CN110278170B - Short wave communication frequency offset estimation method based on maximum likelihood - Google Patents

Short wave communication frequency offset estimation method based on maximum likelihood Download PDF

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CN110278170B
CN110278170B CN201910631108.3A CN201910631108A CN110278170B CN 110278170 B CN110278170 B CN 110278170B CN 201910631108 A CN201910631108 A CN 201910631108A CN 110278170 B CN110278170 B CN 110278170B
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frequency offset
sequence
offset estimation
data
frequency
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CN110278170A (en
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张凯
陈测库
王小军
仇妙月
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Shaanxi Fenghuo Communication Group Co Ltd
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00—Modulated-carrier systems
    • H04L27/0014—Carrier regulation
    • 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
    • H04L27/2649—Demodulators
    • H04L27/265—Fourier transform demodulators, e.g. fast Fourier transform [FFT] or discrete Fourier transform [DFT] demodulators
    • 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
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00—Modulated-carrier systems
    • H04L27/0014—Carrier regulation
    • H04L2027/0024—Carrier regulation at the receiver end
    • H04L2027/0026—Correction of carrier offset

Abstract

The invention discloses a short wave communication frequency offset estimation method based on maximum likelihood, which comprises the following specific steps: the transmitting terminal transmits data to be transmitted by a user, and the data to be transmitted by the user and a synchronous sequence at the front end of the data to be transmitted form a data frame structure; the data frame structure is subjected to digital up-conversion processing to obtain a transmitting data sequence; transmitting data sequences, transmitting the data sequences through a short wave channel and synchronously sampling, and obtaining receiving data sequences at a receiving end; and carrying out frequency offset estimation on the received data sequence by adopting a maximum likelihood criterion to obtain a frequency offset estimation value of the received data sequence. The invention solves the problems of rotation of signal phase, uncorrectable error, rapid deterioration of system performance and the like caused by large error; the estimation precision is improved, and meanwhile, the channel estimation is not needed, so that the calculation complexity is greatly reduced; meanwhile, the frequent change of the crystal oscillation frequency of the receiver is avoided, and the equipment cost is not required to be increased.

Description

Short wave communication frequency offset estimation method based on maximum likelihood
Technical Field
The invention belongs to the technical field of short-wave communication, and particularly relates to a frequency offset estimation method for short-wave communication based on maximum likelihood.
Background
Short-wave communication refers to a radio communication technology with a wavelength of 100-10 m and a frequency range of 3-30 MHz. The electric wave transmitted by short wave communication can reach the receiving end only by the reflection of the ionized layer, and the communication distance is long, which is the main means of remote communication. Despite the continuous emergence of new radio communication systems, the ancient and traditional communication method of short-wave communication is still receiving universal attention all over the world, and not only is not eliminated, but also is continuously and rapidly developed, because it has the advantages that other communication systems do not have: first, shortwave is the only means of telecommunications that is not constrained by networks and relays. For example, in the case of war or disaster, when the satellite is attacked, the short-wave survivability and the autonomous communication ability cannot be compared favorably with other communication equipment; secondly, communication in remote areas such as mountainous areas, Gobi areas and oceans mainly depends on short waves; finally, the low communication costs also make shortwaves have a broad market.
In order to facilitate information transmission during short-wave communication, a low-frequency signal carrying information is usually up-converted to a high-frequency signal with a frequency range of 3MHz to 30MHz at a transmitting end, and a high-frequency carrier is required in the process. After channel transmission, in order to extract useful information, a receiving end needs to down-convert a received high-frequency signal to a low-frequency signal, and a high-frequency carrier with the same frequency as that of a transmitting end is needed in the process. However, due to the influence of the manufacturing process of the electronic components, the wiring of the circuit board and other factors, the carrier frequencies generated at the transmitting end and the receiving end cannot be completely the same, and an error always exists. When this error is small, the receiver can receive and demodulate the signal normally, but its performance can be greatly degraded; when the error is large, the phase of the signal is rotated, which generates an uncorrectable error, and the performance of the communication system is rapidly deteriorated.
