Laser communication test system based on code Doppler and code Doppler generation method thereof

Abstract

The present invention belongs to the field of laser Doppler technology, and specifically relates to a laser communication test system based on code Doppler and a code Doppler generation method thereof, including: S1, parameter initialization; the initialized parameters include the original sampling period, the original symbol rate, the rate offset, the new symbol rate, the number of symbol sampling points, and the code Doppler step amount; S2, using random binary data to generate a binary phase shift keying BPSK signal; S3, shaping filtering the BPSK signal through a square root raised cosine filter; S4, calculating the sampling time index through a time scaling ratio, and judging whether the sampling time index is within a target index range; if so, going to step S5; S5, interpolating and resampling the BPSK signal after shaping filtering based on the sampling time index and the Doppler phase offset. When performing Doppler frequency shift compensation, the present invention realizes the adjustment of the symbol rate through the calculation of the time scaling ratio, and combines interpolation to ensure the accuracy of the signal after resampling.

Description

Technical Field

[0001] The invention belongs to the technical field of laser Doppler, and in particular relates to a laser communication test system based on code Doppler and a code Doppler generating method thereof. Background Art

[0002] The laser Doppler effect is a wave-based frequency shift effect used to measure the speed of an object relative to a light source. In modern measurement and communication systems, laser Doppler technology is widely used in speed measurement, displacement detection and other fields due to its high precision and non-contact measurement characteristics. In addition, in wireless communications and laser communications, the frequency shift of the Doppler effect also has a profound impact on data transmission. Especially in high-speed mobile environments, such as satellite communications, drone communications, and high-speed train communications, the Doppler frequency shift poses a severe challenge to signal integrity and transmission quality.

[0003] In the above scenario, the signal frequency will change with the relative speed between the transmitter and the receiver, resulting in spectral expansion and inter-symbol interference of the signal. This frequency offset is more obvious in high-frequency environments (such as millimeter wave and terahertz communications), which greatly affects the signal quality of the communication system, the design of the modem, and the synchronization accuracy of the signal. Traditional optical signal transmitters often face many challenges when facing the requirements of high speed, large capacity and high reliability, especially in dynamic channel environments. Existing technologies have limitations in simulating Doppler frequency shift and cannot effectively deal with signal distortion and delay caused by complex communication conditions.

[0004] The frequency shift problem caused by the Doppler effect is mainly reflected in the following aspects:

[0005] (1) Signal distortion: Frequency shift can cause received signal distortion, especially for high-order modulation. Symbol points can deviate from their original positions, leading to demodulation errors.

[0006] (2) Inter-symbol interference (ISI): Due to frequency shift, the time intervals between symbols are no longer uniform, resulting in inter-symbol interference, which further degrades the performance of the communication system.

[0007] (3) Increased demodulator complexity: Existing demodulation algorithms need to deal with nonlinear distortion caused by frequency shift, and usually require complex preprocessing algorithms to compensate for it. Although many studies have proposed frequency shift compensation methods based on traditional signal processing, such as phase-locked loops (PLLs) and fast Fourier transforms (FFTs), these methods have certain limitations in high frequency, multipath, and complex motion environments. In particular, when dynamically adjusting the symbol rate and compensating for Doppler frequency shift, it is difficult to ensure both computational complexity and real-time performance. In addition, existing code Doppler generators also face many challenges in practical applications, including:

[0008] 1. Slow response speed: Traditional code Doppler generators often cannot quickly adapt to changes in the channel environment, resulting in delays in frequency shift compensation and affecting signal quality.

[0009] (ii) Lack of flexibility: Many existing systems can only support fixed modulation formats and lack the ability to flexibly adapt to multiple modulation methods, which is particularly important in high-speed and dynamic environments;

[0010] (III) Large consumption of computing resources: The existing frequency shift compensation algorithm consumes a large amount of computing resources when processing high-frequency signals, which limits the real-time processing capability of the system, especially in a multipath environment. Summary of the invention

[0011] Based on the above-mentioned shortcomings and deficiencies in the prior art, one of the objects of the present invention is to at least solve one or more of the above-mentioned problems in the prior art. In other words, one of the objects of the present invention is to provide a code Doppler-based laser communication test system and a code Doppler generation method thereof that meet one or more of the above-mentioned needs.

