Arc tangent Costas ring and carrier synchronization method based on low-frequency time code synchronization

Abstract

The invention discloses an arc tangent Costas ring based on low-frequency time code synchronization and a carrier synchronization method, and relates to the technical field of information processing of low-frequency time codes. The arc tangent Costas loop based on low-frequency time code synchronization comprises a first multiplier, a first low-pass filter, a second multiplier, a second low-pass filter, an arc tangent phase discriminator, a loop filter, a voltage-controlled oscillator and a # imgabs0 # phase shifter. By implementing the arc tangent Costas ring based on low-frequency time code synchronization and the carrier synchronization method provided by the invention, the phase tracking speed and efficiency can be improved.

Description

Technical Field

[0001] The present invention relates to the technical field of information processing of low-frequency time code, and more specifically, to a Costas loop based on low-frequency time code synchronization and an arctangent carrier synchronization method. Background Art

[0002] During the carrier modulation of low-frequency time code (BPC), the time information is first converted into BCD code and then subjected to negative polarity amplitude modulation with a period of 1 s. The information of low-frequency time code changes every 1 s, and within this 1 s interval, it contains standard second pulse information and time coding information. When each second arrives, amplitude shift keying modulation needs to be performed on the time code data. Except at the moments of 19 s, 39 s, and 59 s, the amplitude of the signal carrier will drop to 10% of the original amplitude at other moments. The occurrence of UTC (NTSC) moment is represented by the starting point of the descending pulse signal, and the width of the descending pulse is used to encode the time information according to the specified calendar protocol. There is 600 ms of pure carrier during the combined modulation process of low-frequency time code, and spread spectrum modulation can be performed during this period. At the beginning of each second, AM modulation is performed on the carrier signal whose amplitude has dropped to 10% of the original. After 400 ms, PSK modulation is performed on the pseudo-random sequence. This modulation is preferably performed starting from a zero-crossing point of a certain carrier and stopped a few ms before the start of the next second, which is beneficial for saving resources and maintaining the original information structure of BPC pulse width amplitude modulation. Finally, the combined modulated signal is sent out by an RF transmitter through a band-pass filter. The low-frequency time code information generated by the specified calendar protocol is encoded in quaternary, with one code element transmitted per second and the frame repeated three times per minute to represent the current time. The first 19 s are used to generate time information such as year, month, day, week, hour, and minute, and the 20th s indicates the arrival of the whole 20 s.

[0003] In the process of low-frequency spread-spectrum signals, carrier synchronization plays a very important role. When performing coherent demodulation, it is necessary to recover the local carrier with the same amplitude and phase as the transmitting end for demodulation. One of the better carrier synchronization methods is the Costas loop method. The Costas loop can directly extract the carrier phase information from the received modulated signal without the need for an additional local oscillator to generate a reference carrier. This enables it to achieve carrier synchronization more simply and can adapt to different modulation formats. Since the Costas loop is adjusted based on the phase error, it has a high tolerance for amplitude variations and noise. Even in the presence of large channel fading or additive white Gaussian noise (AWGN), the Costas loop can effectively track and recover the carrier phase. Some other carrier recovery methods may require the transmission of dedicated pilot signals to assist the synchronization process, but the Costas loop can operate without pilot signals, thus saving valuable bandwidth resources. Once locked to the correct phase, the Costas loop usually provides a very stable synchronization state, reducing the bit error rate (BER) and improving the overall reliability of the communication system.

[0004] In reality, there are often situations with relatively large frequency offsets. When using the traditional Costas loop for phase tracking in the case of a large frequency offset, the tracking speed is often extremely slow and it is prone to phase-locking failure, and it has limitations in the range of phase tracking.

[0005] The above content is only used to assist in understanding the technical solution of the present invention and does not represent an admission that the above content is prior art. Summary of the Invention

[0006] The object of the present invention is to provide a low-frequency time code synchronous arctangent Costas loop and a carrier synchronization method, which can improve the phase tracking speed and efficiency.