In a patent with application number CN201010608140.9 entitled "a method and apparatus for frequency offset estimation", frequency offset precompensation is performed on received data through a historical frequency offset value; performing channel estimation and frequency offset estimation on the compensated data to obtain a first frequency offset estimation value of the current subframe; and performing secondary frequency offset compensation on the data subjected to the frequency offset pre-compensation by using the first frequency offset estimation value of the current subframe. In the estimation method, channel estimation is required during frequency offset estimation, which increases the calculation amount. In a patent with application number CN201310283549.1 entitled "a method for estimating and compensating frequency offset", when the adjustment period of the crystal oscillator in the second half of the received radio frame reaches, the frequency offset Δ f estimated by the current frame is used to adjust the frequency of the crystal oscillator, thereby eliminating the frequency offset. Although the method does not need channel estimation, the frequency of the crystal oscillator of the receiver needs to be continuously changed to achieve the purpose of removing frequency deviation, so that the crystal oscillator is required to be a controllable oscillator, the requirement on the oscillator is very high, and the equipment cost is increased.
Disclosure of Invention
In order to solve the above problems, the present invention aims to provide a method for estimating frequency offset of short-wave communication based on maximum likelihood, which solves the problems of rotation of signal phase, generation of uncorrectable error, rapid deterioration of system performance and the like caused by large error; the estimation precision is improved, and meanwhile, the channel estimation is not needed, so that the calculation complexity is greatly reduced; meanwhile, the frequent change of the crystal oscillation frequency of the receiver is avoided, and the equipment cost is not required to be increased.
The technical principle of the invention is as follows: aiming at the performance deterioration caused by frequency errors (frequency offset for short) at the receiving and transmitting ends, before demodulation is carried out after down-conversion, the maximum likelihood criterion is adopted to carry out frequency offset estimation on signals, the frequency offset is artificially removed from the down-converted signals, and then the data entering a demodulator is frequency offset-free data.
In order to achieve the above object, the present invention is achieved by the following means.
The short wave communication frequency offset estimation method based on the maximum likelihood comprises the following steps:
step 1, a transmitting terminal transmits data to be transmitted by a user, wherein the data to be transmitted by the user and a synchronous sequence at the front end of the data to be transmitted by the user form a data frame structure; the data frame structure is subjected to digital up-conversion processing to obtain a transmitting data sequence;
step 2, the transmitting data sequence is transmitted through a short wave channel and synchronously sampled, and a receiving data sequence is obtained at a receiving end;
and 3, carrying out frequency offset estimation on the received data sequence by adopting a maximum likelihood criterion to obtain a frequency offset estimation value of the received data sequence.
Further, the synchronization sequence C is generated by modulating a pseudo-random sequence; and C ═ C0,…,cj,…,cn-1)，cjJ data indicating a sync sequence, and n is the length of the sync sequence.
Furthermore, the short wave channel has p + q +1 orders, wherein p orders are arranged in front of the main path, and q orders are arranged behind the main path; the short wave channel has the characteristic of H (j delta t) ═ H at the j delta t moment-p(j△t),…,h0(j△t),…,hq(j△t)]，h-p(j Δ t) represents the characteristic of the-p-th order of the short-wave channel at the time j Δ t, Δ t being the time interval between two transmitted symbols,
Figure GDA0003472281180000031
Rsymis the transmission baud rate of the transmitting end.
Further, the received data sequence R ═ (R)0,…,rj,…,rn-1)，
Figure GDA0003472281180000032
0≤j<n; wherein r'z＝h-p(z△t)xp+z+…+h-1(z△t)x1+z+h0(z△t)xz+h1(z△t)x-1+z+…+hq(z△t)x-q+z+wz，(-p≤z<n + q), when z is>0 r'z＝r'j；
Figure GDA0003472281180000033
xjIs the jth data of a pseudo-random sequence, and xj＝{0,1}；wzObeying a mean of 0 and a variance of σ2Is normally distributed, two-dimensional noise sample values.
Further, the frequency offset estimation of the received data sequence by using the maximum likelihood criterion includes the following specific steps:
3.1 setting the likelihood function of the frequency offset estimation to
Figure GDA0003472281180000041
3.2, converting the problem of frequency deviation estimation of the received data sequence by adopting the maximum likelihood criterion into solving likelihood function
Figure GDA0003472281180000042
Maximum time frequency deviation estimated value fbias(ii) a The frequency offset estimation formula based on the likelihood function is obtained as follows:
Figure GDA0003472281180000043
3.3, setting the prior probability and the posterior probability of each frequency deviation estimation value to be equal, the frequency deviation estimation formula based on the likelihood function can be written as the following form:
Figure GDA0003472281180000044
solving a frequency deviation estimation formula based on a likelihood function to obtain a frequency deviation estimation value f of a received data sequence bias(ii) a Wherein the content of the first and second substances,
Figure GDA0003472281180000045
Figure GDA0003472281180000046
denotes the prior probability of frequency offset, p (R) denotes the probability of reception of the received data sequence R,
Figure GDA0003472281180000047
is the a posteriori probability of the frequency offset.