[0012] In order to achieve the above-mentioned object of the invention, the present invention adopts the following technical solutions:

[0013] A laser communication test system based on code Doppler, comprising:

[0014] The host computer is used to generate an original inter-satellite transmission frame; wherein the original inter-satellite transmission frame includes an inter-satellite data frame and a ranging frame;

[0015] The baseband simulator is used to receive the original inter-satellite transmission frame, and perform code Doppler generation and code modulation processing on the inter-satellite transmission frame according to the laser inter-satellite link signal system to obtain baseband data with code Doppler effect, and send the baseband data with code Doppler effect to the laser generator;

[0016] The time-frequency module is used to provide a reference clock for the baseband simulator;

[0017] The laser generator includes a tunable signal light source and a tunable local oscillator light source, which is used to modulate baseband data onto the tunable signal light source and transmit a binary phase shift keying BPSK signal to the laser terminal under test; and is also used to coherently demodulate the BPSK signal fed back by the laser terminal under test using the tunable local oscillator light source to obtain baseband data, and send it to a baseband simulator;

[0018] The baseband simulator is also used to sequentially demodulate, decode, and deframe the baseband data fed back by the laser generator, and send the deframed inter-satellite transmission frame to the host computer;

[0019] The host computer compares the inter-satellite transmission frame after the de-framing process with the original inter-satellite transmission frame to determine whether the laser terminal under test has the code Doppler processing capability.

[0020] As a preferred solution, the coding and modulation processing includes sequentially performing code Doppler generation, coding, interleaving, scrambling, framing and modulation mapping on the inter-satellite frame.

[0021] As a preferred solution, the baseband data with code Doppler effect is sent to the laser generator via a digital-to-analog converter.

[0022] As a preferred solution, the demodulation, decoding and de-framing processing includes sampling, carrier synchronization tracking, code element synchronization, de-interleaving, descrambling, decoding and de-framing of the baseband data in sequence.

[0023] The present invention also provides a code Doppler generation method for a laser communication test system as described in any one of the above schemes, comprising the following steps:

[0024] S1, parameter initialization; the initialized parameters include original sampling period, original symbol rate, rate offset, new symbol rate, number of symbol sampling points, and code Doppler step size;

[0025] S2, generating a binary phase shift keying BPSK signal using random binary data;

[0026] S3, performing shaping filtering on the BPSK signal through a square root raised cosine filter;

[0027] S4, calculating the sampling time index by the time scaling ratio, and determining whether the sampling time index is within the target index range; if so, proceeding to step S5;

[0028] S5. Based on the sampling time index and the Doppler phase shift, interpolate and resample the BPSK signal after the shaping filter.

[0029] As a preferred solution, step S2 includes the following steps:

[0030] S21, randomly generate binary signal: , represents the generation of a 1*N pseudo-random integer matrix whose element value range is [0, 1], where N is the number of data of the randomly generated binary signal;

[0031] S22, perform BPSK modulation on the binary signal: , and get the BPSK signal.

[0032] As a preferred solution, in step S4, the sampling time index The calculation formula is:

[0033] ;

[0034] Time Scaling ;

[0035] Among them, round is the rounding function, m is the current processing symbol index, sps is the number of symbol sampling points, R symbol is the original symbol rate, R new is the new symbol rate, which is the sum of the original symbol rate and the rate offset.

[0036] As a preferred solution, the target index range is ;in, BPSK signal array for shaping filter The length of the maximum dimension.

[0037] As a preferred solution, in step S5, the Doppler phase shift for:

[0038] ;

[0039] ;

[0040] Where j is the imaginary unit, is the current Doppler frequency shift, T s is the original sampling period, is the code Doppler step size.

[0041] As a preferred solution, in step S5, the BPSK signal after shaping filtering is interpolated to align with the transformed signal array y:

[0042] ;

[0043] in, Indicates the 1st symbol sampling point to the spsth symbol sampling point.