[0007] The present invention provides a low-frequency time code synchronous arctangent Costas loop, including a first multiplier, a first low-pass filter, a second multiplier, a second low-pass filter, an arctangent phase detector, a loop filter, a voltage-controlled oscillator and a phase shifter; the output end of the first multiplier is connected to the input end of the first low-pass filter, and the output end of the first low-pass filter is connected to the first input end of the arctangent phase detector; the output end of the second multiplier is connected to the input end of the second low-pass filter, and the output end of the second low-pass filter is connected to the second input end of the arctangent phase detector; the output end of the arctangent phase detector is connected to the input end of the loop filter, and the output end of the loop filter is connected to the input end of the voltage-controlled oscillator; the output end of the voltage-controlled oscillator is connected to the second input end of the second multiplier, and the output end of the voltage-controlled oscillator is also connected to the connected to the input end of the phase shifter, the output end of the phase shifter is connected to the second input end of the first multiplier; the first input end of the first multiplier is connected to the first input end of the second multiplier for inputting the modulated signal.

[0008] The present invention also provides a carrier synchronization method applied to the above-mentioned arctangent Costas loop based on low-frequency time code synchronization, including: S1: According to the current time, perform low-frequency time code encoding to obtain a quaternary time code frame; S2: According to the quaternary time code frame, perform code-to-wave encoding using a pulse wave to obtain a code-to-wave signal; S3: According to a preset threshold, perform bipolar transformation on the code-to-wave signal to obtain a binary waveform; S4: Perform spreading operation on the binary waveform using a Gold code to obtain a spread signal; S5: Perform BPSK modulation on the binary waveform using an arctangent Costas loop based on low-frequency time code synchronization to obtain a carrier-synchronized signal.

[0009] Implementing the arctangent Costas loop based on low-frequency time code synchronization and the carrier synchronization method provided by the present invention has the following beneficial effects: In view of the defect of slow phase-locking speed of the existing Costas loop, the present invention proposes an arctangent Costas loop based on low-frequency time code synchronization and a carrier synchronization method. Among them, the arctangent Costas loop based on low-frequency time code synchronization includes a first multiplier, a first low-pass filter, a second multiplier, a second low-pass filter, an arctangent phase discriminator, a loop filter, a voltage-controlled oscillator and a phase shifter; at the same time, design and analysis are carried out for different frequency offsets and different equivalent loop noises, and the phase-locking speed and accuracy under different frequency offsets and the influence of different equivalent loop noises on the tracking speed are discussed. Implementing the arctangent Costas loop based on low-frequency time code synchronization and the carrier synchronization method provided by the present invention can accelerate the phase-locking speed of the Costas loop, enable it to perform fast phase-locking in a very short time, and greatly improve the phase tracking speed and tracking efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0010] The present invention will be further described below in conjunction with the drawings and embodiments. In the drawings: Figure 1 is the BPC time domain diagram provided by the present invention; Figure 2 is the principle block diagram of the Costas loop provided by the present invention; Figure 3 is the second-order loop filter structure block diagram provided by the present invention; Figure 4It is the overall transmission flow block diagram provided by the present invention; Figure 5 It is the overall simulation block diagram provided by the present invention; Figure 6 It is the phase tracking rate diagram of different Costas loops under a signal-to-noise ratio of 15 db provided by the present invention; Figure 7 It is the phase tracking rate diagram of different Costas loops under a signal-to-noise ratio of 50 db provided by the present invention; Figure 8 It is the phase tracking curve diagram under the equivalent noise bandwidth of the same loop provided by the present invention; Figure 9 It is the phase tracking curve diagram under different frequency offsets provided by the present invention; Figure 10 It is the phase tracking curve diagram under different signal-to-noise ratios provided by the present invention. Detailed implementation manners

[0011] For a clearer understanding of the technical features, objectives, and effects of the present invention, the detailed implementation manners of the present invention will now be described in detail with reference to the accompanying drawings.

