CN105188129A - Synchronization acquisition and tracking method based on multi-angle fractional order related coordination - Google Patents

Abstract

The invention relates to a synchronous acquisition and tracking method based on multi-angle fractional correlation cooperation, which relates to the field of wireless communication. It is to realize fast synchronization acquisition and precise synchronization tracking of synchronization code. The present invention is based on the characteristics of the same peak value and different sharpness of the fractional autocorrelation function at different rotation angles, and selects the fractional autocorrelation function with different sharpness through the rotation angle according to the system signal parameters and performance indicators for the synchronization code of the communication signal Synchronous capture and tracking, that is, select a fractional correlation function with a relatively wide peak value through the rotation angle to quickly capture the synchronization code, and then use a fractional correlation function with a sharper peak value corresponding to the rotation angle to achieve precise tracking of the synchronization code. The invention is used for synchronous capture and tracking of synchronous codes in wireless communication.

Description

Synchronous Acquisition and Tracking Method Based on Multi-angle Fractional Correlation Synergy

technical field

The invention relates to the field of wireless communication.

Background technique

Synchronization is one of the key technologies of mobile communication. Its purpose is to realize the time synchronization of the signals at both ends of the transceiver, which directly affects the quality of communication. Therefore, how to realize stable, reliable and accurate synchronization is the primary problem to be solved in the communication system. In digital communication, the information flow is often transmitted in a frame composed of one or several symbols. The receiving end must know the start and end moments of these frames, otherwise the information cannot be recovered correctly. The purpose of synchronization is to mark the beginning and end of the frame, and the frame is identified at the receiving end according to these marks. These marks are often represented by some special code groups, such as Barker codes, PN sequences, Zadoff-Chu sequences, etc.

Existing synchronization methods are usually based on traditional correlation calculations. In practical engineering applications, the method of setting detection thresholds is usually used to find the peak of the correlation function to obtain synchronization information. In order to improve the detection probability and reduce the false alarm probability, it is often required that the correlation function of the synchronous signal has a sharp characteristic. However, due to the influence of the channel during the detection process, the calculated correlation function of the synchronization signal is not a sharp peak as expected, so it is difficult to find the synchronization accurately. In addition, if the synchronization accuracy is to be improved, the sampling frequency of the signal needs to be increased, which will greatly increase the computational overhead of the system.

Contents of the invention

The present invention aims to realize fast synchronization capture and precise synchronization tracking of synchronization codes, thereby providing a synchronization capture and tracking method based on multi-angle fractional correlation cooperation.

A synchronous acquisition and tracking method based on multi-angle fractional correlation synergy, which is realized by the following steps:

Step 1. The receiving end determines the synchronization acquisition parameters, which include the rotation angle α _acq of the fractional order correlator, the detection threshold V _th of the comparator, and the variation Δτ _acq of the phase of the synchronization code output by the phase search control module;

At the same time, the receiving end determines the synchronization tracking parameters, which include the rotation angle α _tra of the fractional order correlator, the change amount Δτ _{tra of the synchronization code phase output by the phase search control module, and the leading and lagging amounts τ tra of} the local synchronization code , and 2τ _tra ≤ T _c ; T _c is the symbol width;

Synchronous capture process:

Step 2: Use the capture parameter control module to pass the received signal r(t) and the local synchronization code through the fractional order correlator according to the capture parameters determined in step 1, and calculate the peak value of the fractional order correlation function between the two at a rotation angle of α _{acq Vacq} ;

Step 3, sending the output value V _acq of the fractional order correlator in step 2 to the threshold comparator, and judging whether the output value V _acq of the fractional order correlator is less than the detection threshold V _th ;

