indicates (x)4Frequency spectrum peak power.It should be noted that the condition that formula (7) meet is no phase
Noise and ASE.If considering the factors such as phase noise and ASE, have
Formula (6) and formula (7), which are substituted into formula (5), can obtain formula (8):
Further, the PAPR of amplified signal sequence may be expressed as:
To obtain the maximum value of formula (9), enableIt can obtain:
The peak power and mean power of each signal can be measured by experiment in formula (10), and then can determine each amplification system
Proportionate relationship between number.After determining any one amplification coefficient, other four amplification systems can determine according to formula (10)
Number.
In order to further examine the performance of frequency deviation estimating method proposed by the present invention and system, to 10G baud rate 32-QAM
System has carried out simulation study.In order to focus offset estimation, frequency deviation and ASE noise are only accounted in emulation and does not consider that phase is made an uproar
The influence of sound.The simulation result provided is obtained at relatively small data length (L=512).
Fig. 6 gives the relationship between the mean power and signal-to-noise ratio of certain signals.As seen from Figure 6, by signalIt obtains
Mean powerEqual to the mean power obtained by formula (6)Sufficiently demonstrate the correctness of formula (6).Another party
Face, Fig. 7 give the relationship between the peak power and signal-to-noise ratio of these types of signal.As SNR >=18dB, peak powerClosely
The peak power approximately equal to obtained by formula (7)In low signal-to-noise ratio region, the phase of these signal spectrum peak values
Very big, no longer same phase is influenced by ASE noise, so that
Optimal coefficient k using the simulation result and formula (10) of Fig. 6, Fig. 7, under available difference signal-to-noise ratio1,k2,…,
k5, as a result as shown in Figure 8.As previously mentioned, obtained optimal coefficient is only just meaningful in SNR >=18dB.Work as SNR=
When 18dB, optimal coefficient k1=3.6155, k2=1.7029, k3=1.4318, k4=1.1422, k5=1.A large amount of numerical value is imitative
Very the result shows that, under this group of parameter, the frequency deviation estimating method proposed can get optimal snr threshold performance.It is subsequent imitative
True result obtains under these parameters, no longer repeats one by one.Fig. 9 givesWithIn different noises
Than when numerical curve.Obviously, method proposed by the inventionBy being significantly improved after rotation and enhanced processing.
It is influenced by FFT points, the offset estimation resolution ratio of the frequency deviation estimating method based on FFT isTherefore, if
In certain emulationHave exceeded rangeIt is considered that this time frequency deviation is estimated
There is mistake in meter, otherwise estimation is correct.Figure 10 gives error probability curve when different signal-to-noise ratio.When FFT points are only
When 512, frequency deviation estimating method (PAPRA-FFT-FOE) proposed by the present invention can be realized in the case where signal-to-noise ratio is higher than 17dB
Faultless offset estimation, and show the snr threshold performance better than other methods.In order to more clearly from react frequency
The precision estimated partially, Figure 11 give normalized frequency variance and (are defined asPass between signal-to-noise ratio
System.As it can be seen that method evaluated error proposed by the present invention is minimum, estimated accuracy highest.
Finally, Figure 12 gives the ber curve of each method.To give additivity in Figure 12 together also convenient for comparing
Bit error rate theoretical boundary in the case of white Gaussian noise (Additive White Gaussian Noise, AWGN).The present invention
The method of proposition is equal to 2 × 10 at the bit error rate (Bit Error Rate, BER)-2The signal-to-noise ratio and theoretical boundary of Shi Suoxu is only
There is the signal-to-noise ratio cost of 1dB.This also sufficiently demonstrates frequency deviation estimating method provided by the invention with more higher than other methods
Estimated accuracy.In emulation, phase recovery method uses quasi- QPSK segmentation and cross constellation to convert (CCT) method, the length of block
Degree is respectively 128 and 32.
The present invention proposes that the computational complexity of method can be multiplied by used reality, sum it up the number of comparison operation in fact to weigh
Amount.Table 1 gives the complexity analyzing result of these methods.The edge effect unrelated with data length L is had ignored in calculating process
It answers.Compared with traditional FFT-FOE method, PAPRA-FFT-FOE method proposed by the present invention increases selection, rotation and amplification
Operation, operand increased.Specifically, it needs (i) 2 real multipliers and 1 real add musical instruments used in a Buddhist or Taoist mass each to calculate
The amplitude of signal；Comparator number are as follows: 1 × 4/32+2 × 8/32+3 × 4/32+4 × 8/32+4 × 8/32=3 needs 3
The size relation of amplitude and threshold value that comparator carrys out comparison each signal determines which class the signal belongs to；(ii) 2 real numbers multiply
Musical instruments used in a Buddhist or Taoist mass amplifies the amplitude (probability 8/32) of each I class and Group III signal；4 real multipliers and 2 real add musical instruments used in a Buddhist or Taoist mass come
Rotate and amplify each II class and IV class signal (probability 16/32)；Real multipliers and real addition are not necessarily to for V class signal
Device (probability 8/32).It is compared with other methods, PAPRA-FFT-FOE method proposed by the invention increases only a small amount of calculating
Burden but obtains being obviously improved for estimated accuracy and snr threshold performance.
