CN111740814B - Low-complexity folding product synchronization algorithm suitable for short-wave communication - Google Patents
Low-complexity folding product synchronization algorithm suitable for short-wave communication Download PDFInfo
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- H04L2027/0024—Carrier regulation at the receiver end
- H04L2027/0026—Correction of carrier offset
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Abstract
The invention discloses a low-complexity folding product synchronization algorithm suitable for short-wave communication, which specifically comprises the following 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 data frame structure information; transmitting the data frame structure information through a Gaussian channel, and acquiring a receiving sequence at a receiving end; processing each sliding window and the synchronous sequence of the receiving sequence by adopting a folding product synchronization algorithm to obtain a peak value of each sliding window; comparing the peak values of different sections of sliding windows, and selecting the window position corresponding to the section of sliding window with the maximum peak value as an estimated synchronization point; the algorithm solves the problems that the synchronization algorithm is complex and the estimated synchronization point position is inaccurate in a communication system, particularly short-wave communication, has the advantages of simplicity, easiness in implementation, high synchronization accuracy and the like, can realize the synchronous capture of the short-wave communication under the condition of large frequency deviation, can flexibly set the calculation range, and reduces the calculation amount according to the signal-to-noise ratio.
Description
Technical Field
The invention relates to the field of short-wave communication, in particular to a low-complexity folding product synchronization algorithm suitable for short-wave communication, which is used for reducing the calculated amount of the synchronization algorithm and improving the accuracy of synchronization point estimation.
Background
Short-wave communication refers to a radio communication technology with the wavelength of 10 meters to 100 meters and the frequency range of 3MHz to 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 emerging 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 it not eliminated, but it is also developing rapidly because it has advantages that other communication systems do not have. First, shortwave is the only means of telecommunication that is not restricted by networks and relays, for example, in case of war or disaster, and when satellite is attacked, the survivability and autonomous communication ability of shortwave are not comparable to other communication devices. Secondly, remote areas such as mountainous areas, gobi and oceans mainly rely on short waves for communication. Finally, the low communication costs also make shortwaves have a broad market.
In order to facilitate information transmission during short-wave communication, a transmitting end generally up-converts a low-frequency signal carrying information into a high-frequency signal with a frequency range of 3MHz to 30MHz, which requires a high-frequency carrier. 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.
After obtaining the low-frequency signal, in order to perform normal demodulation and decoding, the receiver first needs to determine the starting position of useful information in the low-frequency signal (also called synchronization estimation), and then can perform subsequent processing on the down-converted signal. However, because an error exists between carrier frequencies at the transmitting end and the receiving end, when the error is small, a common sequence cross-correlation algorithm can be adopted to find a synchronization point; when the error is large, phase rotation is generated, so that the receiving and transmitting sequences no longer have correlation characteristics, and therefore, a sequence cross-correlation algorithm cannot be adopted for synchronous estimation.
The existing unequal error protection technical scheme is basically realized by adopting an autocorrelation algorithm and performing Fourier transform. For example, in the publication No. CN108270707a "a method and apparatus for signal synchronization", a local differential sequence and a received differential sequence are used to perform correlation operation, and then Fast Fourier Transform (FFT) is performed, and a frequency offset therein is calculated according to a correlation result, so as to obtain a differential sequence in a received signal, thereby determining a synchronization position. The algorithm based on fast fourier transform has the following disadvantages: 1) The FFT-based algorithm needs to perform FFT once every time when passing through one point in the window sliding process, so that the estimation algorithm of the synchronization point is complex, the calculated amount is large, the requirement on hardware storage space is high, the working time of subsequent modules (such as demodulation, decoding and the like) can be directly occupied, and the application scene of real-time information transmission is not facilitated; 2) The algorithm based on FFT carries out synchronous estimation and frequency offset estimation at the same time, and two modules cannot be divided, so that the design and module replacement of the whole system are not facilitated; 3) The two-sequence related synchronization algorithm works normally only under the condition of no frequency deviation or small frequency deviation, and a correct information starting point cannot be found under the condition of large frequency deviation, so that the estimated accuracy of a synchronization point can influence the performance of the whole communication system.
Therefore, how to search the information starting position in the signal with frequency deviation and improve the accuracy of the position estimation becomes a problem to be solved urgently in a communication system, especially a short-wave communication system.