When V _acq is less than the detection threshold V _th , the phase of the local synchronous code is different from the phase of the received synchronous code, and the threshold comparator outputs a signal to the synchronous code phase search control module. Under the control of the phase search control module, the local The synchronous code generator changes the phase state of the output synchronous code, and the variation of the synchronous code phase is △τ _acq ; if the changed phase state of the local synchronous code is still different from the phase state of the received synchronous code, the threshold comparator continues to output a signal Give the phase search control module to make the phase search control module change the phase of the local reference synchronization code again;

Until the phase state of the local reference synchronous code approaches the phase state of the received synchronous code, the output V _acq of the fractional order correlator exceeds the detection threshold V _th , that is, the synchronous capture of the synchronous code is completed, and the synchronous tracking process is transferred to;

Synchronous tracking process:

Step 4, the received signal is divided into three paths, and the tracking parameter control module, according to the tracking parameters determined in step 1, combines the signals of two paths with the leading code c(t-τ′ _d +τ _tra ) and the local reference synchronization code respectively Lag code c( _t -τ′d-τ _tra ) carries out the fractional order correlation operation whose rotation angle is α _tra ;

Carry out the fractional order correlation operation with the rotation angle of α _tra between the other signal and the local reference synchronization code c(t-τ′ _d ), where τ′ _d is the estimated value of the unknown time delay τ _d of receiving the synchronization code. After network detection, it is sent to the decision device for information data recovery;

Step 5. Send the output of the leading and lagging related branches in step 4 to the adder through envelope detection to generate an error signal; and filter the error signal through a low-pass filter to smooth the influence of noise on synchronous tracking ;

And judge whether the error signal is positive, if the judgment result is yes, then execute step 51; if the judgment result is no, then execute step 52;

Step 51, then the phase state of the leading code of the local synchronizing code is closer to the phase state of receiving the synchronizing code than the phase state of the lagging code, then under the control of the phase search control module, the local synchronizing code generator is output to the phase state of the synchronizing code The phase state is adjusted in advance, and the change amount of the phase adjustment is △τ _tra ;

If the adjusted error signal is still positive, the phase search control module adjusts the phase of the local reference synchronization code in advance again until the phase state of the local reference synchronization code approaches the phase state of the received synchronization code, then the synchronization tracking of the synchronization code is realized;

Step 52, then the phase state of the delayed code of the local synchronous code is closer to the phase state of the received synchronous code than the phase state of the advanced code, and the phase search control module will adjust the phase of the local reference synchronous code laggingly until the phase of the local reference synchronous code The state is close to the phase state of receiving the synchronization code, and the synchronization tracking of the synchronization code is realized.

The present invention is based on the characteristics of the same peak value and different sharpness of the fractional autocorrelation function at different rotation angles, and selects the fractional autocorrelation function with different sharpness through the rotation angle according to the system signal parameters and performance indicators for the synchronization code of the communication signal Synchronous capture and tracking, that is, select a fractional correlation function with a relatively wide peak value through the rotation angle to quickly capture the synchronization code, and then use a fractional correlation function with a sharper peak value corresponding to the rotation angle to achieve precise tracking of the synchronization code. Compared with the traditional synchronization method based on classical correlation, this method reduces clock jitter and contributes to signal processing such as positioning. In addition, the bit error performance of the system is improved to a certain extent.

Description of drawings

Figure 1 is a schematic diagram of the simulation of the fractional autocorrelation function of the rectangular pulse signal at different rotation angles;

Fig. 2 is a schematic diagram of the simulation of the fractional autocorrelation function of the Barker code under different rotation angles;

Fig. 3 is in the case of k=-1, ω ₀ =4, the fractional order autocorrelation function simulation schematic diagram of chirp signal under different rotation angles;

Fig. 4 is in the case of q=4, N _ZC =7, l=0, the fractional order autocorrelation function simulation schematic diagram of Zadoff-Chu sequence under different rotation angles;

Fig. 5 is a schematic diagram of the principle of the synchronous capture system;

Fig. 6 is a schematic diagram of the principle of the synchronous tracking system;

Fig. 7 is a schematic diagram of bit error rate comparison simulation based on classical correlation and fractional order correlation synchronization methods;

