CN109246044B - Frequency offset estimation method and system for 32-ary quadrature amplitude modulated signal - Google Patents

Abstract

The invention discloses a frequency offset estimation method and system for a 32-ary quadrature amplitude modulation signal. The frequency offset estimation method and system provided by the present invention firstly rotate the type II signal sequence and the IV type signal sequence in the received 32-ary quadrature amplitude modulation signal sequence in the same direction to form a rotation modulation signal sequence, and then use the Each amplification factor with the largest peak-to-average power ratio amplifies the rotation modulation signal sequence to obtain the amplified modulation signal sequence; on this basis, the fourth power of the amplified modulation signal sequence is subjected to fast Fourier transform, so that the spectrum amplitude can be obtained. The frequency corresponding to the peak value; finally, the frequency offset estimation value of the 32-ary quadrature amplitude modulation signal sequence is determined according to the frequency corresponding to the peak value of the spectrum amplitude. The frequency offset estimation method and system provided by the invention have high frequency offset estimation accuracy, good signal-to-noise ratio threshold performance, strong practicability and good application prospect.

Description

Frequency offset estimation method and system for 32-ary quadrature amplitude modulated signal

technical field

The invention relates to the field of coherent optical communication systems, in particular to a frequency offset estimation method and system for a 32-ary quadrature amplitude modulation signal.

Background technique

The 32-ary quadrature amplitude modulation (32-QAM) coherent optical communication system is very likely to become the next-generation optical communication system with data rates as high as 400Gb/s to 1Tb/s. This is mainly because the system has higher spectral efficiency and channel capacity than previous transmission systems under Quadrature Phase Shift Keying (QPSK) and 16-QAM modulation formats. In a digital coherent receiver, the frequency offset (FO) estimation method needs to be used to estimate and compensate the frequency offset between the transmitting laser and the local oscillator laser before the carrier phase is recovered.

Due to the particularity of the constellation diagram of the 32-QAM system, there are very few high-performance frequency offset estimation methods. The traditional frequency offset estimation method (FFT-FOE) based on fast Fourier transform (FFT) cannot be successfully used for frequency offset estimation of 32-QAM system in the case of small data length (eg several hundreds). The reason is that the constellation diagram of 32-QAM is different from that of 16-QAM and 64-QAM, and it is not strictly rectangular distribution, which causes the spectral peaks in the low signal-to-noise ratio area to be severely weakened.

SUMMARY OF THE INVENTION

The purpose of the present invention is to provide a frequency offset estimation method and system for a 32-ary quadrature amplitude modulation signal, which has high frequency offset estimation accuracy and good signal-to-noise ratio threshold performance.

For achieving the above object, the present invention provides the following scheme:

A frequency offset estimation method for a 32-ary quadrature amplitude modulation signal, the frequency offset estimation method comprising:

Acquire the received 32-ary quadrature amplitude modulation signal sequence, wherein the 32-ary quadrature amplitude modulation signal sequence includes: type I signal sequence, type II signal sequence, type III signal sequence, type IV signal sequence and V class signal sequence;

Rotating the class II signal sequence and the class IV signal sequence in the same direction by π/4 to obtain the rotated class II signal sequence and the rotated class IV signal sequence;

Determining a rotational modulation signal sequence, the rotational modulation signal sequence is based on the type I signal sequence, the rotated type II signal sequence, the type III signal sequence, the rotated type IV signal sequence and the The quadrature amplitude modulation signal sequence determined by the class V signal sequence;

Acquiring amplification coefficients corresponding to various signal sequences that maximize the peak-to-average power ratio, and performing amplification processing on the rotational modulation signal sequence according to each of the amplification coefficients to obtain an amplified modulation signal sequence;

performing fast Fourier transform on the fourth power of the amplified modulation signal sequence to obtain discrete frequency spectrum;

Determine the frequency corresponding to the peak value of the spectrum amplitude according to the discrete spectrum;

The frequency offset estimation value of the 32-ary quadrature amplitude modulation signal sequence is determined according to the frequency.

Optionally, the method for determining the amplification factor corresponding to each type of signal sequence that maximizes the peak-to-average power ratio includes:

Obtain the formula for calculating the peak-to-average power ratio of the amplified modulated signal: in, represents the peak-to-average power ratio, represents the peak power of the spectrum of the class I signal sequence, represents the peak power of the spectrum of the rotated class II signal sequence, represents the peak power of the spectrum of the class III signal sequence, represents the peak power of the spectrum of the rotated class IV signal sequence, Indicates the peak power of the spectrum of the class V signal sequence, k ₁ denotes the amplification factor of the class I signal sequence, k ₂ denotes the amplification factor of the rotated class II signal sequence, k ₃ denotes the amplification factor of the class III signal sequence, k ₄ denotes the amplification factor of the class III signal sequence The amplification factor of the rotated class IV signal sequence, k ₅ represents the amplification factor of the class V signal sequence, represents the average power of the spectrum of the class I signal sequence, represents the average power of the spectrum of the rotated class II signal sequence, represents the average power of the spectrum of the class III signal sequence, represents the average power of the spectrum of the rotated class IV signal sequence, Represents the average power of the spectrum of a class V signal sequence.

