A GMSK coherent receiving method based on optimal sampling point

Abstract

This invention belongs to the field of continuous phase modulation technology and proposes a GMSK coherent reception method based on optimal sampling points. At the transmitter, phase decoupling and π / 2 phase rotation between symbols are achieved by constructing a precoding method. At the receiver, optimal sampling point decimation is achieved at the moment of minimum inter-symbol crosstalk, eliminating the need for oversampling. The modulation phase at the optimal sampling point within each symbol is reconstructed using the synchronization sequence to cancel the modulation phase component of the receiving synchronization segment. Coherent estimation of Doppler phase and frequency is achieved through coherent processing, improving the resistance to Doppler frequency offset and the accuracy of Doppler frequency offset and phase offset estimation. The compensated signal is then linearly superimposed with the two optimal sampling points before and after the in-direction and quadrature branches to recover the original information symbols, effectively reducing the sampling signal processing length, processing delay, and hardware overhead. Simultaneously, a resampling algorithm based on correlation curve fitting is introduced to effectively reduce the system reception performance loss caused by sampling errors.

Description

Technical Field

[0001] This invention relates to the field of continuous phase modulation technology, and in particular to a GMSK coherent reception method based on optimal sampling points. Background Technology

[0002] Gaussian Minimum Shift Keying (GMSK) is a special case of continuous phase modulation. Due to its high spectral and power efficiency, it achieves strong out-of-band rejection without filtering, while maintaining its original constant envelope characteristic. This allows it to operate in the nonlinear saturation region of high-power amplifiers, enabling high-power amplification. Therefore, GMSK has been widely studied in fields where power and bandwidth are limited, such as satellite navigation, satellite communication, and deep space communication.

[0003] Compared to incoherent demodulation, coherent demodulation algorithms offer performance close to theoretical values. Carrier synchronization is a crucial step in coherent reception processing, and the accuracy of Doppler frequency and phase estimation directly impacts the coherent demodulation performance of the communication system. For high-dynamic GMSK burst communication systems, to overcome the short-time rapid fading introduced by the time-frequency dual-selection channel, several synchronization segments are typically inserted uniformly into the data frame structure. A data-assisted open-loop synchronization method is used to quickly estimate short-time Doppler frequency and phase changes, achieving carrier synchronization. Due to the phase continuity of GMSK, unknown data segments introduce ambiguous initial phases into subsequent synchronization segments, making it impossible to eliminate the GMSK modulation phase in the synchronization segments and thus affecting the accurate estimation of the Doppler frequency. Although the frequency doubling method can be an effective solution, eliminating the influence of ambiguous initial phases by amplifying the phase by an integer multiple and achieving accurate frequency offset estimation, the Doppler frequency estimation range will decrease proportionally. The phase estimation range shrinks to -π / 4 to π / 4, and the frequency estimation range shrinks to -1 / 8T. interval ~1 / 8T interval It is not suitable for high dynamic doppler scenes. Summary of the Invention

[0004] To address the problems existing in the prior art, a GMSK coherent reception method based on optimal sampling points is provided. The service data is split into multiple data segments, and mutually orthogonal synchronization sequences are inserted before and after each data segment to form a pulse signal. The pulse signal is pre-coded and then GMSK modulated. The phase decoupling and π / 2 phase rotation between GMSK symbols are completed to obtain the GMSK modulated signal. The GMSK modulated signal is then converted from digital to analog and then up-converted to analog before being radiated. The receiver resamples the received signal after detection, approximating the sampling time to the minimum inter-symbol interference (ISI). Optimal sampling point extraction is achieved at the minimum ISI. Using a data-assisted open-loop synchronization method, oversampling is unnecessary. The modulation phase of each symbol within the two synchronization sequences before and after each pulse is reconstructed using the local synchronization sequence. This cancels the modulation phase components of the two synchronization segments before and after each received pulse, achieving Doppler phase estimation for the two synchronization sequences before and after each pulse. The Doppler phase estimates from the two synchronization sequences before and after each pulse data segment are differentially calculated to achieve Doppler frequency estimation for each pulse. The Doppler frequency estimation results from multiple pulses are averaged to achieve coherent Doppler frequency estimation. The coherent estimation results of the Doppler frequency and the Doppler phase estimation results of each pulse's post-synchronization sequence are obtained through linear backtracking to obtain the fitted pre-synchronization sequence Doppler phase for each pulse. The pre-synchronization sequence Doppler phase and the fitted pre-synchronization sequence Doppler phase are averaged to achieve coherent estimation of the pre-synchronization sequence Doppler phase for each pulse. The Doppler phase change of each pulse data segment is fitted using the coherent estimation results of the Doppler frequency and the pre-synchronization sequence Doppler phase, yielding the channel fading response. After equalization processing of the channel fading response for each received pulse signal, GMSK demodulation and hard decision are performed. The hard decision results of multiple pulses are framed to recover the service data. This invention eliminates the need for oversampling, requiring only 1x symbol rate sampling to complete baseband carrier recovery and coherent demodulation. Coherent processing increases the processing gain to improve the estimation accuracy of Doppler phase and frequency. It not only possesses the ability to resist large Doppler frequency offsets but also reduces hardware overhead, sampling signal processing length, and processing delay with minimal performance loss, making it more suitable for engineering implementation.