Fig. 8 is a schematic diagram of a comparison simulation of synchronous jitter based on fractional order correlation and classical correlation;

Schematic diagram of variance comparison simulation of synchronous tracking jitter based on fractional order correlation and classical correlation in Fig. 9;

Detailed ways

The specific embodiment one, based on the multi-angle fractional order correlation synchronous acquisition and tracking method, it is realized by the following steps:

Step 1. The receiving end determines the rotation angle α _acq of the fractional correlator, the detection threshold V _th of the comparator, and the phase change of the synchronization code output by the phase search control module during the synchronization acquisition process according to the system performance index and the parameters of the selected synchronization code. Δτ _acq ; at the same time, determine the rotation angle α _tra of the fractional correlator in the process of synchronous tracking, the change amount Δτ _{tra of the output synchronization code phase of the phase search control module, and the lead and lag τ tra of} the local synchronization code, and 2τ _tra ≤ T _c .

Step 2. Under the action of the capture parameter control module determined in step 1, the received signal r(t) and the local synchronization code are passed through the fractional order correlator to calculate the peak value of the fractional order correlation function whose angle is α _acq V _acq .

Step 3: Send the output V _acq of the fractional-order correlator in step 2 to the threshold comparator. When V _acq is less than the detection threshold V _th , it means that the phase of the local synchronous code is different from the phase of the received synchronous code, and the threshold comparator outputs a signal to the synchronous code phase search control module. Under the action of the phase search control module, the local The synchronous code generator changes the phase state of the output synchronous code, and the variation of the phase is Δτ _acq . If the phase state of the changed local synchronous code is still different from the phase state of the received synchronous code, the threshold comparator continues to output a signal to the phase search control module to make it change the phase of the local reference synchronous code again until the local reference synchronous code When the phase state of the phase state is very close to the phase state of the received synchronous code, the output V _acq of the fractional order correlator exceeds the detection threshold V _th , which means that the synchronous capture of the synchronous code has been realized, and then it turns into synchronous tracking.

Step 4, after step 3 completes the synchronous capture, the received signal is divided into three paths, and under the action of the tracking parameter determined in the step 1 by the tracking parameter control module, two of them are respectively with the leading code c(t of the local reference synchronization code -τ′ _d +τ _tra ) and the lagging code c(t-τ′ _d -τ _tra ) carry out the fractional correlation operation of the α _tra angle; the other way and the local reference synchronous code c(t-τ′ _d ) carry out an angle of The fractional order correlation operation of α _tra , where τ′ _d is the estimate of the unknown time delay τ _d of the received synchronization code, which is sent to the decision device for information data recovery after envelope detection.

Step 5: Send the output of the leading and lagging related branches in step 4 to the adder through envelope detection to generate an error signal. Pass the error signal through a low-pass filter to smooth out the effect of noise on synchronous tracking. If the error signal is positive, it means that the phase state of the leading code of the local synchronization code is closer to the phase state of the receiving synchronization code than the phase state of the lagging code, so under the action of the phase search control module, the local synchronization code generator will output the synchronization code The phase state of the phase is adjusted in advance, and the amount of change of the phase adjustment is △τ _tra . If the error signal is still positive after adjustment, the phase search control module adjusts the phase of the local reference synchronization code in advance again until the phase state of the local reference synchronization code is very close to the phase state of the received synchronization code. On the contrary, if the error signal is negative, it means that the phase state of the lagging code of the local synchronization code is closer to the phase state of the receiving synchronization code than the phase state of the leading code, and the phase search control module will adjust the phase of the local reference synchronization code laggingly until the local reference The phase state of the synchronization code is very close to the phase state of the received synchronization code, which means that the synchronization tracking of the synchronization code is realized.