Further, the solving of the frequency offset estimation formula based on the likelihood function is performed according to the following steps:
(a) calculating the frequency resolution D, and dividing the frequency resolution D into m equal parts to obtain the frequency stepping length D:
Figure GDA0003472281180000048
wherein N is the number of points of fast Fourier transform;
(b) let i be an index variable and initialize it to i-0;
(c) calculating the frequency offset of the ith section;
first, an offset sequence is calculated
Figure GDA0003472281180000049
Wherein
Figure GDA00034722811800000410
Secondly, the synchronization sequence C and the Fourier transform method are adopted to carry out RiPerforming frequency offset estimation to obtain the i-th frequency offset
Figure GDA00034722811800000411
And its corresponding amplitude Vi；
Finally, adding 1 to the index variable i, and judging the sizes of i and m; if i < m, skipping to step c); otherwise, entering the step (d);
(d) find magnitude vector V ═ V0,…Vi,…Vm-1) Index number I corresponding to the medium maximum value and frequency deviation estimation value corresponding to the index number I
Figure GDA0003472281180000051
(e) Computing
Figure GDA0003472281180000052
And will be
Figure GDA0003472281180000053
Frequency offset estimation f as a received sequencebias。
Further, the pair R adopts a synchronization sequence C and a fast Fourier transform methodiPerforming frequency offset estimation, which specifically comprises:
first, according to the offset sequence
Figure GDA0003472281180000054
And the synchronization sequence C ═ C0,…,cj,…,cn-1) And constructing a quasi-sinusoidal signal sequence:
Figure GDA00034722811800000511
Wherein
Figure GDA0003472281180000055
Secondly, aligning the sinusoidal signal sequence
Figure GDA0003472281180000056
Performing fast Fourier transform of N points and estimating range of frequency offset [ -f [ ]max,fmax]In the interior, the maximum value V of the amplitude is foundiAnd corresponding frequency
Figure GDA0003472281180000057
Further, the aligned sinusoidal signal
Figure GDA0003472281180000058
Performing a fast fourier transform of N points: when N is more than or equal to N, intercepting quasi-sinusoidal signal sequence
Figure GDA0003472281180000059
Performing fast Fourier transform on the first N data; when n is<At N time, in a quasi-sinusoidal signal sequence
Figure GDA00034722811800000510
Adding (N-N) data 0 at the end of the signal sequence to obtain a quasi-sinusoidal signal sequence with the length of N, and then carrying out fast Fourier transform on the quasi-sinusoidal signal sequence with the length of N.
Compared with the prior art, the invention has the beneficial effects that:
(1) the invention solves the problem of larger frequency deviation estimation error caused by discrete frequency spectrum through the maximum likelihood criterion without increasing the number of Fast Fourier Transform (FFT) points, greatly improves the frequency resolution, reduces the frequency deviation estimation error, does not need to carry out channel estimation, greatly reduces the calculation complexity, and greatly improves the estimation precision on the premise of not increasing the hardware complexity.
(2) The invention adopts the maximum likelihood criterion to estimate the frequency deviation, introduces the concept of frequency stepping length, estimates the frequency deviation of the offset sequences with different stepping lengths, and has wide application range; according to the resource amount of the short wave communication system, on the premise of meeting the requirement on frequency resolution, a smaller FFT point number is selected, so that the resource space of the system is saved.
Drawings
The invention is described in further detail below with reference to the figures and specific embodiments.
FIG. 1 is a flow chart of an implementation of the present invention;
FIG. 2 is a schematic diagram of a data frame structure in the present invention;
FIG. 3 is a time-varying characteristic diagram of a short-wave channel with fading parameters of 2ms/1Hz in the embodiment;
FIG. 4 is a graph comparing frequency spectra corresponding to different frequency offset values according to an embodiment of the present invention;
FIG. 5 is a diagram illustrating an embodiment of the present invention in which the frequency resolution is divided into m equal parts;
FIG. 6 is a diagram of a power spectrum of a short-wave baseband signal according to an embodiment of the present invention;
FIG. 7 is a statistical histogram of frequency offset estimation values under SNR of-5 dB according to the method of the present invention and the conventional fast Fourier transform;
FIG. 8 is a graph of standard deviation and signal-to-noise ratio of estimation errors for different partition parameters in an embodiment of the present invention;
fig. 9 is a diagram of frequency offset estimation results of different FFT points in the embodiment of the present invention.