Disclosure of Invention
Aiming at the problems in the prior art, the invention aims to provide a low-complexity folding product synchronization algorithm suitable for short-wave communication, solves the problems of more complex synchronization algorithm and inaccurate estimated synchronization point position in a communication system, particularly short-wave communication, has the advantages of simplicity, easiness in realization, high synchronization accuracy rate and the like, and can realize the synchronous capture of the short-wave communication under the condition of large frequency deviation.
In order to achieve the purpose, the invention is realized by adopting the following technical scheme.
A low-complexity folding product synchronization algorithm suitable for short-wave communication comprises the following steps:
and 4, comparing the peak values of different sections of sliding windows, and selecting the window position corresponding to the section of sliding window with the maximum peak value as an estimated synchronization point.
Further, in step 1, the synchronization sequence X = (X) 0 ,x 1 ,…,x n ,…,x N-1 ) Where N is the length of the synchronization sequence, x n Is the nth data of the synchronization sequence.
Further, in step 2, the receiving sequence Y = (Y) 0 ,y 1 ,…,y n ,…,y N-1 ) Wherein, in the step (A),
θ is the initial phase superimposed on the received sequence; w is a n Obeying a mean of 0 and a variance of σ 2 The two-dimensional Gaussian noise sampling value; Δ Ω is the radian increment between two symbols.
Further, in step 2, radian increment between two symbols Δ Ω =2 pi × Δ f × Δ t, where Δ f is a carrier frequency deviation between the transmitting end and the receiving end, Δ f = f-f ', and f' is a carrier frequency of the transmitting end; f is the carrier frequency of the receiving end; at is the time interval of two symbols,
R sym is the transmit baud rate.
Further, step 3 specifically includes the following substeps:
substep 3.1, let w n =0, calculating the reception sequence Y = (Y) 0 ,y 1 ,…,y n ,…,y N-1 ) With the synchronization sequence X = (X) 0 ,x 1 ,…,x n ,…,x N-1 ) Conjugate product Z = (Z) 0 ,z 1 ,…,z n ,…,z N-1 ) Wherein, in the step (A),
wherein, conj (x) n ) Denotes x n Conjugation of (1);
substep 3.2 of calculating the maximum of the product Z at different depths k
The method specifically comprises the following steps:
1) When k =0, z is calculated 0 And z N-1 、z 1 And z N-2 、...、z N/2-1 And z N/2 Product of (2)
Jointly->
An item; wherein, the first and the second end of the pipe are connected with each other,
calculating the product
Sum of all elements in (1) S: />
Due to the product Z of the preceding and following terms p All of them have the same depression angle2 theta + (N-1) delta omega, and the sum S of the two is continuously accumulated in the direction of the depression angle 2 theta + (N-1) delta omega to finally reach a maximum value
2) Similarly, when k = -1, calculate z 0 And z N-2 、...、z N/2-2 And z N/2 Are multiplied and summed to obtain a maximum value of 2 theta + (N-2) delta omega
When k = -2, calculate z 0 And z N-3 、...、z N/2-3 And z N/2 Are multiplied and summed to obtain a maximum value of 2 theta + (N-3) delta omega
When k =1, calculate z N-1 And z 1 、...、z N/2+1 And z N/2-1 Are multiplied and summed to obtain a maximum value of 2 theta + N delta omega
When k =2, calculate z N-1 And z 2 、...、z N/2+2 And z N/2-1 Are multiplied and summed to obtain the maximum value of 2 θ + (N + 1) Δ Ω
When k = k, the maximum value of 2 θ + (N-1+k) Δ Ω is obtained
Substep 3.3, for maxima at different depths
And summing, wherein the summed value is taken as the peak value of each sliding window.
Further, in sub-step 3.3, the summation is formulated as
Wherein [ K ] min ,K max ]To calculate the range.
Further, in step 4, assuming that the deviation between the estimated synchronization point and the real synchronization point is Δ p, the synchronization error is normalized
Where P denotes that one symbol waveform is composed of P sampling points.
Compared with the prior art, the invention has the beneficial effects that:
(1) In the low-complexity folding product synchronization algorithm applicable to short-wave communication, in each sliding window, the product of a receiving sequence and the conjugate of a known synchronization sequence is calculated; secondly, calculating and summing the folding products of the conjugate sequence at different depths to obtain the maximum value of the conjugate sequence at different depths
Finally maximum values at different depths>
And summing, wherein the summed value is taken as the peak value of each sliding window. And comparing the peak values of different sliding windows, and selecting the window position corresponding to the sliding window with the maximum peak value as an estimated synchronization point. The algorithm has the advantages of simplicity, easy realization and synchronous accuracyThe method has the advantages of realizing the synchronous capture of the short-wave communication under the condition of large frequency offset, and the like; and the calculation range can be flexibly set, and the calculation amount is reduced according to the signal-to-noise ratio.