Specific embodiment 2. This specific embodiment is a further limitation of the synchronous acquisition and tracking method based on multi-angle fractional correlation cooperation described in specific embodiment 1. During the synchronous acquisition process, the received signal and the local synchronization code are subjected to fractional correlation operations When , the width of the fractional correlation output pulse varies with the rotation angle.

Specific Embodiment 3. This specific embodiment is a further limitation of the synchronous acquisition and tracking method based on multi-angle fractional correlation coordination described in specific embodiment 1. During the synchronous tracking process, the received signal and the local synchronization code are subjected to fractional correlation operations When , the width of the fractional correlation output pulse varies with the rotation angle.

Embodiment 4. This embodiment is a further limitation of the synchronous acquisition and tracking method based on multi-angle fractional correlation collaboration described in Embodiment 1. The rotation angles of the fractional correlation operations are different in the synchronous acquisition process and the synchronous tracking process. .

Specific Embodiment Five. This specific embodiment is a further limitation of the synchronous acquisition and tracking method based on multi-angle fractional-order correlation cooperation described in specific embodiment 2. The rotation angle of the fractional-order correlation operation is calculated according to the system signal parameters and performance indicators get.

Specific Embodiment 6. This specific embodiment is a further limitation of the synchronous acquisition and tracking method based on multi-angle fractional-order correlation cooperation described in specific embodiment 3. The rotation angle of the fractional-order correlation operation is calculated according to the system signal parameters and performance indicators get.

The correlation function and the frequency power spectral density defined by Fourier transform are a Fourier transform pair, which is an important method to describe the time-domain characteristics of signals in traditional signal processing. In recent years, with the continuous deepening of signal processing theory research and the continuous expansion of application scope, a series of new signal processing technologies have emerged on the basis of traditional Fourier transform, which has greatly enriched the connotation and extension of traditional signal processing methods and technologies. . Among them, the fractional Fourier transform is a generalized form of the Fourier transform, which breaks through the limitation that the Fourier transform can only perform signal analysis in a single time domain or frequency domain. between fractional domain analysis and processing signals. Compared with the Fourier transform, the fractional Fourier transform has one more free parameter of the rotation angle. As the angle increases continuously from 0 to π/2, it can show all the characteristics of the signal gradually changing from the time domain to the frequency domain. . Correspondingly, the correlation function under the fractional Fourier transform (usually called the fractional order correlation function) also presents a different form of expression from the traditional correlation function, with a free parameter of the rotation angle, which can show the signal at different rotation angles related features below. The fractional cross-correlation function of two functions x(t) and y(t) is defined as

${\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; j\&tau;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; cot</span>}\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}{<span\; class="notranslate">\; \&Integral;</span>}_{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&infin;</span>}}^{<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&infin;</span>}}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; j</span>}\mathrm{<span\; class="notranslate">\; t</span>}\mathrm{<span\; class="notranslate">\; \&tau;</span>}\mathrm{<span\; class="notranslate">\; cot</span>}\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

where α corresponds to the rotation angle of the fractional Fourier transform. In particular, when x(t)=y(t), the definition of the fractional autocorrelation function can be obtained, namely

${\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; j\&tau;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; cot</span>}\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}{<span\; class="notranslate">\; \&Integral;</span>}_{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&infin;</span>}}^{<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&infin;</span>}}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; j</span>}\mathrm{<span\; class="notranslate">\; t</span>}\mathrm{<span\; class="notranslate">\; \&tau;</span>}\mathrm{<span\; class="notranslate">\; cot</span>}\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

When the angle α=π/2, the fractional-order mutual (auto)correlation function degenerates into a conventional mutual (auto)correlation function, namely

${\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; \&Integral;</span>}_{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&infin;</span>}}^{<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&infin;</span>}}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

${\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; \&Integral;</span>}_{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&infin;</span>}}^{<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&infin;</span>}}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

Therefore, the conventional correlation function can be regarded as a special case of the fractional correlation function at the angle α=π/2.