Detailed Description
The embodiments and effects of the present invention will be described in further detail below with reference to the accompanying drawings.
Referring to fig. 1, a flowchart of a method for estimating frequency offset of short-wave communication based on maximum likelihood according to the present invention is shown, and the method includes the following steps:
step 1, a transmitting terminal transmits data to be transmitted by a user, and the data to be transmitted by the user and a synchronous sequence at the front end of the data to be transmitted form a data frame structure; the data frame structure is subjected to digital up-conversion processing to obtain a transmitting data sequence;
The data frame of the maximum likelihood frequency offset estimation method suitable for short-wave communication has a structure as shown in fig. 2. The synchronization sequence is formed by modulating a pseudo-random sequence, and the data segment is information to be transmitted by a user. The synchronization sequence functions as a determination of a synchronization point, frequency offset estimation, channel estimation, and the like. The following describes how to perform frequency offset estimation by taking a Binary Phase Shift Key (BPSK) modulated baseband communication system as an example.
Specifically, assume that the pseudorandom sequence X ═ X (X)0,…,xj,…,xn-1),xjBPSK-modulated {0,1} to obtain (C) synchronization sequence C0,…,cj,…,cn-1) Wherein c isj＝1-2×xj. The transmission baud rate (number of symbols transmitted per unit time) is RsymOne symbol/second, the time interval for transmitting adjacent symbols is
Figure GDA0003472281180000071
Second; the synchronization sequence is followed by a data segment of the same modulation scheme.
Step 2, the transmitting data sequence is transmitted through a short wave channel and synchronously sampled, and a receiving data sequence is obtained at a receiving end;
the information complying with the frame format in step 1 is transmitted via a short-wave channel, and the received data sequence received at the receiving end is the received data sequence R ═ (R)0,…,rj,…,rn-1)，
Figure GDA0003472281180000072
0≤j<n; wherein r'z＝h-p(z△t)xp+z+…+h-1(z△t)x1+z+h0(z△t)xz+h1(z△t)x-1+z+…+hq(z△t)x-q+z+wz，(-p≤z<n + q), when z is>0 r'z＝r'j；
Figure GDA0003472281180000073
xjIs the jth data of a pseudo-random sequence, and x j＝{0,1}；wzObeying a mean of 0 and a variance of σ2Is normally distributed, two-dimensional noise sample values.
The short wave channel has p + q +1 orders, wherein p orders are arranged in front of the main path, and q orders are arranged behind the main path; the short-wave channel has the characteristic of H (j delta t) ═ H at the j delta t moment-p(j△t),…,h0(j△t),…,hq(j△t)]，h-p(j Δ t) represents the characteristic of the-p-th order of the short-wave channel at the time j Δ t, Δ t being the time interval between two transmitted symbols,
Figure GDA0003472281180000074
Rsymis a transmitting endThe transmission baud rate of.
Short wave transmission channels are characterized by changes over time, which not only cause fading of the signal, but also produce a doppler spectrum. As shown in fig. 3, a characteristic diagram of a short wave channel (real part) with a two-path fading parameter of 2ms/1Hz is shown, and the average fading of each path is 0 dB. Two paths are parameters, 2ms is a time interval between the two paths, 1Hz is a doppler spectrum bandwidth of 1Hz caused by relative motion of the transceiver and multi-angle reflection, and it can be simply understood that the larger the value is, the faster the channel change is.
And 3, carrying out frequency offset estimation on the received data sequence by adopting a maximum likelihood criterion to obtain a frequency offset estimation value of the received data sequence. The method specifically comprises the following substeps:
3.1 setting the likelihood function of the frequency offset estimation to
Figure GDA0003472281180000081
3.2, converting the problem of frequency deviation estimation of the received data sequence by adopting the maximum likelihood criterion into solving likelihood function
Figure GDA0003472281180000082
Maximum time frequency deviation estimated value fbias(ii) a The frequency offset estimation formula based on the likelihood function is obtained as follows:
Figure GDA0003472281180000083
3.3, setting the prior probability and the posterior probability of each frequency deviation estimation value to be equal, the frequency deviation estimation formula based on the likelihood function can be written as the following form:
Figure GDA0003472281180000084
solving a frequency deviation estimation formula based on a likelihood function to obtain a frequency deviation estimation value f of a received data sequencebias；
Wherein the content of the first and second substances,
Figure GDA0003472281180000085
Figure GDA0003472281180000086
denotes the prior probability of frequency offset, p (R) denotes the probability of reception of the received data sequence R,
Figure GDA0003472281180000087
is the a posteriori probability of the frequency offset.