[0044] Compared with the prior art, the present invention has the following beneficial effects:

[0045] The code Doppler-based laser communication test system of the present invention can effectively test whether the laser terminal under test has the code Doppler processing capability;

[0046] The code Doppler generation method of the present invention realizes the adjustment of the symbol rate by calculating the time scaling ratio when performing Doppler frequency shift compensation, and combines interpolation to ensure the accuracy of the signal after resampling. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 1 is a hardware architecture diagram of a laser communication test system based on code Doppler according to Embodiment 1 of the present invention;

[0048] Figure 2 is a test flow chart of a laser communication test system based on code Doppler according to embodiment 1 of the present invention;

[0049] Figure 3 is a comparison diagram of the original signal of Example 1 of the present invention and the signal transformed by the code Doppler generation method;

[0050] Figure 4 This is the signal eye diagram after Doppler generation in Example 1 of the present invention. DETAILED DESCRIPTION

[0051] In order to more clearly illustrate the embodiments of the present invention, the specific implementation methods of the present invention will be described below with reference to the accompanying drawings. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those of ordinary skill in the art, other accompanying drawings and other implementation methods can be obtained based on these accompanying drawings without creative work.

[0052] With the rapid development of communication technology and the increasing shortage of spectrum resources, high-frequency bands such as millimeter waves and terahertz have gradually become the core technologies of future communication systems. In these high-frequency environments, the transmission distance of communication links is short and signals are easily obstructed, but their high speed and large bandwidth advantages make them have wide application potential in future wireless communications. However, the Doppler effect is more obvious at these high frequencies, which puts higher requirements on signal processing.

[0053] The core innovation of the present invention is to provide a laser communication test system based on code Doppler and a code Doppler generation method capable of real-time compensation of Doppler frequency shift. By accurately adjusting the symbol rate and time scaling ratio, the smooth transmission of signals can be achieved in a frequency shift environment, which can effectively reduce the inter-symbol interference caused by frequency shift and maintain the integrity of the signal modulation format. The specific overview is as follows:

[0054] 1. Dynamic symbol rate adjustment;

[0055] By measuring and estimating the frequency shift, the symbol rate is dynamically adjusted to ensure that the symbol interval of the signal is adapted to the transmission environment, thereby avoiding inter-symbol interference (ISI) caused by time mismatch. Compared with traditional methods such as phase-locked loop (PLL), it has higher real-time performance and accuracy.

[0056] 2. Combination of time scaling and interpolation techniques;

[0057] When performing Doppler frequency shift compensation, the present invention realizes the adjustment of the symbol rate by calculating the time scaling ratio, and combines the interpolation method to ensure the accuracy of the signal after resampling. Specifically, according to the change of the symbol rate, the interpolation method is used to realign the symbols on the frequency shift signal, so as to adjust the signal rate without changing the number of sampling points.

[0058] 3. Combine roll-off filtering with binary phase shift keying BPSK modulation to optimize signal spectrum;

[0059] The present invention combines a square root raised cosine filter to ensure signal shaping and spectrum limitation, thereby effectively suppressing out-of-band radiation and making the signal more robust. In particular, under BPSK modulation, combined with the characteristics of the roll-off filter, efficient frequency compensation can be achieved within a limited bandwidth.

[0060] 4. Application in high frequency environment;

[0061] For high-frequency communication systems such as millimeter waves and terahertz, the present invention can significantly improve the frequency shift compensation effect, so that the high-frequency communication system can still maintain stable communication quality in a high-speed mobile environment.

[0062] 5. Integration and intelligence of laser communication test system;

[0063] The laser communication test system of the present invention has the ability to adjust the Doppler frequency shift in real time, and can not only support signal generation of multiple modulation formats, but also dynamically optimize parameters according to channel status to ensure signal stability in complex dynamic environments.

[0064] 6. Adaptive signal processing framework;

[0065] The laser communication test system of the present invention designs an adaptive signal processing framework, which is a system that can dynamically adjust the signal processing strategy according to real-time feedback information, including real-time channel state monitoring, dynamic parameter adjustment, frequency shift compensation, data analysis and optimization, and feedback control mechanism to improve the robustness and adaptability of the system.

[0066] 7. Multifunctional data interaction and analysis;

[0067] The laser communication test system of the present invention has powerful data interaction and analysis capabilities, and can exchange data with a host computer in real time through a network interface to monitor signal quality and system status, thereby providing data support for subsequent system optimization and maintenance.

[0068] Embodiment 1:

[0069] like Figure 1 and Figure 2As shown, the code Doppler-based laser communication test system of this embodiment includes a host computer, a baseband simulator, a time-frequency module and a laser generator.