Make the partial derivative of the peak-to-average power ratio calculation formula to each amplification factor equal to zero, and obtain the proportional relationship formula of each of the amplification factors:

Each amplification factor is determined according to the peak power and average power of various signal sequences and the proportional relationship.

Optionally, the determining the frequency offset estimation value of the 32-ary quadrature amplitude modulation signal sequence according to the frequency specifically includes:

According to the formula: Determine the frequency offset estimation value of the 32-ary quadrature amplitude modulation signal sequence, wherein, represents the estimated frequency offset, L represents the length of the 32-ary quadrature amplitude modulation signal sequence, Indicates the nth element in the amplified modulation signal sequence, n denotes the serial number of the amplified modulation signal sequence, f denotes the frequency of the Fourier spectrum, and T denotes the period of the 32-ary quadrature amplitude modulation signal.

Optionally, rotating the class II signal sequence and the class IV signal sequence by π/4 in the same direction to obtain the rotated class II signal sequence and the rotated class IV signal sequence, specifically including:

Rotating the class II signal sequence counterclockwise by π/4 to obtain the rotated class II signal sequence;

The class IV signal sequence is rotated counterclockwise by π/4 to obtain the rotated class IV signal sequence.

A frequency offset estimation system for a 32-ary quadrature amplitude modulation signal, the frequency offset estimation system comprising:

A signal sequence acquisition module, configured to acquire a received 32-ary quadrature amplitude modulation signal sequence, wherein the 32-ary quadrature amplitude modulation signal sequence includes: a type I signal sequence, a type II signal sequence, and a type III signal sequence , class IV signal sequence and class V signal sequence;

a rotation processing module, configured to rotate the class II signal sequence and the class IV signal sequence in the same direction by π/4 to obtain the rotated class II signal sequence and the rotated class IV signal sequence;

A rotational modulation signal determination module, configured to determine a rotational modulation signal sequence, the rotational modulation signal sequence is based on the type I signal sequence, the rotated type II signal sequence, the type III signal sequence, and the rotated all signal sequence. the quadrature amplitude modulation signal sequence determined by the class IV signal sequence and the class V signal sequence;

an amplification processing module, configured to obtain amplification coefficients corresponding to various signal sequences that maximize the peak-to-average power ratio, and amplify the rotational modulation signal sequence according to each amplification coefficient to obtain an amplified modulation signal sequence;

a Fourier transform module, configured to perform fast Fourier transform on the fourth power of the amplified modulation signal sequence to obtain a discrete spectrum;

a frequency determination module, configured to determine the frequency corresponding to the peak value of the spectrum amplitude according to the discrete spectrum;

The frequency offset estimation value determination module is configured to determine the frequency offset estimation value of the 32-ary quadrature amplitude modulation signal sequence according to the frequency.

Optionally, the frequency offset estimation system further includes an amplification factor determination module, the amplification factor determination module is configured to determine the amplification factor corresponding to the various types of signal sequences that maximize the peak-to-average power ratio, and the amplification factor determination module include:

The peak-to-average power ratio obtaining unit obtains the calculation formula of the peak-to-average power ratio of the amplified modulated signal: in, represents the peak-to-average power ratio, represents the peak power of the spectrum of the class I signal sequence, represents the peak power of the spectrum of the rotated class II signal sequence, represents the peak power of the spectrum of the class III signal sequence, represents the peak power of the spectrum of the rotated class IV signal sequence, Indicates the peak power of the spectrum of the class V signal sequence, k ₁ denotes the amplification factor of the class I signal sequence, k ₂ denotes the amplification factor of the rotated class II signal sequence, k ₃ denotes the amplification factor of the class III signal sequence, k ₄ denotes the amplification factor of the class III signal sequence The amplification factor of the rotated class IV signal sequence, k ₅ represents the amplification factor of the class V signal sequence, represents the average power of the spectrum of the class I signal sequence, represents the average power of the spectrum of the rotated class II signal sequence, represents the average power of the spectrum of the class III signal sequence, represents the average power of the spectrum of the rotated class IV signal sequence, represents the average power of the spectrum of the class V signal sequence;

The coefficient proportional relationship formula determination unit is used to make the partial derivatives of the peak-to-average power ratio calculation formulas to each amplification factor equal to zero, and obtain the proportional relationship formula of each of the amplification coefficients:

The amplification factor determination unit is configured to determine each amplification factor according to the peak power, average power and the proportional relationship formula of various signal sequences.

Optionally, the frequency offset estimation value determination module is based on the formula: Determine the frequency offset estimation value of the 32-ary quadrature amplitude modulation signal sequence, wherein, represents the estimated frequency offset, L represents the length of the 32-ary quadrature amplitude modulation signal sequence, Indicates the nth element in the amplified modulation signal sequence, n denotes the serial number of the amplified modulation signal sequence, f denotes the frequency of the Fourier spectrum, and T denotes the period of the 32-ary quadrature amplitude modulation signal.