Specifically, solving a frequency offset estimation formula based on a likelihood function is implemented according to the following steps:
(a) calculating the frequency resolution D, and dividing the frequency resolution D into m equal parts to obtain the frequency stepping length D:
Figure GDA0003472281180000091
wherein N is the number of points of fast Fourier transform;
(b) let i be an index variable and initialize it to i-0;
(c) calculating the frequency offset of the ith section;
first, an offset sequence is calculated
Figure GDA0003472281180000092
Wherein
Figure GDA0003472281180000093
Secondly, the synchronization sequence C and the Fourier transform method are adopted to carry out RiPerforming frequency offset estimation to obtain the i-th frequency offset
Figure GDA0003472281180000094
And its corresponding amplitude Vi；
Finally, adding 1 to the index variable i, and judging the sizes of i and m; if i < m, skipping to step c); otherwise, entering the step (d);
(d) Find magnitude vector V ═ (V)0,…Vi,…Vm-1) Index number I corresponding to the medium maximum value and frequency deviation estimation value corresponding to the index number I
Figure GDA0003472281180000095
(e) Calculating out
Figure GDA0003472281180000096
And will be
Figure GDA0003472281180000097
Frequency offset estimation f as a received sequencebias。
Further, the pair R adopts a synchronization sequence C and a fast Fourier transform methodiPerforming frequency offset estimation, which specifically comprises:
first, according to the offset sequence
Figure GDA0003472281180000098
And the synchronization sequence C ═ C0,…,cj,…,cn-1) And constructing a quasi-sinusoidal signal sequence:
Figure GDA0003472281180000099
wherein
Figure GDA00034722811800000910
Secondly, aligning the sinusoidal signal sequence
Figure GDA00034722811800000911
Performing fast Fourier transform of N points and estimating range of frequency offset [ -f [ ]max,fmax]In the interior, the maximum value V of the amplitude is foundiAnd corresponding frequency
Figure GDA00034722811800000912
Wherein, when N is more than or equal to N, the quasi-sinusoidal signal sequence is intercepted
Figure GDA0003472281180000101
Fast Fourier transform of the first N dataTransforming; when n is<At N, in quasi-sinusoidal signal sequence
Figure GDA0003472281180000102
Adding (N-N) data 0 at the end of the signal sequence to obtain a quasi-sinusoidal signal sequence with the length of N, and then carrying out fast Fourier transform on the quasi-sinusoidal signal sequence with the length of N.
The following illustrates the advantages and disadvantages of the conventional FFT method and the method of the present invention:
for the conventional FFT method, FFT is a common method in the signal processing field, and has the advantages of simplicity and rapidity, and the essence is to calculate the discrete spectrum of the sequence. The frequency offset estimation precision is specifically analyzed as follows:
Assume that it is based on the received data sequence R ═ R (R)0,…,rj,…,rn-1) And C ═ C0,…,cj,…,cn-1) Constructing quasi-sinusoidal signals
Figure GDA0003472281180000103
Wherein
Figure GDA0003472281180000104
(0≤j<n); aligning sinusoidal signals
Figure GDA0003472281180000105
After N-point FFT, the frequency resolution
Figure GDA0003472281180000106
The observable frequency range is-fFFTHz～fFFTHz, wherein
Figure GDA0003472281180000107
That is, only kD (k is between) can be observed after FFT
Figure GDA0003472281180000108
Or (c) or only approximately reflect the magnitude of the probability of obtaining the respective possible frequency offset value kD based on the received data sequence R, i.e.
Figure GDA0003472281180000109
If the true frequency deviation fbiasNot equal to kD, an estimation error occurs after FFT.
For example, a short wave communication system Rsym＝2.048×103Symbol/s, FFT point N is 128, and frequency resolution D is 16 Hz. When the real frequency offset values are 80H and 88Hz, respectively, the FFT-transformed spectrum is shown in fig. 4.