[0005] The technical solution adopted in this invention is as follows: A GMSK coherent reception method based on optimal sampling points, comprising:

[0006] Transmitter: The service data is split into multiple data segments. Orthogonal synchronization sequences are inserted before and after each data segment to form a pulse signal. The pulse signal is pre-coded and then GMSK modulated. Phase decoupling and π / 2 phase rotation between GMSK symbols are completed to obtain the GMSK modulated signal. The GMSK modulated signal is then converted from digital to analog and then up-converted to analog before being radiated.

[0007] Receiver: The received baseband signal is obtained by analog-to-digital conversion and down-conversion of multiple burst pulse stream signals. Each pulse signal is detected and extracted from the received baseband signal, and resampled to obtain a timing synchronization signal. The moment with the minimum inter-symbol interference (ISI) within the GMSK symbol time is taken as the optimal sampling point. The receiver extracts the optimal sampling point for each pulse timing synchronization signal at the moment of minimum ISI, performs Doppler phase estimation of the two synchronization sequences before and after each pulse, and performs differential operations on the estimated Doppler phases to achieve Doppler frequency estimation for each pulse. The Doppler frequencies of multiple pulses are then combined. The Doppler frequency estimation results yield a coherent estimate of the Doppler frequency. Using the coherent Doppler frequency estimation results and the Doppler phase estimation results of the two synchronization sequences before and after each pulse, a coherent Doppler phase estimation of the synchronization sequence before each pulse is achieved. The Doppler phase change of each pulse data segment is fitted using the coherent Doppler frequency estimation results and the coherent Doppler phase estimation results of the synchronization sequence before each pulse to obtain the channel fading response. After equalization processing of the channel fading response of each received pulse signal, GMSK demodulation and hard decision are performed. The hard decision results of multiple pulses are framed to recover the service data.

[0008] Furthermore, the specific method of precoding is as follows:

[0009]

[0010] Where N is a natural number, d i a is the i-th original bit within the pulse, and its value is ±1. i It represents the i-th precoded bit within the pulse.

[0011] Furthermore, in the process of obtaining the received baseband signal by analog down-conversion and analog-to-digital conversion of the received GMSK modulated signal, the sampling rate is twice the symbol rate.

[0012] Furthermore, the specific method for resampling is as follows:

[0013] The peak time incoherent processing result, the previous incoherent processing result, and the next incoherent processing result of the peak time are obtained after incoherent detection of multiple pulse signal synchronization sequences. The sampling time deviation is estimated by the correlation curve fitting method.

[0014] Construct interpolation filter coefficients based on sampling time deviation;

[0015] The received baseband pulse signal is interpolated based on the interpolation filter coefficients to obtain a timing precision synchronization pulse signal after the sampling time is synchronized with the minimum time of inter-symbol interference.

[0016] Furthermore, the coherent estimation method for the Doppler frequency is as follows:

[0017] Extract the presynchronization sequence and postsynchronization sequence from the timing precision synchronization pulse signal, multiply them by the conjugate of the local sequence, sum them, and take the phase to obtain the Doppler phase estimate of the presynchronization sequence and postsynchronization sequence of the pulse;

[0018] Doppler frequency estimation is performed using the difference between the Doppler phase estimates of the pre-synchronization sequence and the post-synchronization sequence.

[0019] The Doppler frequencies estimated from multiple pulses are averaged to complete the coherent estimation of Doppler frequencies.

[0020] Furthermore, the Doppler phase coherent estimation method for each pulse pre-synchronization sequence is as follows:

[0021] Based on the Doppler frequency coherent estimation results and the Doppler phase estimation results of the post-synchronization sequence within each pulse, the Doppler phase of the pre-synchronization sequence fitted for each pulse is obtained by linear backtracking.

[0022] The Doppler phase of the presynchronous sequence within each pulse and the fitted Doppler phase estimation results of the presynchronous sequence are averaged to obtain the coherent estimation of the Doppler phase of the presynchronous sequence within each pulse.

[0023] Furthermore, the channel fading response acquisition method is as follows: the channel fading response of the pulse is obtained by fitting the results of the intrapulse Doppler frequency coherent estimation and the Doppler phase coherent estimation of the pre-synchronization sequence of each pulse; the channel fading response of each received pulse signal is obtained in the same way.