Optionally, the rotation processing module includes:

The class II counterclockwise rotation unit is used to rotate the class II signal sequence counterclockwise by π/4 to obtain the rotated class II signal sequence;

The class IV counterclockwise rotation unit is configured to rotate the class IV signal sequence counterclockwise by π/4 to obtain the rotated class IV signal sequence.

According to the specific embodiments provided by the present invention, the present invention discloses the following technical effects:

The frequency offset estimation method and system for a 32-ary quadrature amplitude modulation signal provided by the present invention, firstly, the type II signal sequence and the type IV signal sequence in the received 32-ary quadrature amplitude modulation signal sequence are directed in the same direction After rotating by π/4, a rotational modulation signal sequence is formed, and then each amplification factor that maximizes the peak-to-average power ratio is used to amplify the rotational modulation signal sequence to obtain the amplified modulation signal sequence; The frequency corresponding to the peak value of the spectrum amplitude can be obtained by fast Fourier transform of the power; finally, the frequency offset estimation value of the 32-ary quadrature amplitude modulation signal sequence is determined according to the frequency corresponding to the peak value of the spectrum amplitude. The frequency offset estimation method and system provided by the invention have high frequency offset estimation accuracy, good signal-to-noise ratio threshold performance, strong practicability and good application prospect.

Description of drawings

In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the accompanying drawings required in the embodiments will be briefly introduced below. Obviously, the drawings in the following description are only some of the present invention. In the embodiments, for those of ordinary skill in the art, other drawings can also be obtained according to these drawings without any creative effort.

1 is a flowchart of a method for estimating frequency offset for a 32-ary quadrature amplitude modulation signal according to an embodiment of the present invention;

2 is a structural block diagram of a frequency offset estimation system for a 32-ary quadrature amplitude modulation signal provided by an embodiment of the present invention;

3 is an implementation flowchart of frequency offset estimation by a frequency offset estimation system for a 32-ary quadrature amplitude modulation signal provided by an embodiment of the present invention;

Figure 4 is a standard 32-QAM constellation diagram;

FIG. 5 is a constellation diagram after rotation of class II and class IV signals provided by an embodiment of the present invention;

FIG. 6 is a relationship diagram between average power and signal-to-noise ratio provided by an embodiment of the present invention;

FIG. 7 is a relationship diagram between peak power and signal-to-noise ratio provided by an embodiment of the present invention;

FIG. 8 is a relationship diagram between an optimal coefficient and a signal-to-noise ratio provided by an embodiment of the present invention;

FIG. 9 is a relationship diagram between PAPR and signal-to-noise ratio provided by an embodiment of the present invention;

FIG. 10 is a relationship diagram between error probability and signal-to-noise ratio provided by an embodiment of the present invention;

11 is a relationship diagram of normalized variance and signal-to-noise ratio provided by an embodiment of the present invention;

FIG. 12 is a relationship diagram between a bit error rate and a signal-to-noise ratio according to an embodiment of the present invention.

Detailed ways

The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, but not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

The purpose of the present invention is to provide a frequency offset estimation method and system for a 32-ary quadrature amplitude modulation signal, which has high frequency offset estimation accuracy and good signal-to-noise ratio threshold performance.

In order to make the above objects, features and advantages of the present invention more clearly understood, the present invention will be described in further detail below with reference to the accompanying drawings and specific embodiments.

FIG. 1 is a flowchart of a frequency offset estimation method for a 32-ary quadrature amplitude modulation signal according to an embodiment of the present invention. As shown in Figure 1, a frequency offset estimation method for 32-ary quadrature amplitude modulation signal, the frequency offset estimation method includes:

Step 101: Acquire a received 32-ary quadrature amplitude modulation signal sequence, wherein the 32-ary quadrature amplitude modulation signal sequence includes: a type I signal sequence, a type II signal sequence, a type III signal sequence, and a type IV signal sequences and class V signal sequences.

Step 102: Rotate the class II signal sequence and the class IV signal sequence in the same direction by π/4 to obtain the rotated class II signal sequence and the rotated class IV signal sequence.

In this embodiment, the class II signal sequence and the class IV signal sequence are rotated in the same direction by π/4 to obtain the rotated class II signal sequence and the rotated class IV signal sequence, which specifically include:

Rotating the class II signal sequence counterclockwise by π/4 to obtain the rotated class II signal sequence;

The class IV signal sequence is rotated counterclockwise by π/4 to obtain the rotated class IV signal sequence.

Step 103: Determine a rotational modulation signal sequence, the rotational modulation signal sequence is based on the type I signal sequence, the rotated type II signal sequence, the type III signal sequence, and the rotated type IV signal sequence and the class V signal sequence to determine the quadrature amplitude modulation signal sequence.

Step 104: Acquire amplification coefficients corresponding to various signal sequences that maximize the peak-to-average power ratio, and amplify the rotational modulation signal sequence according to each amplification coefficient to obtain an amplified modulation signal sequence, which is a sequence of amplified modulation signals. Including: class I amplified signal sequence, class II amplified signal sequence, class III amplified signal sequence, class IV amplified signal sequence and class V amplified signal sequence.