It can be seen from fig. 4 that when the frequency offset value is 80Hz (i.e. the frequency offset value is an integral multiple of the frequency resolution), there is a unique peak at 80Hz, and the other frequency points are all 0, i.e. the frequency offset value is an integer multiple of the frequency resolution
Figure GDA00034722811800001010
At the maximum, the estimated quantity is considered to be 80 Hz; when the frequency offset value is 88Hz (i.e. the frequency offset value is a non-integral multiple of the frequency resolution), peaks with different amplitudes exist at a plurality of frequency points, and the amplitude corresponding to 96Hz is the maximum, the frequency offset value is considered to be 88Hz
Figure GDA00034722811800001011
At maximum, 96Hz is therefore selected as the frequency offset estimate, with an error of 8Hz between 96Hz and the true 88 Hz.
Generally, to reduce estimation error (i.e. to improve frequency resolution) can be implemented by increasing the number of points of FFT. However, in practical applications, the upper limit of the FFT point is limited due to objective conditions such as the amount of calculation, the storage space, and the operation speed, and therefore, the estimation error cannot be reduced simply by this method in the actual frequency offset estimation.
The frequency offset estimation precision of the method of the invention is specifically analyzed as follows:
assuming that the true frequency offset is kD + id, (0 ≦ i)<m). When the artificially added offset frequency is (m-i) × D, the total frequency offset contained in the offset sequence is exactly (k +1) D. At the moment, the total frequency offset and the corresponding peak value V can be accurately estimated by utilizing a frequency offset estimation algorithm based on Fourier transform(m-i)×d(ii) a And then subtracting the artificially added offset component from the total offset to obtain the true frequency offset of the original sequence. If a personFor an added offset frequency around (m-i) × D (e.g., (m-i +1) × D), a total frequency offset of (k +1) D and a corresponding maximum peak of V can also be estimated using a fourier transform-based frequency offset estimation algorithm(m-i+1)×d(in this case there would be multiple peaks, as shown in FIG. 4), but V(m-i+1)×d<V(m-i)×dThe method of the present invention selects the index number I as m-I and the estimation value corresponding to the index number I
Figure GDA0003472281180000111
Then the final estimated value is obtained through the step 5
Figure GDA0003472281180000112
The results are shown in FIG. 5.
As can be seen from fig. 5, compared with the frequency offset estimation method of the conventional fourier transform, the method of the present invention has greatly reduced error, the higher the equal division parameter m is, the higher the accuracy is, and when m is 1, the frequency offset estimation algorithm based on the maximum likelihood criterion is degenerated to the frequency offset estimation algorithm based on the fourier transform.
In addition, the method of the invention is applicable to various modulation modes: such as QPSK, 8PSK, QAM, etc., in this embodiment, in order to visually show the method flow of the present invention, BPSK modulation is used to describe the whole estimation process.
Simulation experiment
In order to verify the performance of the method, baseband simulation of which the modulation mode is BPSK is performed, wherein pulse shaping after BPSK modulation selects a raised cosine pulse function with the coefficient of 0.4.
The short wave channel parameters are as follows: the double paths are 2ms/1Hz, and the average fading of each path is 0 dB; the sending Baud rate is 2400 Baud/S; the signal-to-noise ratio in simulation is defined as
Figure GDA0003472281180000121
The unit is dB, wherein EsIn order for the received energy of the symbol to be,
Figure GDA0003472281180000122
σ2is a two-dimensional white gaussian noise variance superimposed on the channel. FIG. 6 is a drawing showingAnd generating a short-wave baseband signal power spectrum according to the parameters.
Simulation 1
The method and the traditional fast Fourier transform method are respectively adopted to estimate the frequency offset under the condition that the SNR is-5 dB. 10000 times of simulation are respectively carried out on the two methods, wherein the number of fast fourier transform points is 128 points, the equal division parameter m is 8, the frequency deviation of each time is randomly set in the range of [ -100,100] Hz, the frequency deviation estimation results of the two methods and the error of the real frequency deviation are drawn into a histogram, and the result is shown in fig. 7.
It can be seen from fig. 7 that both methods give errors that swing around 0Hz and that the amplitude of the swing based on the fast fourier transform method is larger than the method of the invention. Meanwhile, the estimation results of the two methods are similar to the Gaussian distribution, so that the quality of the estimation can be evaluated by using the parameters (mean value and standard deviation) describing the Gaussian distribution. The mean value reflects the accuracy of the estimated value from the statistical angle, the standard deviation reflects the dispersion degree of the estimated value, and the larger the standard deviation is, the more dispersed the estimated result is. For example, the results given in simulation 1 are: (1) based on the fast Fourier transform method: the mean error was-0.2812 Hz and the standard deviation was 5.8291 Hz. I.e., the probability of the error falling within the range of-0.2812 ± 3 × 5.8291Hz is 0.9974. (2) The method comprises the following steps: the mean error was-0.1453 Hz and the standard deviation was 2.8576Hz, i.e., the probability of the error falling within the range of-0.1453. + -. 3X 2.8576Hz was 0.9974. As can be seen from the above analysis, the mean value of the frequency offset values estimated by the two methods is basically the same as the true value, but the concentration degree of the errors estimated by the method of the present invention is far higher than that of the fast Fourier transform method.