From the point of view of signal design, synchronization codes can be classified into binary codes and constant-amplitude zero-autocorrelation sequences. For example, Barker codes and PN codes belong to binary codes, which can be regarded as the superposition of rectangular pulses; while constant-amplitude zero-autocorrelation sequences mainly include Zadoff-Chu sequences, Chirp-like sequences and Frank sequences, etc., which essentially satisfy a certain Chirp sequence for parameter constraints. Based on this, in order to obtain generalized results, the signal is modeled as:

$\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\sqrt{{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}}\mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; t</span>}}{{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; kt</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; j\&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

where τ ₀ >0, k and ω ₀ are arbitrary constants, rect(t/τ ₀ ) represents a rectangular pulse signal, and its expression is

According to the definition of the aforementioned fractional autocorrelation function, the fractional autocorrelation function of the signal x(t) can be obtained as

${\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; cot</span>}\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; j\&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\mathrm{<span\; class="notranslate">\; \&tau;</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\frac{<span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; |</span>}{{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; \&lsqb;</span>\frac{\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; cot</span>}\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\frac{<span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; |</span>}{{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 7</span>}<span\; class="notranslate">\; )</span>$

In the formula, |τ|≤τ ₀ , sinc(·)=sinπ(·)/π(·).

When α=-arccot(k)+nπ (n is an integer), the autocorrelation function of signal x(t) can be simplified as

${\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\frac{<span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; |</span>}{{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; cot</span>}\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; j\&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\mathrm{<span\; class="notranslate">\; \&tau;</span>}}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 8</span>}<span\; class="notranslate">\; )</span>$

It can be seen that under this condition, the autocorrelation function of the signal x(t) is a linear frequency modulation signal with an initial frequency of ω ₀ and a frequency modulation slope of -cotα, and its envelope modulation function is a triangular pulse signal with a width of 2τ ₀ , Therefore the width of the autocorrelation function of x(t) is 2τ ₀ .

When α≠-arccot(k)+nπ, the autocorrelation function of the signal x(t) is still a chirp signal with an initial frequency of ω ₀ and a frequency modulation slope of -cotα, but its envelope modulation function is

$<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\frac{<span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; |</span>}{{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; \&lsqb;</span>\frac{\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; cot</span>}\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\frac{<span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; |</span>}{{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 9</span>}<span\; class="notranslate">\; )</span>$

When |τ|<<τ ₀ , the envelope is approximately a sinc function, namely

$\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; \&lsqb;</span>\frac{\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; cot</span>}\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}<span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 10</span>}<span\; class="notranslate">\; )</span>$

When x=π/2, sinc[x/π]=2/π, close to -4dB. Then, let τ′(k+cotα)τ ₀ /2=π/2, and get τ′=π/(k+cotα)τ ₀ , that is, the autocorrelation function of signal x(t) has a -4dB duration of 2| τ′|=2π/(|k+cotα|τ ₀ )<<τ ₀ .

If k=ω ₀ =0, the signal x(t) is a rectangular pulse signal; when α=π/2, its fractional autocorrelation function is that the initial frequency is 0, the frequency modulation slope is -cotα, and the envelope modulation function is The linear frequency modulation signal of the triangular pulse has a duration of 2τ ₀ ; while at other angles of α≠π/2, the envelope modulation function becomes a sinc function, and the duration of -4dB is 2π/(|cotα|τ ₀ ) And it increases with the increase of α in the main value range of angle α (0, π/2), and decreases with the increase of α in [π/2, π), as shown in Fig. 1 . Since the binary code can be regarded as a superposition of rectangular pulses, its fractional autocorrelation function also has this characteristic, as shown in Figure 2. In addition, if k≠0, the signal x(t) is a linear frequency modulation signal, and its fractional autocorrelation function is when α=-arccot(k)+nπ (n is an integer), the initial frequency is ω ₀ , and the frequency modulation slope is - cotα, the envelope modulation function is a linear FM signal of a triangular pulse, and the time width is 2τ ₀ ; while at other α≠-arccot(k)+nπ angles, the envelope modulation function becomes a sinc function, and the -4dB time width is 2π /(|k+cotα|τ ₀ ) and increases with the increase of α in the main value interval of angle α (0,-arccot(k)), while in [-arccot(k),π) with α increases and decreases, as shown in Figure 3. Since the constant-amplitude zero-autocorrelation sequence can be regarded as a discrete chirp signal satisfying certain parameter conditions, its fractional-order autocorrelation function also has such properties, as shown in Figure 4.