Step 105: Perform fast Fourier transform on the fourth power of the amplified modulation signal sequence to obtain a discrete spectrum.

Step 106: Determine the frequency corresponding to the peak value of the spectrum amplitude according to the discrete spectrum.

Step 107: Determine the frequency offset estimation value of the 32-ary quadrature amplitude modulation signal sequence according to the frequency. The determining the frequency offset estimation value of the 32-ary quadrature amplitude modulation signal sequence according to the frequency specifically includes:

According to the formula: Determine the frequency offset estimation value of the 32-ary quadrature amplitude modulation signal sequence, wherein, represents the estimated frequency offset, L represents the length of the 32-ary quadrature amplitude modulation signal sequence, Indicates the nth element in the amplified modulation signal sequence, n denotes the serial number of the amplified modulation signal sequence, f denotes the frequency of the Fourier spectrum, and T denotes the period of the 32-ary quadrature amplitude modulation signal.

In this embodiment, the method for determining the amplification factor corresponding to each type of signal sequence that maximizes the peak-to-average power ratio includes:

Obtain the formula for calculating the peak-to-average power ratio of the amplified modulated signal:

in, represents the peak-to-average power ratio, represents the peak power of the spectrum of the class I signal sequence, represents the peak power of the spectrum of the rotated class II signal sequence, represents the peak power of the spectrum of the class III signal sequence, represents the peak power of the spectrum of the rotated class IV signal sequence, Indicates the peak power of the spectrum of the class V signal sequence, k ₁ denotes the amplification factor of the class I signal sequence, k ₂ denotes the amplification factor of the rotated class II signal sequence, k ₃ denotes the amplification factor of the class III signal sequence, k ₄ denotes the amplification factor of the class III signal sequence The amplification factor of the rotated class IV signal sequence, k ₅ represents the amplification factor of the class V signal sequence, represents the average power of the spectrum of the class I signal sequence, represents the average power of the spectrum of the rotated class II signal sequence, represents the average power of the spectrum of the class III signal sequence, represents the average power of the spectrum of the rotated class IV signal sequence, represents the average power of the spectrum of the class V signal sequence;

Make the partial derivative of the peak-to-average power ratio calculation formula to each amplification factor equal to zero, and obtain the proportional relationship formula of each of the amplification factors:

Each amplification factor is determined according to the peak power and average power of various signal sequences and the proportional relationship.

FIG. 2 is a structural block diagram of a frequency offset estimation system for a 32-ary quadrature amplitude modulation signal according to an embodiment of the present invention. As shown in Figure 2, a frequency offset estimation system for a 32-ary quadrature amplitude modulation signal, the frequency offset estimation system includes:

A signal sequence acquisition module 201, configured to acquire a received 32-ary quadrature amplitude modulation signal sequence, wherein the 32-ary quadrature amplitude modulation signal sequence includes: a type I signal sequence, a type II signal sequence, and a type III signal sequence, class IV signal sequence and class V signal sequence.

The rotation processing module 202 is configured to rotate the class II signal sequence and the class IV signal sequence in the same direction by π/4 to obtain the rotated class II signal sequence and the rotated class IV signal sequence.

Specifically, the rotation processing module 202 in this embodiment includes:

The class II counterclockwise rotation unit is used to rotate the class II signal sequence counterclockwise by π/4 to obtain the rotated class II signal sequence;

The class IV counterclockwise rotation unit is configured to rotate the class IV signal sequence counterclockwise by π/4 to obtain the rotated class IV signal sequence.

A rotational modulation signal determination module 203, configured to determine a rotational modulation signal sequence, the rotational modulation signal sequence is based on the type I signal sequence, the rotated type II signal sequence, the type III signal sequence, the rotated The quadrature amplitude modulation signal sequence determined by the class IV signal sequence and the class V signal sequence.

The amplification processing module 204 is configured to obtain amplification coefficients corresponding to various signal sequences that maximize the peak-to-average power ratio, and perform amplification processing on the rotational modulation signal sequence according to each amplification coefficient to obtain the amplified modulation signal sequence.

The Fourier transform module 205 is configured to perform fast Fourier transform on the fourth power of the amplified modulation signal sequence to obtain a discrete spectrum.

The frequency determination module 206 is configured to determine the frequency corresponding to the peak value of the spectrum amplitude according to the discrete spectrum.

The frequency offset estimation value determination module 207 is configured to determine the frequency offset estimation value of the 32-ary quadrature amplitude modulation signal sequence according to the frequency.

In this embodiment, the frequency offset estimation value determination module 207 is based on the formula: Determine the frequency offset estimation value of the 32-ary quadrature amplitude modulation signal sequence, wherein, represents the estimated frequency offset, L represents the length of the 32-ary quadrature amplitude modulation signal sequence, Indicates the nth element in the amplified modulation signal sequence, n denotes the serial number of the amplified modulation signal sequence, f denotes the frequency of the Fourier spectrum, and T denotes the period of the 32-ary quadrature amplitude modulation signal.