[0012] A carrier is an electrical signal with a constant frequency and signal, and it does not carry information by itself. Modulation is the process of representing an information signal by changing a certain parameter of the carrier signal, such as amplitude, frequency, or phase, according to certain rules. This process enables the information to be encoded onto the carrier so that it can be transmitted over the channel. AM modulation is called amplitude modulation, in which the amplitude of the carrier signal changes according to the information signal. PSK modulation is called phase shift keying, and data is represented by changing the phase of the carrier. In PSK, a binary data stream is used to select one of two or more possible phase angles to modulate the carrier signal. Each phase angle corresponds to a specific data symbol.

[0013] Assume the carrier expression is: (1) The transmitted binary baseband symbol sequence consists of 0 and 1 binary number symbols and is represented as: (2) The low-frequency time code signal after modulation and coding is as follows: (3) In formula (3), is the digital modulation signal of the low-frequency time code, is 68.5 kHz, where starts from 0 s and has a duration of is a rectangular pulse, It is always 1s, n∈[1,N], N is the number of time codes. When the pulse width of each second is reached, it is set to , which can be 100ms, 200ms, 300ms or 400ms. The corresponding modulation signal amplitude as follows: (4) From the above formula, we can get the time domain diagram of low frequency time code as follows: Figure 1 shown.

[0014] The traditional Costas loop is composed of three parts: phase detector (PD), loop filter (LPF) and voltage controlled oscillator (VCO), which work together to achieve carrier synchronization. The principle block diagram is as follows Figure 2 As shown in Figure 1, the phase detector's primary task is to compare the phase difference between the received modulated signal and a locally generated reference carrier. In a BPSK system, the phase detector outputs an error signal that reflects the phase difference between the received signal and the local carrier. This error signal is typically a DC voltage, whose magnitude and polarity indicate the direction and magnitude of the phase error. The loop filter smoothes the error signal from the phase detector, removes high-frequency noise, and adjusts the error signal's dynamic characteristics. It ensures that the control signal transmitted to the voltage-controlled oscillator is stable and responds appropriately to changes in phase error. The voltage-controlled oscillator generates a sinusoidal waveform with the corresponding frequency and phase as the local carrier based on the input control voltage. When the control voltage received from the loop filter changes, the VCO adjusts its output frequency or phase to ensure that the local carrier matches the received signal as closely as possible. The stability of the VCO directly impacts the overall performance of the Costas loop; it must respond quickly to the error signal to achieve synchronization and remain stable once locked to avoid unnecessary drift.

[0015] The phase-locked process of the traditional Costas loop is analyzed, assuming that the input modulation signal is:

[0016] Then the output of the product of the I and Q signals and the input signal is: (5) (6) The output of V3 and V4 after passing through the low-frequency filter is: (7) (8) consider approaches 0, so the output error of the phase detector is approximately: (9) Figure 2 shows a schematic diagram of the low-frequency time code synchronous arctangent Costas loop of this embodiment. In this embodiment, the low-frequency time code synchronous arctangent Costas loop includes a first multiplier, a first low-pass filter, a second multiplier, a second low-pass filter, an arctangent phase discriminator, a loop filter, a voltage-controlled oscillator, and a phase shifter; the output end of the first multiplier is connected to the input end of the first low-pass filter, and the output end of the first low-pass filter is connected to the first input end of the arctangent phase discriminator; the output end of the second multiplier is connected to the input end of the second low-pass filter, and the output end of the second low-pass filter is connected to the second input end of the arctangent phase discriminator; the output end of the arctangent phase discriminator is connected to the input end of the loop filter, and the output end of the loop filter is connected to the input end of the voltage-controlled oscillator; the output end of the voltage-controlled oscillator is connected to the second input end of the second multiplier, and the output end of the voltage-controlled oscillator is also connected to the input end of the phase shifter, and the output end of the phase shifter is connected to the second input end of the first multiplier; the first input end of the first multiplier is connected to the first input end of the second multiplier for inputting the modulated signal.