(2) The relation between the estimation error of the synchronization point and the calculation range is determined, namely, the synchronization error is reduced along with the increase of the signal-to-noise ratio no matter how the calculation range is selected; along with the continuous expansion of the calculation range, the signal-to-noise ratio is gradually reduced when an error flat layer appears; the longer the sync head appears in the flat layer, the lower the signal-to-noise ratio with the same calculation range.
Drawings
The invention is described in further detail below with reference to the figures and specific embodiments.
FIG. 1 (a) is a diagram illustrating a structure of transmission data; FIG. 1b is a diagram illustrating a received data structure;
fig. 2 (a) is a 4QAM modulation constellation; fig. 2 (b) is an 8PSK modulation constellation;
FIG. 3 is a graph of element accumulation results with and without synchronization;
FIG. 4 is a graph of depression angles obtained for different product sequences;
FIG. 5 is a sample and synchronization point diagram of a baseband signal; wherein, the abscissa is time, and the unit is second; the ordinate is the amplitude;
FIG. 6 (a) normalizes the synchronization error map based on the FFT synchronization algorithm; FIG. 6 (b) is a normalized synchronization error map for the folded product synchronization algorithm of the present invention; wherein, the abscissa is normalized synchronous error, and the ordinate is frequency;
FIG. 7 is an estimation error diagram of the folding product synchronization algorithm of the present invention at different calculation ranges and different signal-to-noise ratios; wherein, the length of the synchronization head in the figure (a) is 256; the sync head length in fig. (b) is 512; the abscissa is the signal-to-noise ratio (SNR) in dB; the ordinate is the normalized synchronization error.
Detailed Description
Embodiments of the present invention will be described in detail below with reference to examples, but it will be understood by those skilled in the art that the following examples are only illustrative of the present invention and should not be construed as limiting the scope of the present invention.
A low-complexity folding product synchronization algorithm suitable for short-wave communication comprises the following steps:
Generally, a transmission data frame of any communication system has a structure as shown in fig. 1 (a). The synchronous sequence is formed by modulating a pseudo-random sequence, and the data segment is the data information to be transmitted by the user. The function of the synchronization sequence is determination of synchronization point, frequency offset estimation, channel estimation, etc.
The specific modulation mode is as follows:
assume that M =2 in the corresponding modulation constellation m Each constellation point is(s) 0 ,…,s j ,…,s M-1 ) And record them as a set
Each constellation point can be represented by a 0, 1 bit sequence of length m. In 8PSK modulation, as shown in fig. 2 (b), the symbol '4' may be represented by a bit sequence (100) in which bit 1 is the 0 th bit. For any given constellation, the sign average energy ≧>
Where | s j | 2 ＝R 2 (s j )+I 2 (s j ) The symbol R (x) represents the real part of x; i (x) represents the imaginary part of x. In general, to facilitate theoretical analysis and computer simulation, it is customary to let @>
Specifically, a synchronization sequence X = (X) modulated from a pseudorandom sequence is provided 0 ,x 1 ,…,x n ,…,x N-1 )，
The transmission baud rate (number of symbols transmitted per unit time) is R sym One symbol/second, receiveTransmitting both-end carrier frequency deviation delta f = f-f'; wherein f' is the carrier frequency of the transmitting end, f is the carrier frequency of the receiving end, and the time interval between two symbols is
And seconds. The synchronization sequence is followed by a data segment of the same modulation scheme.
And 2, transmitting the data frame structure information through a Gaussian channel, and acquiring a receiving sequence Y at a receiving end.
Specifically, as shown in fig. 1 (b), after the information of the data frame structure according to step 1 is transmitted through the gaussian channel, the receiving end obtains a receiving sequence Y, and it can be seen that an interference sequence with an unknown length is added in front of the synchronization sequence in the receiving sequence. Wherein the receiving sequence is Y = (Y) 0 ,y 1 ,…,y n ,…,y N-1 )；
θ is the initial phase superimposed on the received sequence, Δ Ω is the increment of radians between two symbols, Δ Ω =2 π × Δ f × Δ t. w is a n Obeying a mean of 0 and a variance of σ 2 The noise variance of each dimension is 0.5 sigma 2 。
And 3, processing each section of sliding window and the synchronous sequence of the receiving sequence by adopting a folding product synchronization algorithm to obtain the peak value of each section of sliding window.