Further, the frequency offset estimation system further includes an amplification factor determination module, the amplification factor determination module is used to determine the amplification factor corresponding to each type of signal sequence that maximizes the peak-to-average power ratio, and the amplification factor determination module includes: :

The peak-to-average power ratio acquisition unit is used to obtain the calculation formula of the peak-to-average power ratio of the amplified modulated signal: in, represents the peak-to-average power ratio, represents the peak power of the spectrum of the class I signal sequence, represents the peak power of the spectrum of the rotated class II signal sequence, represents the peak power of the spectrum of the class III signal sequence, represents the peak power of the spectrum of the rotated class IV signal sequence, Indicates the peak power of the spectrum of the class V signal sequence, k ₁ denotes the amplification factor of the class I signal sequence, k ₂ denotes the amplification factor of the rotated class II signal sequence, k ₃ denotes the amplification factor of the class III signal sequence, k ₄ denotes the amplification factor of the class III signal sequence The amplification factor of the rotated class IV signal sequence, k ₅ represents the amplification factor of the class V signal sequence, represents the average power of the spectrum of the class I signal sequence, represents the average power of the spectrum of the rotated class II signal sequence, represents the average power of the spectrum of the class III signal sequence, represents the average power of the spectrum of the rotated class IV signal sequence, represents the average power of the spectrum of the class V signal sequence;

The coefficient proportional relationship formula determination unit is used to make the partial derivatives of the peak-to-average power ratio calculation formulas to each amplification factor equal to zero, and obtain the proportional relationship formula of each of the amplification coefficients:

The amplification factor determination unit is configured to determine each amplification factor according to the peak power, average power and the proportional relationship formula of various signal sequences.

FIG. 3 is a flow chart of the implementation of frequency offset estimation using the frequency offset estimation system for 32-ary quadrature amplitude modulation signals provided by the present invention. As shown in FIG. 3 , the implementation process of frequency offset estimation by the frequency offset estimation system for 32-ary quadrature amplitude modulation signal provided by the present invention is as follows:

(1) Obtain the received 32-ary quadrature amplitude modulation signal sequence.

Denote the nth received 32-QAM signal sequence as:

Among them, C _n is the transmitted 32-QAM signal, the constellation diagram is shown in Figure 4, L is the length of the 32-ary quadrature amplitude modulation signal sequence, n=0,1,...,L-1, φ _l,n is the phase noise described by the Wiener process, f _d is the frequency offset, T is the period of the 32-QAM signal, N _n is the amplified spontaneous emission (ASE) noise that describes the optical communication link, mathematically Modeled as complex additive white Gaussian noise.

As shown in Figure 4, there are 32 different constellation points in 32-QAM, which are located on 5 rings with different amplitudes, and the amplitudes are The four thresholds are the average values of the amplitudes of adjacent rings to distinguish the class to which they belong. in The 32-QAM signals can be divided into five categories of I, II, III, IV, and V by using the thresholds R ₁ , R ₂ , R ₃ and R ₄ in ascending order of amplitude. The received signal sequence can be represented as a row vector S=[S ₀ S ₁ . . . S _L-1 ]. Similarly, the signal sequence of class i is defined as where i∈{I,II,III,IV,V}.

(2) Rotate the class II signal sequence and the class IV signal sequence in the same direction by π/4 to obtain the rotated class II signal sequence and the rotated class IV signal sequence, and rotate according to the class I signal sequence, rotation The rotated quadrature amplitude modulation signal sequence determined by the latter class II signal sequence, the class III signal sequence, the rotated class IV signal sequence and the class V signal sequence.

When Sn ∈ class _i , otherwise n=0,1,...,L-1. Since there is no intersection between classes, that is, each signal can only belong to a certain class, so S=S ^I +S ^II +S ^III +S ^IV +S ^V and a 5×L matrix [(S ^I ) ^T (S ^II ) ^T (S ^III ) ^T (S ^IV ) ^T (S ^V ) ^T ] In any column of ^T , there must be an element equal to the signal in the same column in S, and the rest of the elements in this column are all zero, (·) ^T stands for transpose operation. Standard Class I and Class III signals form two Quadrature Phase Shift Keying (QPSK) constellations with different amplitudes, which allow data phases ±π/4 and ±3π/4 to be calculated by the power of 4 Remove all. However, classes II, IV and V are different. If the class II and IV signals are rotated by an angle of π/4, then all the constellation points will be gathered around the two diagonal lines with slopes equal to ±1, and the existing error can be regarded as noise. The rotated constellation diagram is shown as shown in Figure 5. Therefore, after the rotation process, all signals can substantially remove the phase of the modulated data using a power of 4 operation.

Selecting class II and class IV signals and rotating them by π/4 can be expressed as:

and

The signal sequence after rotation is defined as:

(3) Use five amplification coefficients to amplify various types of signals, so that the spectrum obtained in the next step has the maximum peak to average power ratio (PAPR), and this group of amplification coefficients is the optimal coefficient. The amplified signal sequence is defined as:

(4) For the signal sequence The fourth power of the FFT operation is performed, and the estimated value of the frequency offset is obtained by searching for the peak value of the spectrum

In the formula, is the signal sequence elements in .