In summary, the peak value of the fractional autocorrelation function of different rotation angles of a signal is the same, but the decay speed of the correlation value outside the peak is different, that is, the sharpness of the fractional autocorrelation function is different. Based on this feature, by selecting an appropriate rotation angle according to the system signal parameters and performance indicators, fast synchronization can be achieved based on the fractional-order correlation function with a relatively wide correlation peak, and then the accurate Sync tracking.

The purpose of synchronous acquisition is to make the phase difference between the local synchronous code and the synchronous code in the received signal less than T _c /2 ⁿ , where T _c is the symbol width, n is a positive integer and its specific value depends on the detection accuracy of the system. According to spread spectrum communication theory, sliding correlation detection is the simplest and most practical synchronization acquisition method. In sliding correlation detection based on conventional correlation operations, in order to reduce noise and increase detection probability, the bandwidth after correlation is limited by the system bandwidth; from the perspective of shortening the capture time, the sliding speed should be accelerated, that is, the frequency of the transceiver clock should be increased Poor, and requires a wider bandwidth after correlation, the two contradict each other. Considering that the fractional autocorrelation function with different rotation angles has the same peak value but different sharpness, the width of the correlation pulse output by the fractional order correlator can be controlled by the rotation angle α _acq . That is to say, when the sliding is fast, an appropriate angle α _acq can be selected so that the correlated bandwidth meets the system requirements. In view of this, Fig. 5 shows the block diagram of sliding correlation synchronous capture based on fractional order correlation operation.

Once the receiver achieves synchronization acquisition, the local reference synchronization code must track the changes of the received signal as accurately as possible, so that the difference between the phase of the local synchronization code and the phase of the received synchronization code is as small as possible, so that the fractional order correlator can obtain the maximum Correlation output, this process is called synchronous tracking. Suppose the observed signal model is r(t)=Ac(t;τ _d )+n(t), 0≤t≤T, where n(t) is Gaussian white noise with zero mean and power spectral density of N ₀ /2 ; c(t; τ _d ) represents the normalized synchronous code signal component in the received signal, where τ _d is the unknown time delay to be estimated, and A is the signal amplitude. Discuss the noise-free interference and channel delay first, in order to get some inspiration from it. According to the signal detection theory in the fractional Fourier transform domain, the output c _o (t) of the fractional domain matched filter to the synchronous code signal is a fractional autocorrelation function of c(t), and reaches the maximum value when t=T. That is to say, the sampling time t=T at which the output of the fractional-domain matched filter reaches the maximum, that is, at the peak point of the fractional-order correlation function. In the background of noise, it is generally difficult to identify the correlation peak. Assuming that sampling is not performed at the peak point, early sampling is performed when t=T-τ _tra , and late sampling is performed when t=T+τ _tra , the delay between these two sampling points is 2τ _tra ≤ T _c . In the sense of statistical average, the absolute value of the early sample and the absolute value of the late sample are smaller than the peak sample value. Because the fractional autocorrelation function is an even function relative to the optimal sampling time t=T, the absolute values of the fractional autocorrelation functions at the time t=T-τ _tra and t=T+τ _tra are equal. Under this condition, the appropriate sampling instant is the midpoint between t=T-τ _tra and t=T+τ _tra . Based on this, Figure 6 shows a functional block diagram of synchronous tracking.