The following description focuses on the principles and processes of the folding product synchronization algorithm proposed by the present invention, and in order to facilitate the description of the folding product synchronization algorithm, the length N of the synchronization sequence is made to be an even number, and it is assumed that the receiving sequence only has frequency offset and no gaussian noise, i.e., w n =0. The effectiveness of the synchronization algorithm provided by the invention in a noisy environment is verified in subsequent performance simulation. The folding product synchronization algorithm specifically comprises the following substeps:
substep 3.1 of calculating the reception sequence Y = (Y) 0 ,y 1 ,…,y n ,…,y N-1 ) With the synchronization sequence X = (X) 0 ,x 1 ,…,x n ,…,x N-1 ) Conjugate product Z = (Z) 0 ,z 1 ,…,z n ,…,z N-1 ) Wherein, in the step (A),
wherein, conj (x) n ) Represents x n Conjugation of (1);
substep 3.2 of calculating the maximum of the product Z at different depths k
The method comprises the following specific steps:
1) When k =0, z is calculated 0 And z N-1 、z 1 And z N-2 、...、z N/2-1 And z N/2 Product of (2)
Jointly->
An item; wherein the content of the first and second substances,
it can be seen that the depression angle of any one element of the product of the preceding and following terms is 2 θ + (N-1) Δ Ω.
Calculating the product
Sum of all elements in (1) S:
due to the product Z of the preceding and following terms p The depression angles of any elements are the same and are 2 theta + (N-1) delta omega, and the sum result S of the depression angles is continuously accumulated in the direction of the depression angle 2 theta + (N-1) delta omega, and finally reaches a maximum value
After the calculation, whether the peak value appears can be judged according to whether the peak value appears. If the received sequence and the known synchronous sequence are not synchronous, the product Z of the front term and the back term calculated according to the above process p The depression angle of each element in the group is different, in which case its mathematical expectation should be 0 if they are summed; if synchronized, a peak in a certain direction will occur. As shown in fig. 3, the figure shows the case where all elements are summed up in synchronization and in non-synchronization. It is seen from fig. 3 that the magnitude of the sum accumulated without synchronization is small and concentrated near the origin, and peaks at a certain depression angle only when synchronized. Meanwhile, it can be seen from equation (3) that the position where the maximum value (i.e., the synchronization point) occurs is independent of the initial phase θ and the radian increment Δ Ω, that is, the value does not affect the accuracy of the synchronization estimation regardless of the magnitude of the frequency offset.
2) From the description of the synchronization principle in 1), it can be seen that the essence of the folding product synchronization algorithm is the process of accumulating the values at the same depression angle (direction).
Similarly, when k = -1, calculate z 0 And z N-2 、...、z N/2-2 And z N/2 Are multiplied and summed to obtain a maximum value of 2 theta + (N-2) delta omega
When k = -2, calculate z 0 And z N-3 、...、z N/2-3 And z N/2 Are multiplied and summed to obtain the maximum value of 2 theta + (N-3) delta omega
When k =1, calculate z N-1 And z 1 、...、z N/2+1 And z N/2-1 Are multiplied and summed to obtain a maximum value of 2 theta + N delta omega
When k =2, calculate z N-1 And z 2 、...、z N/2+2 And z N/2-1 Are multiplied and summed to obtain the maximum value of 2 θ + (N + 1) Δ Ω
When k = k, the specific product order is shown in fig. 4, resulting in a maximum value of 2 θ + (N-1+k) Δ Ω
Substep 3.3, for maxima at different depths
And summing, wherein the summed value is taken as the peak value of each sliding window.
Specifically, to further improve the accuracy of the synchronization estimation, a calculation is performed
To increase the size of the peak, where [ K ] min ,K max ]For calculating the range, i.e. for determining a peak value>
As the basis for evaluation. Obviously, the wider the k value range is, the more prominent the peak value is, the higher the estimation accuracy is. General calculation Range K min And K max There is no particular requirement, however, for the sake of simplicity, the symbol k N Represents the calculation range [ -N, + N]。
And 4, comparing the peak values of different sections of sliding windows, and selecting the window position corresponding to the section of sliding window with the maximum peak value as an estimated synchronization point.