1. computational complexity of table
As it can be seen that the present invention is directed to 32-QAM coherent light system, high-precision frequency deviation can be realized using only 512 signals and estimate
Meter, and snr threshold performance is good.
Each embodiment in this specification is described in a progressive manner, the highlights of each of the examples are with other
The difference of embodiment, the same or similar parts in each embodiment may refer to each other.For system disclosed in embodiment
For, since it is corresponded to the methods disclosed in the examples, so being described relatively simple, related place is said referring to method part
It is bright.
Used herein a specific example illustrates the principle and implementation of the invention, and above embodiments are said
It is bright to be merely used to help understand method and its core concept of the invention；At the same time, for those skilled in the art, foundation
Thought of the invention, there will be changes in the specific implementation manner and application range.In conclusion the content of the present specification is not
It is interpreted as limitation of the present invention.
Claims (8)
1. a kind of frequency deviation estimating method for 32 ary quadrature amplitude-modulated signals, which is characterized in that the offset estimation side
Method includes:
Obtain the 32 ary quadrature amplitude-modulated signal sequences received, wherein the 32 ary quadrature amplitude-modulated signal sequence
Column include: I class signal sequence, II class signal sequence, Group III signal sequence, IV class signal sequence and V class signal sequence；
The II class signal sequence and the IV class signal sequence are rotated in the same direction into π/4, obtain postrotational II class letter
Number sequence and postrotational IV class signal sequence；
Determine rotating modulation signals sequence, the rotating modulation signals sequence is according to the I class signal sequence, postrotational institute
It is true to state II class signal sequence, the Group III signal sequence, the postrotational IV class signal sequence and the V class signal sequence
Fixed quadrature amplitude modulation signal sequence；
Acquisition makes the corresponding amplification coefficient of the maximum various types of signal sequence of peak-to-average power ratio, and according to each amplification coefficient pair
The rotating modulation signals sequence amplifies processing, obtains amplification modulated signal sequences；
Fast Fourier Transform (FFT) is carried out to the bipyramid of the amplification modulated signal sequences, obtains discrete spectrum；
The corresponding frequency of peak value of spectrum amplitude is determined according to the discrete spectrum；
The offset estimation value of the 32 ary quadrature amplitude-modulated signal sequence is determined according to the frequency.
2. frequency deviation estimating method according to claim 1, which is characterized in that make the maximum various types of signal sequence of peak-to-average power ratio
The determination method for arranging the corresponding amplification coefficient includes:
Obtain the peak-to-average power ratio calculation formula of the amplification modulated signal:
Wherein,Indicate peak
Equal power ratio,Indicate the peak power of the frequency spectrum of I class signal sequence,Indicate the frequency spectrum of postrotational II class signal sequence
Peak power,Indicate the peak power of the frequency spectrum of Group III signal sequence,Indicate postrotational IV class signal sequence
The peak power of frequency spectrum,Indicate the peak power of the frequency spectrum of V class signal sequence, k1Indicate the amplification system of I class signal sequence
Number, k2Indicate the amplification coefficient of postrotational II class signal sequence, k3Indicate the amplification coefficient of Group III signal sequence, k4Indicate rotation
The amplification coefficient of IV class signal sequence after turning, k5Indicate the amplification coefficient of V class signal sequence,Indicate I class signal sequence
The mean power of frequency spectrum,Indicate the mean power of the frequency spectrum of postrotational II class signal sequence,Indicate Group III signal sequence
The mean power of the frequency spectrum of column,Indicate the mean power of the frequency spectrum of postrotational IV class signal sequence,Indicate V class signal
The mean power of the frequency spectrum of sequence；
So that the peak-to-average power ratio calculation formula is equal to zero to the local derviation of each amplification coefficient respectively, obtains each amplification system
Several scale relations:
Each amplification coefficient is determined according to the peak power of various types of signal sequence, mean power and the scale relation.
3. frequency deviation estimating method according to claim 1, which is characterized in that determining 32 system just according to the frequency
The offset estimation value for handing over amplitude-modulated signal sequence, specifically includes:
According to formula:Determine the 32 ary quadrature amplitude-modulated signal sequence
Offset estimation value, whereinIndicating offset estimation value, L indicates the length of 32 ary quadrature amplitude-modulated signal sequences,Table
Show the nth elements in amplification modulated signal sequences, n indicates the serial number of amplification modulated signal sequences, and f indicates Fourier spectrum
Frequency, T indicate the period of 32 ary quadrature amplitude-modulated signals.