[0070] The host computer of this embodiment is used to generate an original inter-satellite transmission frame; wherein the original inter-satellite transmission frame includes an inter-satellite data frame and a ranging frame; then, the original inter-satellite transmission frame is sent to a baseband simulator;

[0071] The baseband simulator of this embodiment is used to receive the original inter-satellite transmission frame, and use the modulation and demodulation module to perform code Doppler generation and code modulation processing on the inter-satellite transmission frame according to the laser inter-satellite link signal system to obtain baseband data with code Doppler effect, and send the baseband data with code Doppler effect to the laser generator;

[0072] Specifically, the coding and modulation processing includes code Doppler generation, 7 / 8 LDPC coding, interleaving, scrambling, framing and modulation mapping of the intersatellite frame in sequence. The baseband data with code Doppler effect is converted by a digital-to-analog converter (DAC) and sent to the laser generator. In addition, LDPC coding is a matrix-based coding technology that uses sparse matrices to represent the coding and decoding process.

[0073] The time-frequency module of this embodiment is used to provide a reference clock for the baseband simulator;

[0074] The laser generator of this embodiment includes a tunable signal light source and a tunable local oscillator light source, which is used for laser modulation, that is, modulating baseband data onto the tunable signal light source and transmitting a binary phase shift keying BPSK signal to the laser terminal under test; and is also used for coherently demodulating the BPSK signal fed back by the laser terminal under test using the tunable local oscillator light source to obtain baseband data, and sending it to the baseband simulator;

[0075] The baseband simulator is also used to sequentially demodulate, decode, and deframe the baseband data fed back by the laser generator, and send the deframed intersatellite transmission frame to the host computer; wherein the demodulation, decoding, and deframe processing include sampling, synchronization and tracking (carrier synchronization tracking, symbol synchronization), deinterleaving, descrambling, 7 / 8LPDC decoding, and deframe of the baseband data in sequence. The sampling is collected by analog-to-digital conversion ADC.

[0076] The specific processes of the above-mentioned code Doppler generation, encoding, interleaving, scrambling, framing, modulation mapping, sampling, carrier synchronization tracking, symbol synchronization, deinterleaving, descrambling, decoding, and deframing can be referred to the existing technology and will not be repeated here.

[0077] The host computer of this embodiment compares the inter-satellite transmission frame after the de-framing process with the original inter-satellite transmission frame to determine whether the laser terminal under test has the code Doppler processing capability. Specifically, if the comparison results are the same, the laser terminal under test has the code Doppler processing capability; if the comparison results are different, the laser terminal under test does not have the code Doppler processing capability.

[0078] Based on the above laser communication test system, the code Doppler generation method of this embodiment includes the following steps:

[0079] (1) Parameter initialization: the parameters to be initialized include the original symbol rate, rate offset, new symbol rate, number of symbol sampling points, Doppler frequency shift range, code Doppler frequency shift simulation accuracy, code Doppler frequency shift interval, code Doppler step size, and code Doppler change rate.

[0080] Specifically, the original symbol rate R symbol =10MHz;

[0081] Rate Deviation ;

[0082] New symbol rate ;

[0083] Symbol sampling points sps=16;

[0084] Set the Doppler shift range ;

[0085] Set the code Doppler shift simulation accuracy ;

[0086] Set the code Doppler frequency shift interval ;

[0087] Set the code Doppler step size ;

[0088] Set the code Doppler change rate ;

[0089] (2) Generate a binary phase shift keying BPSK signal using random binary data;

[0090] Use random binary data to generate a BPSK signal, and map 0 to -1 and 1 to 1 through mapping, as follows:

[0091] First, generate a random binary signal: , represents the generation of a 1*N pseudo-random integer matrix whose element value range is [0, 1], where N is the number of data of the randomly generated binary signal;

[0092] Then, the binary signal is modulated by BPSK: , and get the BPSK signal.

[0093] (3) Perform shaping filtering on the BPSK signal through a square root raised cosine filter;

[0094] The BPSK signal is shaped by a square root raised cosine filter to ensure a smooth transition of the signal spectrum, and a square root raised cosine filter (with a roll-off factor of 0.5) is used to limit the signal bandwidth.