[0024] Furthermore, the equalization processing method is as follows: based on the acquired channel fading response, the zero-forcing algorithm is used to directly cancel the channel fading response of the received pulse signal.

[0025] Furthermore, the specific method for recovering the business data includes:

[0026] Extract the equalized signal obtained after channel equalization processing, and the sampling time is the optimal sampling point time with the minimum inter-symbol crosstalk of GMSK symbols.

[0027] GMSK demodulation is performed on the channel equalization signal to obtain the demodulation soft information for each symbol of each pulse:

[0028]

[0029] Where imag(·) is the imaginary part operation, real(·) is the real part operation, dem(k) is the observation of the k-th symbol of the equalized signal within the pulse, and DemSig(k) is the demodulation soft information of the k-th symbol within the pulse.

[0030] Hard decision is made on the demodulated soft information of each symbol in each pulse to recover the service data.

[0031] Furthermore, the hard decision specifically refers to:

[0032]

[0033] Where OutSig(k) is the service data corresponding to the kth symbol, and DemSig(k) is the demodulation information corresponding to the kth symbol.

[0034] Compared with existing technologies, the beneficial effects of adopting the above technical solution are as follows:

[0035] 1) Improved Doppler immunity and reduced receiver processing complexity: The transmitter achieves phase decoupling and π / 2 phase rotation between symbols through a precoding method. The receiver extracts the optimal sampling point at the moment of minimum inter-symbol interference, transforming GMSK into OQPSK-like modulation. This eliminates the need for oversampling, requiring only sampling at 1x the symbol rate. The modulation phase of the optimal sampling point within each symbol is reconstructed using the local synchronization sequence to cancel the modulation phase component of the receiving synchronization segment. Coherent processing is used to increase the processing gain, improving the estimation accuracy of Doppler phase and frequency, and completing baseband carrier recovery and coherent demodulation. Compared to the traditional frequency doubling method, this method improves the phase estimation range to -π to π and the frequency estimation range to -1 / 2T. interval ~1 / 2T interval It possesses the capability to resist Doppler frequency offset. Simultaneously, the demodulation module processes only the optimal sampling points within the GMSK symbol, recovering the original information symbol by linearly superimposing the two optimal sampling points before and after the Doppler frequency offset and phase offset compensation signals, respectively. This process requires only two delay units and two adders to achieve coherent demodulation. Compared to the optimal GMSK demodulation receiver, the proposed GMSK coherent reception method has lower complexity, its performance is comparable to the optimal demodulation receiver, and it reduces hardware overhead, sampling signal processing length, and processing delay with minimal performance loss, making it more suitable for engineering implementation.

[0036] 2) Suppress sampling time error and improve demodulation and decoding performance: A resampling algorithm based on correlation curve fitting is proposed. The non-coherent processing results at the peak of the correlation curve, the non-coherent processing results before the peak, and the non-coherent processing results after the peak are used to estimate the sampling time deviation through the correlation curve fitting method. The interpolation filter is then reconstructed to filter the sampling deviation signal, so that the sampling time is close to the time of minimum inter-symbol interference, effectively reducing the demodulation and decoding performance loss of the receiving platform caused by sampling error. Attached Figure Description

[0037] Figure 1This is a schematic diagram of the GMSK coherent reception method based on the optimal sampling point proposed in this invention.

[0038] Figure 2 This is a schematic diagram illustrating the frequency and phase estimation accuracy of the multi-frequency bandgap in one embodiment of the present invention.

[0039] Figure 3 (a)~ Figure 3 (d) is a schematic diagram of the decoding performance of the correlation curve fitting algorithm during the resampling process in one embodiment of the present invention.

[0040] Figure 4 (a)~ Figure 4 (b) is a schematic diagram of the GMSK demodulation performance and processing method in one embodiment of the present invention. Detailed Implementation

[0041] The embodiments of this application are described in detail below, examples of which are illustrated in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar modules or modules having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain this application, and should not be construed as limiting this application. Rather, the embodiments of this application include all variations, modifications, and equivalents falling within the spirit and scope of the appended claims.