4. frequency deviation estimating method according to claim 1, which is characterized in that described by the II class signal sequence and described
IV class signal sequence rotates in the same direction π/4, obtains postrotational II class signal sequence and postrotational IV class signal sequence,
It specifically includes:
The II class signal sequence is rotated counterclockwise into π/4, obtains postrotational II class signal sequence；
The IV class signal sequence is rotated counterclockwise into π/4, obtains postrotational IV class signal sequence.
5. a kind of frequency deviation estimation system for 32 ary quadrature amplitude-modulated signals, which is characterized in that the offset estimation system
System includes:
Signal sequence obtain module, for obtaining the 32 ary quadrature amplitude-modulated signal sequences received, wherein described 32 into
Quadrature amplitude modulation signal sequence processed includes: I class signal sequence, II class signal sequence, Group III signal sequence, IV class signal sequence
Column and V class signal sequence；
Rotation processing module is obtained for the II class signal sequence and the IV class signal sequence to be rotated in the same direction π/4
Obtain postrotational II class signal sequence and postrotational IV class signal sequence；
Rotating modulation signals determining module, for determining rotating modulation signals sequence, according to the rotating modulation signals sequence
The I class signal sequence, the postrotational II class signal sequence, the Group III signal sequence, the postrotational IV class letter
The quadrature amplitude modulation signal sequence that number sequence and the V class signal sequence determine；
Enhanced processing module makes the corresponding amplification coefficient of the maximum various types of signal sequence of peak-to-average power ratio for obtaining, and according to
Each amplification coefficient amplifies processing to the rotating modulation signals sequence, obtains amplification modulated signal sequences；
Fourier transformation module carries out Fast Fourier Transform (FFT) for the bipyramid to the amplification modulated signal sequences, obtains
Discrete spectrum；
Frequency determining module, the corresponding frequency of peak value for determining spectrum amplitude according to the discrete spectrum；
Offset estimation value determining module, for determining the frequency of the 32 ary quadrature amplitude-modulated signal sequence according to the frequency
Inclined estimated value.
6. frequency deviation estimation system according to claim 5, which is characterized in that the frequency deviation estimation system further includes amplification system
Number determining module, the amplification coefficient determining module make the corresponding institute of the maximum various types of signal sequence of peak-to-average power ratio for determination
Amplification coefficient is stated, the amplification coefficient determining module includes:
Peak-to-average power ratio acquiring unit, for obtaining the peak-to-average power ratio calculation formula of the amplification modulated signal:Wherein,Indicate that peak is equal
Power ratio,Indicate the peak power of the frequency spectrum of I class signal sequence,Indicate the frequency spectrum of postrotational II class signal sequence
Peak power,Indicate the peak power of the frequency spectrum of Group III signal sequence,Indicate the frequency of postrotational IV class signal sequence
The peak power of spectrum,Indicate the peak power of the frequency spectrum of V class signal sequence, k1Indicate the amplification coefficient of I class signal sequence, k2
Indicate the amplification coefficient of postrotational II class signal sequence, k3Indicate the amplification coefficient of Group III signal sequence, k4After indicating rotation
IV class signal sequence amplification coefficient, k5Indicate the amplification coefficient of V class signal sequence,Indicate the frequency spectrum of I class signal sequence
Mean power,Indicate the mean power of the frequency spectrum of postrotational II class signal sequence,Indicate Group III signal sequence
The mean power of frequency spectrum,Indicate the mean power of the frequency spectrum of postrotational IV class signal sequence,Indicate V class signal sequence
Frequency spectrum mean power；
Coefficient scale relation determination unit, for making the peak-to-average power ratio calculation formula respectively to the inclined of each amplification coefficient
It leads and is equal to zero, obtain the scale relation of each amplification coefficient:
Amplification coefficient determination unit, for according to the peak power of various types of signal sequence, mean power and the scale relation
Determine each amplification coefficient.
7. frequency deviation estimation system according to claim 5, which is characterized in that the offset estimation value determining module is according to public affairs
Formula:Determine the offset estimation of the 32 ary quadrature amplitude-modulated signal sequence
Value, whereinIndicating offset estimation value, L indicates the length of 32 ary quadrature amplitude-modulated signal sequences,Indicate that amplification is adjusted
Nth elements in signal sequence processed, n indicate the serial number of amplification modulated signal sequences, and f indicates the frequency of Fourier spectrum, T table
Show the period of 32 ary quadrature amplitude-modulated signals.
8. frequency deviation estimation system according to claim 5, which is characterized in that the rotation processing module includes:
II class is counterclockwise rotary unit obtains postrotational II for the II class signal sequence to be rotated counterclockwise π/4
Class signal sequence；
IV class is counterclockwise rotary unit obtains postrotational IV for the IV class signal sequence to be rotated counterclockwise π/4
Class signal sequence.
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