[0017] In an exemplary embodiment, the first low-pass filter and the second low-pass filter are second-order Butterworth filters, and their cut-off frequency bandwidth is 110 Hz; the first gain coefficient of the loop filter is 2, the second gain coefficient is 0.01, and the damping coefficient is 0.707.

[0018] This embodiment provides a carrier synchronization method applied to the above-mentioned low-frequency time code synchronous arctangent Costas loop, including: S1: According to the current time, perform low-frequency time code encoding to obtain a quaternary time code frame; In an exemplary embodiment, step S1 specifically includes: According to the current time, perform low-frequency time code encoding to obtain a quaternary time code frame, as the formula: , , , , where, is the generated 38-bit binary time code frame, represents the bit numbered in the binary time code frame, is the 19-bit quaternary time code frame, Indicates the bit numbered in the quaternary time code frame, is a decimal number, indicating a modulo operation; S2: According to the quaternary time code frame, use a pulse wave to perform code-to-wave encoding to obtain a code-to-wave signal; In an exemplary embodiment, step S2 specifically includes: According to the quaternary time code frame, use a pulse wave to perform code-to-wave encoding to obtain a code-to-wave signal, as shown in the formula: , , , , , , , , , where, is the generated repeating sequence, used as a control signal to sequentially output a 20-bit time code frame; represents the th control signal; represents the output of the th multiplexer; , , are to connect the outputs of the multiplexer to the output of the signal selector respectively; is the output after adding the outputs of the multiplexer; is a periodic signal; is a square wave, is the period, and are the duty cycles, is the transformed signal, is the code-to-wave signal; S3: According to a preset threshold, perform bipolar transformation on the code-to-wave signal to obtain a binary waveform; In an exemplary embodiment, the preset threshold is 0.5; S4: Use a Gold code to perform spreading operation on the binary waveform to obtain a spread signal; In an exemplary embodiment, step S4 specifically includes: Use a Gold code to perform spreading operation on the binary waveform to obtain a spread signal, as shown in the formula: , , wherein, is the Gold code, is the Gold code length, i.e., the chip index, is the rectangular pulse function, is the duration of each chip, is the spread-spectrum signal, is the binary sequence obtained by making a decision with a threshold of 0.5, is the number of bits, is the value of the nth data symbol; S5: Use the arctangent Costas loop based on low-frequency time code synchronization to perform BPSK modulation on the binary waveform to obtain the signal after carrier synchronization; In an exemplary embodiment, step S5 specifically includes: using the arctangent Costas loop based on low-frequency time code synchronization to perform BPSK modulation on the binary waveform to obtain the signal after carrier synchronization, as shown in the formula: , wherein, is the signal after carrier synchronization, is the amplitude of the sine wave, is its initial phase, is the carrier frequency; It should be noted that the magnitude of the carrier frequency is much larger than the baseband bandwidth.

[0019] In some embodiments, the above-mentioned arctangent Costas loop based on low-frequency time code synchronization can also be implemented in the following manner.

[0020] In this embodiment, the arctangent Costas loop is used to replace the traditional Costas loop for phase discrimination output, and the output error of the arctangent Costas loop is approximately: (10) In the Costas loop circuit, the loop filter is a linear low-pass filter. It can not only filter out the high-frequency components in the instantaneous phase difference signal, but also play a decisive role in adjusting the loop parameters. In addition, it can provide a short-term memory for the loop, ensuring that the phase-locked loop can quickly recapture the signal when the system loses lock due to instantaneous noise. Moreover, the loop filter also has a great impact on the capture bandwidth and time of the loop. Different values of the loop equivalent noise bandwidth directly affect the values of C1 and C2. The smaller the loop equivalent noise bandwidth, the better the loop's anti-noise performance, but the longer the loop tracking time. At the same time, increasing the bandwidth can reduce the capture time, but the loop's noise filtering performance will decline. Therefore, the loop filter is of great importance in the design of carrier synchronization loops. To meet the system requirements, in actual design, it is necessary to make appropriate adjustments to the actual values based on theoretical calculations. Common loop filters include second-order loops and third-order loops. Although the third-order loop has higher accuracy, it also has higher requirements for the hardware level. Under general conditions, the second-order loop can better meet the requirements. Therefore, considering resources, the order of the loop filter is determined to be second-order. Its structural block diagram is as shown in Figure 3 shown.