Specifically, at the receiving end, the received signal waveform needs to be sampled for subsequent processing. For example, a constellation diagram corresponding to Binary Phase Shift Key (BPSK) includes two symbols, which are-1 and +1, respectively, and is represented by sampling a raised cosine pulse waveform during baseband transmission, as shown in fig. 5. Fig. 5 shows a sampling waveform of an information sequence [ +1-1-1], where a symbol waveform is composed of P sampling points, and T is a symbol duration. The purpose of synchronization is to find the start of the actual information in these samples.
Due to the interference of noise during transmission, the estimated synchronization point may have a certain deviation, may lead or may lag the true synchronization point. A quality judgment standard of the performance of the synchronization estimator is to examine the error between the estimated synchronization point and the real synchronization point in a statistical sense, and the performance is better when the error is smaller. If there is no error between the estimated synchronization point and the true value for the sample signal shown in FIG. 5, it is possible to determine the time [0T 2T ] at]Accurately sampling to obtain transmitted information sequence [ +1-1 [ ]](ii) a Normalizing the synchronization error if the synchronization estimate is offset by 1 sample point
(the estimated synchronization point leads the true value) or ^ er>
(the estimated synchronization point lags behind the true value). It is clear that if e =1, the estimated synchronization point lags the true value by 1 symbol duration. Generally, let the normalized synchronization error->
Where Δ P is the deviation between the estimated synchronization point and the true synchronization point, and P denotes that a symbol waveform is composed of P sampling points.
Simulation experiment
Comparative analysis of the folding product synchronization algorithm of the present invention with existingAnd estimating accuracy under the Gaussian channel based on the FFT synchronization algorithm. The simulation parameters are set as follows: the method comprises the steps that an m sequence with the length of 256 is selected as a synchronous sequence, the symbol rate is 2.4KBaud, raised cosine pulse alpha =0.4, the signal bandwidth is 3KHz, each symbol samples 256 points, the band-limited Gaussian noise is generated, the signal to noise ratio is-5 dB, the test times are 10000, and the calculation range in the folding product synchronization algorithm is k 3 . Histogram statistics is performed on the test results, and a normalized synchronization error e is calculated, and the test results are shown in fig. 6.
As can be seen from fig. 6:
(1) The normalized synchronous error e of the folding product synchronous algorithm and the prior FFT synchronous algorithm is basically between [ -0.25,0.25 ];
(2) The frequency of occurrence of normalized synchronization error of 0 in the folding product synchronization algorithm is higher than that of the FFT-based synchronization algorithm;
(3) The errors of the folding product synchronization algorithm and the estimation based on the FFT synchronization algorithm are Gaussian distribution, the standard deviation sigma =0.0725 based on the FFT synchronization algorithm, and the standard deviation sigma =0.0655 based on the folding product synchronization algorithm, which shows that the estimation accuracy of the folding product synchronization algorithm is higher than that based on the FFT synchronization algorithm.
Because the normalized synchronous error presents a Gaussian distribution characteristic, the normalized synchronous error can be analyzed by using a mathematical statistics correlation tool, and the normalized synchronous error is between [ e ] min ,e max ]Has a probability of
As shown in FIG. 6 (b), in the folded product algorithm, the normalized synchronization error is between [ -0.05,0.05]P =0.5638; normalized synchronous error is between [ -0.1,0.1]P =0.8751; normalized synchronous error is between [ -0.2,0.2]With a probability of p =0.9977.
And observing the estimation errors of the folding product synchronization algorithm in different calculation ranges and different signal-to-noise ratios. Sampling 8 points for each symbol, and selecting 256 and 512 synchronous head lengths respectively; the simulation results are shown in fig. 7.
As can be seen from fig. 7:
(1) Regardless of the choice of the calculation range, the synchronization error decreases as the signal-to-noise ratio increases. When the signal-to-noise ratio is increased to a certain value, the speed of synchronous error decline is obviously slowed down, and an error leveling layer is generated at the same time. E.g. a sync head length of 256, calculation range k 4 Then, leveling appears at the SNR (signal to noise ratio) = -5 dB;
(2) With the continuous expansion of the calculation range, the signal-to-noise ratio is gradually reduced when the error floor appears. For example, the calculation range k is 256 at the sync head length 4 、k 6 The signal-to-noise ratios of the flat layers are-5 dB and-6 dB respectively;
(3) The longer the sync head appears in the flat layer, the lower the signal-to-noise ratio with the same calculation range. For example in the calculation range k 6 The signal-to-noise ratio for the sync head 256 at the time of leveling is-6 dB, and the signal-to-noise ratio for the sync head 512 at the time of leveling is-8 dB.