In Figure 6, a fractional-order correlator replaces the equivalent fractional-domain matched filter. The three fractional correlators are integrated on the symbol interval T, and two of the fractional correlators start integrating earlier than the estimated optimal sampling time τ _tra and delayed τ _tra respectively, and the difference between the absolute values of their outputs forms an error signal. To smooth the effect of noise on tracking performance, the error signal is passed through a low-pass filter. If the timing deviates from the best sampling moment, the average error signal output by the low-pass filter is non-zero, and the sign of the error determines whether the phase of the synchronization code output by the phase search control module is late or advanced. The numerical analysis results are given below.

Based on the above analysis, the 13-bit Barker code is used as the synchronization code, followed by the data information bits spread by the 13-bit Barker code, and the information modulation method adopts bipolar modulation. In the simulation, each chip is sampled 4 times, and the simulation channel is a Gaussian white noise channel. Figure 7 shows the bit error performance comparison of synchronization algorithms based on fractional correlation and classical correlation methods. It can be seen that the synchronous bit error performance based on fractional correlation is slightly better than the traditional synchronous bit error performance based on classical correlation, but the difference is not large, because the correlation peak of the classical correlation function of Barker code itself is very sharp. Figure 8 shows the synchronization tracking jitter of the two synchronization methods when the signal-to-noise ratio is 8dB. The abscissa in the figure is 0, indicating that no synchronization jitter occurs. Since each chip is sampled by 4 times, 1 indicates jitter 1/4 chip, 2 means 1/2 chip jitter; and the positive and negative signs of the abscissa represent jitter in the direction of lag and advance respectively. Further, Fig. 9 shows the variation curve of the jitter variance of the synchronous tracking based on the fractional order correlation and the classical correlation with the signal-to-noise ratio, taking the sampling interval as the basic unit. It can be seen that although the synchronization bit error performance based on fractional correlation and classical correlation is not much different, the former has better synchronization tracking performance, that is, its synchronization jitter is smaller.

The present invention is based on the characteristics of the same peak value and different sharpness of the fractional autocorrelation function at different rotation angles, and selects the fractional autocorrelation function with different sharpness through the rotation angle according to the system signal parameters and performance indicators for the synchronization code of the communication signal Synchronous capture and tracking, that is, select a fractional correlation function with a relatively wide peak value through the rotation angle to quickly capture the synchronization code, and then use a fractional correlation function with a sharper peak value corresponding to the rotation angle to achieve precise tracking of the synchronization code. Compared with the traditional synchronization method based on classical correlation, this method reduces clock jitter and contributes to signal processing such as positioning. In addition, the bit error performance of the system is improved to a certain extent.

Claims (7)