[0021] C1 and C2 are the coefficients of the loop filter, and their approximate expressions are: (11) (12) where is the gain of the voltage-controlled oscillator, is the gain of the phase detector, is the natural angular frequency of the loop, is the damping coefficient of the loop. The damping coefficient of the loop has a certain impact on both the system stability and speed. From the perspective of suppressing Gaussian white noise, it is set that = 0.5 as the optimal value. From the perspective of loop stability, the larger the value, the more stable the loop. After weighing, it is generally selected that = 0.707 as the optimal value.

[0022] The natural angular frequency of the loop can be expressed as: (13) is the natural angular frequency of the loop, is the damping coefficient of the loop, is the equivalent noise bandwidth of the loop. The value of the equivalent noise bandwidth of the loop well reflects the loop's ability to filter out the input noise. The smaller the value, the stronger the ability to filter out noise. In engineering, it is generally selected that is less than or equal to 0.01Rb, where Rb is the information transmission rate.

[0023] In some embodiments, the above carrier synchronization method can also be implemented in the following manner.

[0024] During the information transmission process, carrier synchronization is very important. To better transmit data, in this embodiment, low-frequency time code is adopted as the transmission code, which generates a 38-bit binary time code frame according to the current time of the computer in the frame format of BPC. Then the generated 38-bit binary time code frame is converted into a 19-bit quaternary time code frame for subsequent encoding operations. The 19-bit quaternary sequence is encoded using the code-to-wave encoding format. Four rectangular pulse waves with different duty cycles are involved in the encoding process, and their duty cycles are 0.1, 0.2, 0.3, and 0.4 respectively. Adopting this encoding method can simplify the complexity of carrier synchronization, and the encoding of low-frequency time code will directly generate modulation sidebands on the carrier.

[0025] The receiver can extract synchronization information by detecting the periodic changes of these sidebands without a complex carrier recovery circuit. At the same time, adopting low-frequency time code can avoid high-frequency carrier synchronization. The wavelength of low-frequency signals is longer, and the phase stability is high during propagation. The code-to-wave encoding embeds the synchronization information into the low-frequency modulation. The receiver only needs to demodulate the envelope or phase change without high-frequency carrier phase locking. Secondly, the anti-interference ability during the transmission process can be enhanced. The code-to-wave encoding usually repeats the synchronization information in each second pulse. This time-domain redundancy allows the receiver to suppress noise through multiple integrations or averaging and stably extract the synchronization signal. Low-frequency signals have strong diffraction ability, can penetrate buildings, and have relatively stable phase delays. The code-to-wave encoding further reduces the influence of multipath effects through slow modulation.

[0026] The overall transmission flow block diagram of this embodiment is as Figure 4 shown: The time code generated according to the current time of the computer is transmitted in accordance with the code-to-wave encoding method. The generated binary sequence is subjected to bipolar transformation and then spread-spectrum operation with the generated Gold code. The signal obtained after spread-spectrum is modulated in the BPSK manner, and after passing through the AWGN channel, despreading and demodulation operations are performed, where the demodulation process involves carrier synchronization. In this embodiment, the arctangent Costas loop phase discrimination method is adopted for carrier synchronization, and the optimal gain coefficients C1 and C2 are calculated. Under these parameters, the arctangent phase-locked loop exhibits better tracking speed and phase-locking effect.

[0027] The following is the establishment of the mathematical model for the low-frequency time code encoding process: Assume the generated 38-bit binary time code frame , and convert it into a 19-bit quaternary time code frame . The 38-bit binary time code frame Convert to decimal:

[0028] Then convert from decimal to a 19-bit quaternary time code frame:

[0029] Add an element 4 to the head of the generated 19-bit quaternary time code frame to generate a new 20-bit time code frame .