[0095] Specifically, a square root raised cosine filter is used for shaping, and the filter design is as follows:

[0096] rcos_fir=rcosdesign(roll-off, span, sps, 'sqrt');

[0097] rcosdesign is a function used to design filters, especially square root raised cosine filters; the roll-off coefficient roll-off represents the relationship between the bandwidth of the filter and the signal bandwidth, and its value is usually between 0 and 1. The larger the value, the wider the bandwidth and the smoother the transition zone of the signal; span represents the duration of the filter, in symbol periods, which specifies the length of the filter; sps represents the number of sampling points per symbol, that is, the number of symbol sampling points, which is the upsampling factor, indicating the number of times each symbol is sampled; 'sqrt' indicates the specified filter type, that is, square root raised cosine filter; square root raised cosine filters are usually used for signal shaping to reduce inter-symbol interference (ISI).

[0098] (4) Calculate the sampling time index by the time scaling ratio, and determine whether the sampling time index is within the target index range; if so, go to step (5); if not, alarm to indicate an error;

[0099] Specifically, the time scaling is calculated according to the new symbol rate:

[0100] ;

[0101] R new R is the new symbol rate, which indicates the signal transmission rate after the frequency shift is applied. This value is the original symbol rate plus the rate offset. symbol It is the original symbol rate, which means the transmission rate when the signal does not undergo any frequency shift or adjustment.

[0102] The time scaling ratio of this embodiment Indicates the proportional relationship between the new symbol rate and the original symbol rate. This value is used to adjust the sampling time of the signal to ensure the correct alignment of the signal at the new rate.

[0103] The sampling time index of this embodiment The calculation formula is:

[0104] ;

[0105] Among them, round is the rounding function, m is the current processing symbol index, sps is the number of symbol sampling points, R symbol is the original symbol rate, R new is the new symbol rate, which is the sum of the original symbol rate and the rate offset.

[0106] In addition, the target index range of this embodiment is ;in, BPSK signal array for shaping filter The length of the maximum dimension.

[0107] (5) Interpolate and resample the BPSK signal after shaping filtering based on the sampling time index and Doppler phase offset;

[0108] The Doppler phase shift of this embodiment for:

[0109] ;

[0110] ;

[0111] Where j is the imaginary unit, is the current Doppler frequency shift, T s is the original sampling period, is the code Doppler step size.

[0112] Specifically, the BPSK signal after shaping filtering is interpolated to align with the transformed signal array y:

[0113] ;

[0114] in, Indicates the 1st symbol sampling point to the spsth symbol sampling point.

[0115] This embodiment adjusts the sampling rate of the signal by an interpolation method, so as to maintain the integrity of the signal at the new sampling rate.

[0116] The above code Doppler generation method is simulated and tested, and the signal waveforms before and after compensation are plotted to show the effect of time scaling on signal frequency offset compensation. Figure 3As shown, the comparison before and after the symbol rate change is intuitively displayed. By simulating the signal morphology under different symbol rates, the influence of Doppler frequency shift on the communication signal is revealed; for the original signal generated at a symbol rate of 10MHz, its waveform is smooth and periodic, representing the signal that was not initially affected by frequency offset or transformation; representing the signal after frequency offset, that is, the transformed signal, its symbol rate has increased by 25kHz to 10MHz+25kHz, and it can be observed that the period of the waveform has changed, the overall phase has shifted, and the amplitude has also changed over time, indicating that the signal has been affected by Doppler frequency shift or other dynamic changes.

[0117] like Figure 4 As shown, the signal eye diagram after code Doppler generation is used to evaluate the signal quality and inter-symbol interference in the communication system; the horizontal axis represents time, and the unit is usually code element period; the vertical axis represents the signal amplitude, and the intersection (opening area): the superposition of multiple signals with different code element periods forms an eye-like figure, and the shape of the opening reflects the quality of the signal; the horizontal opening width of the eye diagram represents the time margin between symbols, and the larger opening width of the signal generated by the code Doppler generation method of this embodiment means that the inter-symbol interference is smaller, and the system clock recovery is easier; the height of the vertical opening represents the noise tolerance; the signal opening generated by the code Doppler generation method of this embodiment is high, indicating that the system has a strong anti-interference ability to noise; signals of different symbols have obvious overlap at the intersection, indicating that there is a certain amount of inter-symbol interference ISI, and the lines do not completely overlap on the horizontal axis, indicating that there is clock jitter.