1. The synchronous acquisition and tracking method based on multi-angle fractional order correlation collaboration is characterized in that: it is realized by the following steps: Step 1. The receiving end determines the synchronous acquisition parameters, and the acquisition parameters include the rotation angle α _acq of the fractional order correlator, the detection threshold V _th of the comparator, and the variation Δτ _acq of the phase of the synchronous code output by the phase search control module; At the same time, the receiving end determines the synchronous tracking parameters, the synchronous tracking parameters include the rotation angle α _tra of the fractional order correlator, the variation Δτ _tra of the phase of the synchronization code output by the phase search control module, and the lead and lag τ _tra of the local synchronization code, And 2τ _tra ≤ T _c ; T _c is the symbol width; Synchronous capture process: Step 2: Use the capture parameter control module to pass the received signal r(t) and the local synchronization code through the fractional order correlator according to the capture parameters determined in step 1, and calculate the peak value of the fractional order correlation function between the two at a rotation angle of α _{acq Vacq} ; Step 3, sending the output value V _acq of the fractional order correlator in step 2 to the threshold comparator, and judging whether the output value V _acq of the fractional order correlator is less than the detection threshold V _th ; When V _acq is less than the detection threshold V _th , the phase of the local synchronous code is different from the phase of the received synchronous code, and the threshold comparator outputs a signal to the synchronous code phase search control module. Under the control of the phase search control module, the local The synchronous code generator changes the phase state of the output synchronous code, and the variation of the synchronous code phase is Δτ _acq ; if the phase state of the changed local synchronous code is still different from the phase state of the received synchronous code, the threshold comparator continues to output a signal to The phase search control module makes the phase search control module change the phase of the local reference synchronization code again; Until the phase state of the local reference synchronous code approaches the phase state of the received synchronous code, the output V _acq of the fractional order correlator exceeds the detection threshold V _th , that is, the synchronous capture of the synchronous code is completed, and the synchronous tracking process is transferred to; Synchronous tracking process: Step 4, the received signal is divided into three paths, and the tracking parameter control module, according to the tracking parameters determined in step 1, combines the signals of two paths with the leading code c(t-τ′ _d +τ _tra ) and the local reference synchronization code respectively Lag code c( _t -τ′d-τ _tra ) carries out the fractional order correlation operation whose rotation angle is α _tra ; Carry out the fractional order correlation operation with the rotation angle of α _tra between the other signal and the local reference synchronization code c(t-τ′ _d ), where τ′ _d is the estimated value of the unknown time delay τ _d of receiving the synchronization code. After network detection, it is sent to the decision device for information data recovery; Step 5. Send the output of the leading and lagging related branches in step 4 to the adder through envelope detection to generate an error signal; and filter the error signal through a low-pass filter to smooth the influence of noise on synchronous tracking ; And judge whether the error signal is positive, if the judgment result is yes, then execute step 51; if the judgment result is no, then execute step 52; Step 51, then the phase state of the leading code of the local synchronizing code is closer to the phase state of receiving the synchronizing code than the phase state of the lagging code, then under the control of the phase search control module, the local synchronizing code generator is output to the phase state of the synchronizing code The phase state is adjusted in advance, and the change amount of the phase adjustment is Δτ _tra ; If the adjusted error signal is still positive, the phase search control module adjusts the phase of the local reference synchronization code in advance again until the phase state of the local reference synchronization code approaches the phase state of the received synchronization code, then the synchronization tracking of the synchronization code is realized; Step 52, then the phase state of the delayed code of the local synchronous code is closer to the phase state of the received synchronous code than the phase state of the advanced code, and the phase search control module will adjust the phase of the local reference synchronous code laggingly until the phase of the local reference synchronous code The state is close to the phase state of receiving the synchronization code, and the synchronization tracking of the synchronization code is realized. 2. The synchronous acquisition and tracking method based on multi-angle fractional correlation coordination according to claim 1, characterized in that in step 1, the receiving end determines that the synchronous acquisition parameters are determined according to the system performance index and the parameters of the selected synchronous code. 3. The synchronous acquisition and tracking method based on multi-angle fractional correlation coordination according to claim 1, wherein in the synchronous acquisition process, when the received signal and the local synchronization code carry out the fractional correlation operation, the fractional correlation output pulse The width changes with the rotation angle. 4. The synchronous capture and tracking method based on multi-angle fractional correlation coordination according to claim 1, characterized in that in the synchronous tracking process, when the received signal and the local synchronization code carry out the fractional correlation operation, the fractional correlation output pulse The width changes with the rotation angle. 5. The synchronous acquisition and tracking method based on multi-angle fractional correlation collaboration according to claim 1, characterized in that the rotation angles of the fractional correlation operations are different in the synchronous acquisition process and the synchronous tracking process. 6. The synchronous acquisition and tracking method based on multi-angle fractional correlation coordination according to claim 3, characterized in that the rotation angle of the fractional correlation operation is calculated according to system signal parameters and performance indicators. 7. The synchronous acquisition and tracking method based on multi-angle fractional correlation coordination according to claim 4, characterized in that the rotation angle of the fractional correlation operation is calculated according to system signal parameters and performance indicators.