[0030] Generate a repeating sequence , and output the 20-bit time code frame as a control signal in sequence.

[0031] Set the th control signal to be . The output through the Multiport Switch i.e., the output of the i-th Multiport Switch . Connect the outputs of 20 Multiport Switches to the Selector respectively, and its output . Add the outputs of 20 Selectors and output:

[0032] Use the above output Out as the control signal of the Multiport Switch with a data port of 5, and take the values outside the range as 1 by default. Input by generating four pulse waves with duty cycles of 0.1, 0.2, 0.3, and 0.4 as data signals.

[0033] Set four periodic signals as:

[0034] is a square wave with a duty cycle of , where , corresponds to the duty cycles of four pulse waveforms, and its expression is:

[0035] Perform signal transformation on the obtained signal , and the obtained signal is , and its expression is:

[0036] According to the above four pulse waveforms as data signals for input, the above output is used as the control signal for input. The finally output signal is:

[0037] The generated is discriminated with 0.5 as the threshold to output a standard binary waveform .

[0038] For the generated binary waveform, a spreading operation is performed. Assume the expression of the Gold code is:

[0039] where represents the duration of each chip, is the rectangular pulse function.

[0040] For the spread signal , its expression is:

[0041] For the spread signal BPSK modulation is performed. The modulation signal adopts a sine wave. The expression of the modulated signal is:

[0042] where is the amplitude of the sine wave, is its initial phase.

[0043] At the receiving end, despreading, demodulation, and decoding operations are performed to complete the information transmission.

[0044] During the above operations, carrier synchronization is very important. In this embodiment, the carrier sampling time is set to 0.001, and the carrier is assigned a value of 1.

[0045] The information transmission rate of the spread sequence is set to 400 bps. A second-order Butterworth filter is used as the low-pass filter, and the cut-off frequency bandwidth is set to 110 Hz. The traditional multiplication phase discriminator is changed to an arctangent phase discriminator. Second-order loop filtering is adopted, and the values of C1 and C2 in the second-order loop filtering are set according to parameters such as the free angular frequency, phase discriminator gain, loop filter gain, information transmission rate, and loop equivalent noise. The voltage-controlled sensitivity of the voltage-controlled oscillator is set to 5 Hz / V.

[0046] This embodiment discusses the phase tracking speed of the arctangent Costas loop compared with the traditional Costas loop in the case of C1 = 2 and C2 = 0.01. According to Less than or equal to 0.01Rb, the phase tracking rates of the arctangent Costas loop are designed respectively under the conditions that the equivalent loop noise is 0.1Rb, 0.05Rb and 0.025Rb and the sum frequency deviation magnitudes are 101Hz, 102Hz, 103Hz and 104Hz, and the damping coefficient = 0.707. Finally, by comparing the phase tracking performances under different signal-to-noise ratios, it is verified whether the experimental structure meets the expectations.

[0047] In this embodiment, the overall program block diagram executed by the carrier synchronization method is as Figure 5 shown.

[0048] In order to compare the phase-locking performances of the traditional Costas loop and the improved Costas loop based on arctangent phase discrimination, simulation tests are carried out on the Simulink platform in Matlab; the signal-to-noise ratio is set to 15db, the carrier frequency transmitted by the transmitter is 100Hz, the information transmission rate Rb = 400bps, and C1 = 2 and C2 = 0.01 are taken as the two gain coefficients of the loop filter. The phase tracking rate diagrams of the traditional Costas loop and the arctangent Costas loop are as Figure 6 shown.

[0049] From Figure 6 the phase tracking curves output by the two Costas loops, it can be seen that the phase tracking curve of the traditional phase-locked loop converges at about 1s, and the phase tracking curve of the arctangent phase discrimination converges at about 0.01s. The phase tracking speed of the Costas loop with arctangent phase discrimination is significantly faster than that of the traditional Costas loop.