Although the present invention has been described in detail in this specification with reference to specific embodiments and illustrative embodiments, it will be apparent to those skilled in the art that modifications and improvements can be made thereto based on the present invention. Accordingly, such modifications and improvements are intended to be within the scope of the invention as claimed.
Claims (6)
1. A low-complexity folding product synchronization algorithm suitable for short-wave communication is characterized by comprising 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 X at the front end of the data to be transmitted by the user form data frame structure information;
step 2, the data frame structure information is transmitted through a Gaussian channel, and a receiving sequence Y is obtained at a receiving end;
step 3, processing each sliding window and synchronous sequence of the receiving sequence by adopting a folding product synchronous algorithm to obtain a peak value of each sliding window;
the step 3 specifically comprises the following substeps:
substep 3.1, let w n =0, calculating the reception sequence Y = (Y) 0 ,y 1 ,…,y n ,…,y N-1 ) With the synchronization sequence X = (X) 0 ,x 1 ,…,x n ,…,x N-1 ) Conjugate product Z = (Z) 0 ,z 1 ,…,z n ,…,z N-1 ) Wherein, in the step (A),
wherein, conj (x) n ) Denotes x n Conjugation of (2);
substep 3.2 of calculating the maximum of the product Z at different depths k
The method comprises the following specific steps:
1) When k =0, calculate z 0 And z N-1 、z 1 And z N-2 、...、z N/2-1 And z N/2 Product of (2)
Jointly->
An item; wherein, the first and the second end of the pipe are connected with each other,
calculating the product
Sum of all elements in (1) S:
due to the product Z of the preceding and following terms p The depression angles of any elements in the image are the same and are 2 theta + (N-1) delta omega, and the sum result S of the depression angles is continuously accumulated in the direction of the depression angle 2 theta + (N-1) delta omega, and finally reaches a maximum value
2) Similarly, when k = -1, calculate z 0 And z N-2 、...、z N/2-2 And z N/2 Are multiplied and summed to obtain the maximum value of 2 theta + (N-2) delta omega
When k = -2, calculate z 0 And z N-3 、...、z N/2-3 And z N/2 Are multiplied and summed to obtain a maximum value of 2 theta + (N-3) delta omega
When k =1, calculate z N-1 And z 1 、...、z N/2+1 And z N/2-1 Are multiplied and summed to obtain the maximum value of 2 theta + N delta omega
When k =2, calculate z N-1 And z 2 、...、z N/2+2 And z N/2-1 Are multiplied and summed to obtain the maximum value of 2 θ + (N + 1) Δ Ω
/>
When k = k, the maximum value of 2 θ + (N-1+k) DELTA.OMEGA is obtained
Substep 3.3, for maximum values at different depths
Summing, and taking the summed value as the peak value of each sliding window;
and 4, comparing the peak values of different sections of sliding windows, and selecting the window position corresponding to the section of sliding window with the maximum peak value as an estimated synchronization point.
2. The low complexity folding product synchronization algorithm for short wave communication according to claim 1, wherein in step 1, the synchronization sequence X = (X =) 0 ,x 1 ,…,x n ,…,x N-1 ) Where N is the length of the synchronization sequence, x n Is the nth data of the synchronization sequence.
3. The low complexity folding product synchronization algorithm for short wave communication according to claim 2, wherein in step 2, the receiving sequence Y = (Y =) 0 ,y 1 ,…,y n ,…,y N-1 ) Wherein, in the step (A),
θ is the initial phase superimposed on the received sequence; w is a n Obeying a mean of 0 and a variance of σ 2 The two-dimensional Gaussian noise sampling value; Δ Ω is the radian increment between two symbols.
4. The low complexity convolution product synchronization algorithm for short wave communication of claim 3 wherein in step 2, the radian increment Δ Ω =2 π x Δ between two symbolsf x Δ t, wherein Δ f is a carrier frequency deviation at both transmitting and receiving ends, Δ f = f-f ', and f' is a carrier frequency of a transmitting end; f is the carrier frequency of the receiving end; Δ t is the time interval of two symbols,
R sym is the transmit baud rate.
5. The low complexity folding product synchronization algorithm for short wave communication according to claim 1, wherein in sub-step 3.3, the summation is given by the formula:
wherein [ K ] min ,K max ]To calculate the range.
6. The low complexity folding product synchronization algorithm for short wave communication according to claim 1, wherein in step 4, assuming the deviation between the estimated synchronization point and the true synchronization point as Δ p, the synchronization error is normalized
Where P denotes that one symbol waveform is composed of P sampling points. />
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