It can be seen from equation (4) that the estimated value of the frequency offset is calculated from the frequency corresponding to the peak value of the spectrum amplitude. In the frequency domain, PAPR can be defined as:

where P and A are the peak power and average power of the spectrum, respectively.

The relationship between the average power of each signal is as follows:

use and Respectively S ^I , S ^III , and the row vector obtained by ^{exponentiating} each element in SV to the fourth power. Obviously, and a 5×L matrix In any column, there must be an element equal to elements in the same column, and the rest of the elements in that column are all zeros. Therefore, in the time domain, the signal The average power of is equal to the signal (S ^I ) ⁴ , (S ^III ) ⁴ , (S ^V ) The sum of the average powers of ⁴ . Transformed to the frequency domain, the relationship still holds and can be expressed as:

In the formula, A _x represents the average power of the spectrum of (x) ⁴ .

The relationship between the peak power of each signal is as follows:

If phase noise and ASE are not considered, then the mean value E[(S ^I ) ⁴ ] of each random signal in the time domain, E[(S ^III ) ⁴ ], and E[(S ^V ) ⁴ ] are negative real numbers, where E[x] represents the mathematical expectation of x. And because the mean in the time domain corresponds to the peak in the spectrum (located at frequency 4f _d ), the peaks of the complex form of their spectrum are in phase. According to the linearity of the FFT, the amplitude of the total peak is equal to the sum of the amplitudes of the individual peaks. Therefore, in theory, the relationship between peak power can be expressed as:

where P _x represents the peak power of the spectrum of (x) ⁴ . It should be noted that the condition that equation (7) satisfies is that there is no phase noise and ASE. If factors such as phase noise and ASE are considered, there will be

Substituting Equation (6) and Equation (7) into Equation (5), Equation (8) can be obtained:

Further, the PAPR of the amplified signal sequence can be expressed as:

To get the maximum value of Equation (9), let Available:

The peak power and average power of each signal in formula (10) can be measured experimentally, and then the proportional relationship between each amplification factor can be determined. After any one of the amplification factors is determined, the other four amplification factors can be determined according to formula (10).

In order to further test the performance of the frequency offset estimation method and system proposed by the present invention, a simulation study is carried out on a 10G baud rate 32-QAM system. In order to focus on the frequency offset estimation, only the frequency offset and ASE noise are considered in the simulation, but the effect of phase noise is not considered. The simulation results presented are all obtained at a relatively small data length (L=512).

Figure 6 shows the relationship between average power and signal-to-noise ratio for some signals. As can be seen from Figure 6, by the signal get the average power is equal to the average power obtained from equation (6) The correctness of formula (6) is fully proved. On the other hand, Figure 7 shows the relationship between the peak power of these signals and the signal-to-noise ratio. When SNR≥18dB, peak power is approximately equal to the peak power obtained from equation (7) In the low signal-to-noise ratio region, the phase of these signal spectral peaks is greatly affected by the ASE noise and is no longer in phase, making

Using the simulation results in Fig. 6 and Fig. 7 and equation (10), the optimal coefficients k ₁ , k ₂ , . . . , k ₅ under different signal-to-noise ratios can be obtained, and the results are shown in Fig. 8 . As mentioned before, the obtained optimal coefficients are only meaningful when SNR ≥ 18dB. When SNR=18dB, the optimal coefficients are k ₁ =3.6155, k ₂ =1.7029, k ₃ =1.4318, k ₄ =1.1422, k ₅ =1. A large number of numerical simulation results show that under this set of parameters, the proposed frequency offset estimation method can obtain the optimal performance of SNR threshold. Subsequent simulation results are obtained under these parameters, and will not be repeated one by one. Figure 9 gives and Numerical curves at different signal-to-noise ratios. Obviously, the method proposed in the present invention Significantly improved by rotating and zooming in. Affected by the number of FFT points, the frequency offset estimation resolution of the FFT-based frequency offset estimation method is Therefore, if in a simulation out of range It can be considered that the frequency offset estimation is wrong, otherwise the estimation is correct. Figure 10 shows the error probability curves for different signal-to-noise ratios. When the number of FFT points is only 512, the frequency offset estimation method (PAPRA-FFT-FOE) proposed in the present invention can achieve error-free frequency offset estimation under the condition that the signal-to-noise ratio is higher than 17dB, and shows better performance than other methods. Signal-to-noise ratio threshold performance. In order to more clearly reflect the accuracy of the frequency offset estimation, Figure 11 shows the normalized frequency variance (defined as relationship with the signal-to-noise ratio. It can be seen that the method proposed by the present invention has the smallest estimation error and the highest estimation accuracy.

Finally, Figure 12 presents the bit error rate curves for each method. For the convenience of comparison, FIG. 12 also gives the theoretical limit value of the bit error rate in the case of Additive White Gaussian Noise (AWGN). When the bit error rate (Bit Error Rate, BER) of the method proposed in the present invention is equal to 2×10 ^-2 , the required signal-to-noise ratio and the theoretical limit value are only 1dB signal-to-noise ratio cost. This also fully proves that the frequency offset estimation method provided by the present invention has higher estimation accuracy than other methods. In the simulation, the quasi-QPSK partitioning and cross-constellation transform (CCT) method is used for the phase recovery method, and the block lengths are 128 and 32, respectively.