[0050] When the signal-to-noise ratio is set to 50db, the phase tracking curves of the traditional Costas loop and the arctangent Costas loop are as Figure 7 shown.

[0051] From Figure 6 and Figure 7 it can be found that no matter at high signal-to-noise ratio or low signal-to-noise ratio, the Costas loop with arctangent phase discrimination has a faster convergence speed. The fluctuation range of the phase error of the traditional Costas loop is between -0.05 and 0.05, while the phase fluctuation range of the arctangent is between -0.2 and 0.2. Therefore, the traditional Costas loop has higher accuracy.

[0052] Set the signal-to-noise ratio to 15db, the modulation carrier frequency of the transmitter is 100Hz, and the initial frequency output locally is 102Hz. According to less than or equal to 0.01Rb, set = 0.1Rb, = 0.05Rb and = 0.025Rb, where Rb = 400bps, and the damping coefficient = 0.707, the gain of the phase detector and the gain of the voltage-controlled oscillator are set to 1. The basic parameter settings for system simulation are shown in Table 1.

[0053] Table 1: Basic Parameter Table for System Simulation

[0054] The values of C1 and C2 corresponding to different loop equivalent noises are shown in Table 2.

[0055] Table 2: Comparison Table of C1 and C2 Values under Different Loop Equivalent Noises

[0056] Build a simulation model according to the above parameters to obtain Figure 8 the simulation results.

[0057] From Figure 8 it can be seen that the smaller the loop equivalent noise, the shorter the loop synchronization time and the faster the phase convergence speed. It can also be obtained from the figure that when C1 = 106.71 and C2 = 11.39, the arctangent Costas loop has a faster phase-locking speed.

[0058] Keep other conditions unchanged and only change the frequency offset. Set the local carrier frequencies to 101Hz, 102Hz, 103Hz, and 104Hz, and the frequency offsets to 1Hz, 2Hz, 3Hz, and 4Hz respectively. Study the loop synchronization performance under different initial frequency differences between the signal carrier generated by the local carrier VCO and the signal carrier actually input to the loop, and obtain Figure 9 the simulation results.

[0059] From Figure 9 it can be seen that when other parameters are the same, the smaller the frequency offset, the shorter the loop synchronization time.

[0060] Set the frequency offset to 102Hz, keep other parameters unchanged, and only change the signal-to-noise ratio. Discuss the phase tracking curves at signal-to-noise ratios of 10dB, 20dB, 30dB, and 40dB as Figure 10 shown.

[0061] From Figure 10 it can be seen that there are still some fluctuations at a signal-to-noise ratio of 10dB, but the fluctuations decrease as the signal-to-noise ratio increases. Therefore, the higher the signal-to-noise ratio, the more stable the loop synchronization, which is in line with the experimental expectations.

[0062] The above content includes the comparison of the phase tracking rates of the traditional Costas loop and the improved arctangent Costas loop, and the analysis of the phase tracking rates under different frequency offsets, different loop equivalent noises, and different signal-to-noise ratios. The design analysis method of the arctangent Costas loop based on low-frequency time code synchronization is given, and the optimal values of C1 and C2 using the arctangent Costas loop method are given. The process of low-frequency time code code conversion to wave, the entire spread spectrum modulation, and the despreading and demodulation processes are established, and the carrier synchronization function is completed. The carrier synchronization rate is accelerated on the original basis, and the corresponding important output result diagrams are given during the research process, which has certain reference value for the research of the carrier synchronization module.

[0063] The embodiments of the present invention have been described above in conjunction with the accompanying drawings. However, the present invention is not limited to the above specific embodiments. The above specific embodiments are merely illustrative and not restrictive. Under the inspiration of the present invention, those of ordinary skill in the art can also make many forms without departing from the purpose of the present invention and the scope protected by the claims. All of these are within the protection scope of the present invention.