Simulation 2
And (5) investigating the influence on the estimation performance of the method when the parameter m takes different values. The number of fast Fourier transform points is set to be 128 points, and m is taken to be 1, 2, 4 and 8 respectively to carry out simulation under different signal to noise ratios. The mean value of the estimated frequency offset is substantially the same as the true value, and the standard deviation of the estimation error is counted, and the curve is shown in fig. 8. As can be seen from FIG. 8, no matter what value the equal division parameter m takes, the method of the present invention can be converged quickly; in the range of low signal-to-noise ratio, the estimated standard deviation of the error is rapidly reduced along with the increase of the signal-to-noise ratio; in the high snr range, the snr increase does not effectively reduce the standard deviation. Under the same signal-to-noise ratio, the estimated standard deviation of the error is reduced along with the increase of the equal division parameter m.
Emulation 3
When the method of the present invention is used to estimate the frequency offset, in order to obtain a more concentrated estimation result (higher concentration/smaller standard deviation) under a high signal-to-noise ratio, a method of increasing the number of FFT points may be adopted to achieve the estimation under the condition that hardware conditions allow. Here, the influence of different FFT point numbers (128 points and 512 points) on the estimation result under different signal-to-noise ratios is simulated by the same partition parameter m being 8, and the simulation result is shown in fig. 9.
It can be seen from the figure that, as the number of FFT points increases at a certain time m, the standard deviation of the estimated error decreases, that is, the estimated frequency offset value becomes more and more concentrated. For example, when m is 8 and the signal-to-noise ratio is 0dB, the standard deviations of the errors estimated for the FFT at 128, 256 and 512 points are 2.605Hz, 1.311Hz and 0.953Hz, respectively. The invention can select smaller FFT point number according to the resource amount of the short wave communication system on the premise of reaching the required frequency resolution, thereby saving the resource space of the system.
Those of ordinary skill in the art will understand that: all or part of the steps for implementing the method embodiments may be implemented by hardware related to program instructions, and the program may be stored in a computer readable storage medium, and when executed, the program performs the steps including the method embodiments; and the aforementioned storage medium includes: various media that can store program codes, such as ROM, RAM, magnetic or optical disks.
The above description is only for the specific embodiments of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art can easily conceive of the changes or substitutions within the technical scope of the present invention, and all the changes or substitutions should be covered within the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the appended claims.

Claims (6)

1. The short wave communication frequency offset estimation method based on the maximum likelihood is characterized by comprising the following steps:
step 1, a transmitting terminal transmits data to be transmitted by a user, and the data to be transmitted by the user and a synchronous sequence at the front end of the data to be transmitted form a data frame structure; the data frame structure is subjected to digital up-conversion processing to obtain a transmitting data sequence;
step 2, the transmitting data sequence is transmitted through a short wave channel and synchronously sampled, and a receiving data sequence is obtained at a receiving end;
step 3, carrying out frequency offset estimation on the received data sequence by adopting a maximum likelihood criterion to obtain a frequency offset estimation value of the received data sequence;
in step 3, the frequency offset estimation is performed on the received data sequence by using the maximum likelihood criterion, and the specific steps are as follows:
step 3.1, setting the likelihood function of the frequency offset estimation as
Figure FDA0003472281170000011
Step 3.2, the problem of frequency deviation estimation of the received data sequence by adopting the maximum likelihood criterion is converted into the solution likelihood function
Figure FDA0003472281170000012
Maximum time frequency deviation estimated value fbias(ii) a The frequency offset estimation formula based on the likelihood function is obtained as follows:
Figure FDA0003472281170000013
step 3.3, setting the prior probability and the posterior probability of each frequency offset estimation value to be equal, and then the frequency offset estimation formula based on the likelihood function is as follows:
Figure FDA0003472281170000014
solving a frequency deviation estimation formula based on a likelihood function to obtain a frequency deviation estimation value f of a received data sequence bias；
Wherein the content of the first and second substances,
Figure FDA0003472281170000015
Figure FDA0003472281170000016
denotes the prior probability of frequency offset, p (R) denotes the probability of reception of the received data sequence R,
Figure FDA0003472281170000017
is the posterior probability of the frequency offset;
the frequency offset estimation formula based on the likelihood function is solved according to the following steps:
(a) calculating the frequency resolution D, and dividing the frequency resolution D into m equal parts to obtain the frequency stepping length D:
Figure FDA0003472281170000021
wherein N is the number of points of fast Fourier transform;
(b) let i be an index variable and initialize it to i-0;
(c) calculating the frequency offset of the ith section;
first, an offset sequence is calculated
Figure FDA0003472281170000022
Wherein
Figure FDA0003472281170000023
Secondly, the synchronization sequence C and the Fourier transform method are adopted to carry out RiPerforming frequency offset estimation to obtain the i-th frequency offset
Figure FDA0003472281170000024
And a pair thereofAmplitude V of responsei；
Finally, adding 1 to the index variable i, and judging the sizes of i and m; skipping to step (c) if i < m; otherwise, entering the step (d);
(d) find magnitude vector V ═ V0,…Vi,…Vm-1) Index number I corresponding to the medium maximum value and frequency deviation estimation value corresponding to the index number I
Figure FDA0003472281170000025
(e) Computing
Figure FDA0003472281170000026
And will be
Figure FDA0003472281170000027
Frequency offset estimation f as a received sequencebias。
2. The short-wave communication frequency offset estimation method based on maximum likelihood according to claim 1, wherein in step 1, the synchronization sequence C is generated by modulating a pseudo-random sequence; and C ═ C0,…,cj,…,cn-1)，cjJ data indicating a sync sequence, and n is the length of the sync sequence.
3. The short-wave communication frequency offset estimation method based on maximum likelihood according to claim 1, wherein in step 2, the short-wave channel has p + q +1 orders, wherein p orders are arranged in front of the main path and q orders are arranged behind the main path; the short wave channel has the characteristic of H (j delta t) ═ H at the j delta t moment-p(j△t),…,h0(j△t),…,hq(j△t)]，h-p(j Δ t) represents the characteristic of the-p-th order of the short-wave channel at the time j Δ t, Δ t being the time interval between two transmitted symbols,
Figure FDA0003472281170000031
Rsymis the transmission baud rate of the transmitting end.
4. The short-wave communication frequency offset estimation method based on maximum likelihood according to claim 1, wherein in step 2, the received data sequence R ═ (R ═ R) is determined0,…,rj,…,rn-1)，
Figure FDA0003472281170000032
Wherein r'z＝h-p(z△t)xp+z+…+h-1(z△t)x1+z+h0(z△t)xz+h1(z△t)x-1+z+…+hq(z△t)x-q+z+wz，(-p≤z<n + q), when z is>0 r'z＝r'j；
Figure FDA0003472281170000033
xjIs the jth data of a pseudo-random sequence, and xj＝{0,1}；wzObeying a mean of 0 and a variance of σ2Is normally distributed, two-dimensional noise sample values.
5. The short wave communication frequency offset estimation method based on maximum likelihood as claimed in claim 1, wherein the synchronization sequence C and fast Fourier transform are adopted to RiPerforming frequency offset estimation, which specifically comprises:
first, according to the offset sequence
Figure FDA0003472281170000034
And the synchronization sequence C ═ C0,…,cj,…,cn-1) And constructing a quasi-sinusoidal signal sequence:
Figure FDA0003472281170000035
wherein
Figure FDA0003472281170000036
Secondly, aligning the sinusoidal signal sequence
Figure FDA0003472281170000037
Performing fast Fourier transform of N points and estimating range of frequency offset [ -f [ ] max,fmax]In the interior, the maximum value V of the amplitude is foundiAnd corresponding frequency
Figure FDA0003472281170000038
6. The short-wave communication frequency offset estimation method based on maximum likelihood as claimed in claim 5, wherein the aligned sinusoidal signal
Figure FDA0003472281170000039
Performing a fast fourier transform of the N points: when N is more than or equal to N, intercepting quasi-sinusoidal signal sequence
Figure FDA00034722811700000310
Performing fast Fourier transform on the first N data; when n is<At N, in quasi-sinusoidal signal sequence
Figure FDA00034722811700000311
Adding (N-N) data 0 at the end of the signal sequence to obtain a quasi-sinusoidal signal sequence with the length of N, and then carrying out fast Fourier transform on the quasi-sinusoidal signal sequence with the length of N.
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