[0118] The above description is only a detailed description of the preferred embodiments and principles of the present invention. For ordinary technicians in this field, according to the ideas provided by the present invention, there will be changes in the specific implementation methods, and these changes should also be regarded as the protection scope of the present invention.

Claims

1. A laser communication test system based on code Doppler, characterized in that: include: The host computer is used to generate an original inter-satellite transmission frame; wherein the original inter-satellite transmission frame includes an inter-satellite data frame and a ranging frame; The baseband simulator is used to receive the original inter-satellite transmission frame, and perform code Doppler generation and code modulation processing on the inter-satellite transmission frame according to the laser inter-satellite link signal system to obtain baseband data with code Doppler effect, and send the baseband data with code Doppler effect to the laser generator; The time-frequency module is used to provide a reference clock for the baseband simulator; The laser generator includes a tunable signal light source and a tunable local oscillator light source, which is used to modulate baseband data onto the tunable signal light source and transmit a binary phase shift keying BPSK signal to the laser terminal under test; and is also used to coherently demodulate the BPSK signal fed back by the laser terminal under test using the tunable local oscillator light source to obtain baseband data, and send it to a baseband simulator; The baseband simulator is also used to sequentially demodulate, decode, and deframe the baseband data fed back by the laser generator, and send the deframed inter-satellite transmission frame to the host computer; The host computer compares the inter-satellite transmission frame after the de-framing process with the original inter-satellite transmission frame to determine whether the laser terminal under test has the code Doppler processing capability.

2. The laser communication test system according to claim 1, characterized in that: The coding and modulation processing includes sequentially performing code Doppler generation, coding, interleaving, scrambling, framing and modulation mapping on the inter-satellite frame.

3. The laser communication test system according to claim 2, characterized in that: The baseband data with code Doppler effect is sent to the laser generator through a digital-to-analog converter.

4. The laser communication test system according to claim 2, characterized in that: The demodulation, decoding and de-framing processing includes sampling, carrier synchronization tracking, symbol synchronization, de-interleaving, descrambling, decoding and de-framing of baseband data in sequence.

5. The code Doppler generation method of the laser communication test system according to any one of claims 1 to 4, characterized in that: The following steps are involved: S1, parameter initialization; the initialized parameters include original sampling period, original symbol rate, rate offset, new symbol rate, number of symbol sampling points, and code Doppler step size; S2, generating a binary phase shift keying BPSK signal using random binary data; S3, performing shaping filtering on the BPSK signal through a square root raised cosine filter; S4, calculate the sampling time index, and determine whether the sampling time index is within the target index range; if so, go to step S5; In step S4, the sampling time index n index The calculation formula is: n index =round((m-1)×time_scale×sps); Time Scaling Among them, round is the rounding function, m is the current processing symbol index, sps is the number of symbol sampling points, R symbol is the original symbol rate, R new is the new symbol rate, which is the sum of the original symbol rate and the rate offset; S5. Based on the sampling time index and the Doppler phase shift, interpolate and resample the BPSK signal after the shaping filter.

6. The code Doppler generation method according to claim 5, characterized in that: The step S2 comprises the following steps: S21. Randomly generate a binary signal: msg = randi ([0, 1], 1, N), which means generating a 1*N pseudo-random integer matrix whose element value range is [0, 1], where N is the number of data of the randomly generated binary signal; S22. Perform BPSK modulation on the binary signal: bmsg=2·msg-1 to obtain a BPSK signal.

7. The code Doppler generation method according to claim 5, characterized in that: The target index range is [1, length(x filtered )-sps+1]; where length(x filtered ) is the BPSK signal array x of the shaping filter filtered The length of the maximum dimension.

8. The code Doppler generation method according to claim 5, characterized in that: In step S5, the Doppler phase shift doppler_phase is: current_doppler * =current_doppler+Df D ; Where j is an imaginary unit, current_doppler is the current Doppler frequency shift, T s is the original sampling period, Δf D is the code Doppler step size.

9. The code Doppler generation method according to claim 8, characterized in that: In step S5, the BPSK signal after the shaping filter is interpolated to align with the transformed signal array y: y[(m-1)×sps+(1:sps)]=x filtered (n index +(1:sps)-1)·doppler_phase; Among them, 1:sps represents the 1st symbol sampling point to the spsth symbol sampling point.

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