The computational complexity of the method proposed by the present invention can be measured by the number of real multiplication, real addition and comparison operations used. Table 1 presents the results of the complexity analysis of these methods. Edge effects independent of the data length L are ignored in the calculation. Compared with the traditional FFT-FOE method, the PAPRA-FFT-FOE method proposed by the present invention increases the operations of selection, rotation and enlargement, and the operation amount is increased. Specifically, it requires (i) 2 real multipliers and 1 real adder to calculate the amplitude of each signal; the number of comparators is: 1×4/32+2×8/32+3×4/ 32+4×8/32+4×8/32=3, that is, 3 comparators are needed to compare the magnitude relationship between the amplitude of each signal and the threshold to determine which class the signal belongs to; (ii) 2 real multipliers to amplify the magnitude of each Class I and Class III signal (with probability 8/32); 4 real multipliers and 2 real adders to rotate and amplify each Class II and Class IV signal (with probability 16/32) ; No real multipliers and real adders are required for class V signals (probability 8/32). Compared with other methods, the PAPRA-FFT-FOE method proposed in the present invention only increases a small amount of computational burden but obtains a significant improvement in estimation accuracy and signal-to-noise ratio threshold performance.

Table 1. Computational Complexity

It can be seen that, for the 32-QAM coherent optical system, the present invention can realize high-precision frequency offset estimation using only 512 signals, and has good signal-to-noise ratio threshold performance.

The various embodiments in this specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments, and the same and similar parts between the various embodiments can be referred to each other. For the system disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant part can be referred to the description of the method.

In this paper, specific examples are used to illustrate the principles and implementations of the present invention. The descriptions of the above embodiments are only used to help understand the methods and core ideas of the present invention; meanwhile, for those skilled in the art, according to the present invention There will be changes in the specific implementation and application scope. In conclusion, the contents of this specification should not be construed as limiting the present invention.

Claims (8)

1. A frequency offset estimation method for a 32-ary quadrature amplitude modulation signal, the frequency offset estimation method comprising:

acquiring a received 32-ary quadrature amplitude modulation signal sequence, wherein the 32-ary quadrature amplitude modulation signal sequence comprises: a class I signal sequence, a class II signal sequence, a class III signal sequence, a class IV signal sequence, and a class V signal sequence;

rotating the II-type signal sequence and the IV-type signal sequence in the same direction by pi/4 to obtain a rotated II-type signal sequence and a rotated IV-type signal sequence;

determining a rotation modulation signal sequence which is a quadrature amplitude modulation signal sequence determined according to the class I signal sequence, the rotated class II signal sequence, the rotated class III signal sequence, the rotated class IV signal sequence and the rotated class V signal sequence;

obtaining amplification coefficients corresponding to various signal sequences with the maximum peak-to-average power ratio, and amplifying the rotation modulation signal sequences according to the amplification coefficients to obtain amplification modulation signal sequences;

performing fast Fourier transform on the fourth power of the amplified and modulated signal sequence to obtain a discrete frequency spectrum;

determining the frequency corresponding to the peak value of the spectrum amplitude according to the discrete spectrum;

and determining the frequency offset estimation value of the 32-system quadrature amplitude modulation signal sequence according to the frequency.

2. The frequency offset estimation method according to claim 1, wherein the method for determining the amplification factor corresponding to each class of signal sequence having the largest peak-to-average power ratio comprises:

obtaining a peak-to-average power ratio calculation formula of the amplified modulation signal:

wherein,it is shown that the peak-to-average power ratio,represents the peak power of the spectrum of the class I signal sequence,representing the peak power of the spectrum of the rotated class II signal sequence,representing the peak power of the spectrum of the class III signal sequence,represents the peak power of the spectrum of the rotated class IV signal sequence,peak power, k, representing the frequency spectrum of a class V signal sequence₁Representing the amplification factor, k, of a class I signal sequence₂Representing the amplification factor, k, of the rotated class II signal sequence₃Representing the amplification factor, k, of a class III signal sequence₄Represents the amplification factor, k, of the rotated class IV signal sequence₅Represents the amplification factor of a class V signal sequence,represents the average power of the spectrum of the class I signal sequence,represents the average power of the spectrum of the rotated class II signal sequence,represents the average power of the spectrum of the class III signal sequence,represents the average power of the spectrum of the rotated class IV signal sequence,an average power representing the spectrum of the class V signal sequence;

respectively making the partial derivatives of the peak-to-average power ratio calculation formula on each amplification coefficient equal to zero to obtain a proportional relation formula of each amplification coefficient:

and determining each amplification factor according to the peak power and the average power of each type of signal sequence and the proportional relation.