Claims

1. A low-frequency time code synchronous arctangent Costas loop, characterized in that The low-frequency time-code synchronous arctangent Costas loop includes a first multiplier, a first low-pass filter, a second multiplier, a second low-pass filter, an arctangent phase detector, a loop filter, a voltage-controlled oscillator, and a phase shifter; the output end of the first multiplier is connected to the input end of the first low-pass filter, and the output end of the first low-pass filter is connected to the first input end of the arctangent phase detector; the output end of the second multiplier is connected to the input end of the second low-pass filter, and the output end of the second low-pass filter is connected to the second input end of the arctangent phase detector; the output end of the arctangent phase detector is connected to the input end of the loop filter, and the output end of the loop filter is connected to the input end of the voltage-controlled oscillator; the output end of the voltage-controlled oscillator is connected to the second input end of the second multiplier, and the output end of the voltage-controlled oscillator is also connected to the input end of the phase shifter, and the output end of the phase shifter is connected to the second input end of the first multiplier; the first input end of the first multiplier is connected to the first input end of the second multiplier for inputting a modulated signal.

2. The arctangent Costas loop based on low-frequency time code synchronization according to claim 1, wherein The first low-pass filter and the second low-pass filter are second-order Butterworth filters with a cut-off frequency bandwidth of 110 Hz; the first gain coefficient of the loop filter is 2, the second gain coefficient is 0.01, and the damping coefficient is 0.

707.

3. A carrier synchronization method applied to the low-frequency time code synchronous arctangent Costas loop according to any one of claims 1-2, characterized in that, Including: S1: Perform low-frequency time code encoding according to the current time to obtain a quaternary time code frame; S2: According to the quaternary time code frame, perform code-to-wave encoding using a pulse wave to obtain a code-to-wave signal; S3: Perform bipolar transformation on the code-to-wave signal according to a preset threshold to obtain a binary waveform; S4: Perform spreading operation on the binary waveform using a Gold code to obtain a spread signal; S5: Perform BPSK modulation on the binary waveform using a low-frequency time code synchronous arctangent Costas loop to obtain a carrier-synchronized signal.

4. The carrier synchronization method according to claim 3, wherein Step S1 specifically includes: performing low-frequency time code encoding according to the current time to obtain a quaternary time code frame, as shown in the formula: ， ， ， ， Among them, is the generated 38-bit binary time code frame, represents the bit numbered in the binary time code frame, is the 19-bit quaternary time code frame, represents the bit numbered in the quaternary time code frame, is a decimal number, represents the modulo operation.

5. The carrier synchronization method according to claim 3, wherein Step S2 specifically includes: according to the quaternary time code frame, performing code-to-wave encoding using a pulse wave to obtain a code-to-wave signal, as shown in the formula: ， ， ， ， ， ， ， ， ， Among them, is the generated repeated sequence, which is used as a control signal to output 20-bit time code frames in sequence; represents the th control signal; represents the output of the th multiplexer; , , are to connect the outputs of the multiplexer to the output of the signal selector respectively; is the output after adding the outputs of the multiplexer; is a periodic signal; is a square wave, is the period, and are the duty cycles, is the transformed signal, is the code-to-wave signal.

6. The carrier synchronization method according to claim 3, characterized in that, The preset threshold is 0.

5.

7. The carrier synchronization method according to claim 3, wherein Step S4 specifically includes: performing spreading operation on the binary waveform using a Gold code to obtain a spread signal, as shown in the formula: ， ， Among them, is the Gold code, is the Gold code length, i.e., the chip index, is the rectangular pulse function, is the duration of each chip, is the spread-spectrum signal, is the binary sequence obtained through threshold decision, is the number of bits, is the value of the nth data symbol.

8. The carrier synchronization method according to claim 3, wherein Step S5 specifically includes: performing BPSK modulation on the binary waveform using a low-frequency time code synchronous arctangent Costas loop to obtain a carrier-synchronized signal, as shown in the formula: ， Among them, is the signal after carrier synchronization, is the amplitude of the sine wave, is its initial phase, is the carrier frequency.

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