3. The frequency offset estimation method according to claim 1, wherein determining the frequency offset estimation value of the 32-ary qam signal sequence according to the frequency specifically includes:

according to the formula:determining a frequency offset estimate of the 32-ary quadrature amplitude modulation signal sequence, wherein,representing the estimated value of the frequency offset, L represents the length of the 32-ary quadrature amplitude modulation signal sequence,denotes the nth element in the amplified modulated signal sequence, n denotes the serial number of the amplified modulated signal sequence, f denotes the frequency of the fourier spectrum, and T denotes the period of the 32-ary quadrature amplitude modulated signal.

4. The frequency offset estimation method according to claim 1, wherein the rotating the class II signal sequence and the class IV signal sequence by pi/4 in the same direction to obtain a rotated class II signal sequence and a rotated class IV signal sequence specifically comprises:

rotating the II-type signal sequence by pi/4 in the anticlockwise direction to obtain a rotated II-type signal sequence;

and rotating the IV signal sequence by pi/4 in the anticlockwise direction to obtain the rotated IV signal sequence.

5. A frequency offset estimation system for a 32-ary quadrature amplitude modulated signal, the frequency offset estimation system comprising:

a signal sequence obtaining module, configured to obtain a received 32-ary qam signal sequence, where the 32-ary qam signal sequence includes: a class I signal sequence, a class II signal sequence, a class III signal sequence, a class IV signal sequence, and a class V signal sequence;

the rotation processing module is used for rotating the II-type signal sequence and the IV-type signal sequence in the same direction by pi/4 to obtain a rotated II-type signal sequence and a rotated IV-type signal sequence;

a rotation modulation signal determining module, configured to determine a rotation modulation signal sequence, where the rotation modulation signal sequence is a quadrature amplitude modulation signal sequence determined according to the class I signal sequence, the rotated class II signal sequence, the rotated class III signal sequence, the rotated class IV signal sequence, and the rotated class V signal sequence;

the amplification processing module is used for acquiring amplification coefficients corresponding to various signal sequences with the maximum peak-to-average power ratio, and amplifying the rotation modulation signal sequences according to the amplification coefficients to obtain amplification modulation signal sequences;

the Fourier transform module is used for carrying out fast Fourier transform on the fourth power of the amplified and modulated signal sequence to obtain a discrete frequency spectrum;

the frequency determining module is used for determining the frequency corresponding to the peak value of the spectrum amplitude according to the discrete spectrum;

and the frequency offset estimation value determining module is used for determining the frequency offset estimation value of the 32-system quadrature amplitude modulation signal sequence according to the frequency.

6. The frequency offset estimation system according to claim 5, further comprising an amplification factor determination module for determining the amplification factor corresponding to each class of signal sequence that maximizes the peak-to-average power ratio, wherein the amplification factor determination module comprises:

peak to average power ratioA taking unit, configured to obtain a peak-to-average power ratio calculation formula of the amplified modulation signal:wherein,it is shown that the peak-to-average power ratio,represents the peak power of the spectrum of the class I signal sequence,representing the peak power of the spectrum of the rotated class II signal sequence,representing the peak power of the spectrum of the class III signal sequence,represents the peak power of the spectrum of the rotated class IV signal sequence,peak power, k, representing the frequency spectrum of a class V signal sequence₁Representing the amplification factor, k, of a class I signal sequence₂Representing the amplification factor, k, of the rotated class II signal sequence₃Representing the amplification factor, k, of a class III signal sequence₄Represents the amplification factor, k, of the rotated class IV signal sequence₅Represents the amplification factor of a class V signal sequence,represents the average power of the spectrum of the class I signal sequence,representing rotated class II signalsThe average power of the frequency spectrum of the sequence,represents the average power of the spectrum of the class III signal sequence,represents the average power of the spectrum of the rotated class IV signal sequence,an average power representing the spectrum of the class V signal sequence;

a coefficient proportional relation determining unit, configured to make the partial derivatives of the peak-to-average power ratio calculation formulas for the respective amplification coefficients equal to zero, and obtain proportional relations of the respective amplification coefficients:

and the amplification factor determining unit is used for determining each amplification factor according to the peak power, the average power and the proportional relation of each type of signal sequence.

7. The frequency offset estimation system of claim 5 wherein said frequency offset estimate determination module determines the frequency offset estimate based on the formula:determining a frequency offset estimate of the 32-ary quadrature amplitude modulation signal sequence, wherein,representing the estimated value of the frequency offset, L represents the length of the 32-ary quadrature amplitude modulation signal sequence,representing the nth element of the sequence of amplified modulated signals, n representing the sequence of amplified modulated signalsThe sign, f, denotes the frequency of the fourier spectrum, and T denotes the period of the 32-ary quadrature amplitude modulation signal.

8. The frequency offset estimation system of claim 5 wherein said rotation processing module comprises:

the II-type anticlockwise rotation unit is used for rotating the II-type signal sequence by pi/4 in the anticlockwise direction to obtain a rotated II-type signal sequence;

and the IV-class anticlockwise rotation unit is used for rotating the IV-class signal sequence by pi/4 in the anticlockwise direction to obtain the rotated IV-class signal sequence.