[0042] This embodiment proposes a coherent GMSK reception method based on optimal sampling points. The transmitter constructs a precoding scheme to achieve phase decoupling and π / 2 phase rotation between symbols. The receiver extracts the optimal sampling point at the moment of minimum inter-symbol interference, transforming GMSK into OQPSK-like modulation. This eliminates the need for oversampling, requiring only sampling at one symbol rate. The modulation phase of the optimal sampling point within each symbol is reconstructed using a local synchronization sequence to cancel the modulation phase component of the received synchronization segment. Coherent processing is used to increase the processing gain, improving the estimation accuracy of Doppler phase and frequency, thus completing baseband carrier recovery and enhancing resistance to Doppler frequency offset. The signals compensated for Doppler frequency offset and phase offset are then linearly superimposed with the observations from the two optimal sampling points before and after the in-direction and quadrature branches to recover the original information symbols. Please refer to [reference needed]. Figure 4 The demodulation process requires only two delay units and two adders to achieve coherent demodulation, realizing low-complexity GMSK coherent demodulation processing at low sampling rates. This effectively reduces the processing length and latency of the sampled signal. Simultaneously, a resampling algorithm based on correlation curve fitting is introduced to approximate the optimal sampling time, effectively reducing the system's receiver performance loss caused by sampling errors. The specific scheme is as follows:

[0043] Please refer to Figure 1This GMSK coherent reception method based on optimal sampling points includes two parts: the transmitter and the receiver. The transmitter includes packetization, precoding, GMSK modulation, digital-to-analog conversion, and analog up-conversion. The receiver includes analog down-conversion, analog-to-digital conversion, signal detection, resampling, channel estimation, channel equalization, and GMSK demodulation. The following sections will explain each process at both the transmitter and receiver.

[0044] The transmitting end includes:

[0045] Step S1, Grouping: Divide the business data into multiple data segments, and insert mutually orthogonal synchronization sequences before and after each data segment to form pulse signals.

[0046] Step S2, Precoding. The pulse is precoded. In this embodiment, the precoding method is as follows:

[0047]

[0048] Where N is the set of natural numbers, d i a is the i-th original bit within the pulse, and its value is ±1. i It represents the i-th precoded bit within the pulse.

[0049] Step S3, GMSK modulation. The pre-encoded bits are subjected to GMSK modulation to achieve phase decoupling between GMSK symbols and a phase rotation of π / 2. The output GMSK signal can be considered as OQPSK modulation that depends only on the current input, as detailed below:

[0050]

[0051]

[0052]

[0053]

[0054] Among them, E b Represents symbolic energy. Let represent the imaginary part, erfc(·) represent the complementary error function, L be the correlation length, T be the symbol time, q(t) be the GMSK phase shaping function with a time length of L×T, and B be the 3dB bandwidth of the signal. B×T is the normalized bandwidth and satisfies B×T≥0.25, γ + =β(t+T / 2), γ - =β(tT / 2).

[0055] Step S4: Digital-to-Analog Conversion and Analog Up-Conversion. The GMSK modulated signal is radiated after digital-to-analog conversion and analog up-conversion. The digital-to-analog conversion and analog up-conversion processes are standard procedures and will not be described in detail here.

[0056] The signal radiated by the transmitter can be received by the receiver. The receiver then performs the following process:

[0057] Step S5: Analog Down-Conversion and Analog-to-Digital Conversion. The received GMSK modulated signal with noise interference is subjected to analog down-conversion and analog-to-digital conversion to obtain the received baseband signal. The sampling rate is twice the symbol rate. The analog down-conversion and analog-to-digital conversion process is standard and will not be described in detail here.

[0058] Step S6: Signal Detection. Perform correlation detection on the received baseband signal and extract each pulse signal.

[0059] Step S7: Resampling. The received signal in the radiation band is resampled to obtain the received pulse signal after sampling time synchronization.

[0060] In order to reduce the sampling time deviation and achieve synchronization with the minimum inter-symbol interference, the following resampling process is adopted in this embodiment.

[0061] ① The peak time of the output after incoherent detection of multiple pulse signal synchronization sequences is the incoherent processing result cor(T) peak The incoherent processing result preceding the peak time, cor(T) peak -1) and the subsequent incoherent processing result cor(T) at the peak time. peak +1), and the sampling time deviation is estimated using a correlation curve fitting method. The specific formula is as follows:

[0062]

[0063] Where T is the symbol time, T peak This is the peak time.

[0064] ② Construct the difference filter coefficients based on the sampling time deviation, as follows:

[0065]

[0066] cof = [1 uu 2 ]

[0067] Where cof represents the coefficients of the difference filter.

[0068] ③ The received baseband pulse signal is obtained by interpolating the received baseband pulse signal according to the interpolation filter coefficients. Assume the current symbol sampling point is the k-th sampling point r within the baseband signal after down-conversion of the j-th pulse.j (k), then the interpolated value is:

[0069]

[0070]

[0071] Where [·]′ represents the matrix transpose operation, where, This represents the interpolation matrix.

[0072] Step S8, Channel Estimation. The modulation phase at the optimal sampling point is reconstructed using the local synchronization sequence. This phase is then multiplied by the conjugate of the two synchronization sequences preceding and following each pulse at the optimal sampling point, and the summation and phase operation are performed to estimate the Doppler phase of the two synchronization sequences before and after each pulse. The Doppler phase estimates of the two synchronization sequences before and after each pulse data segment are then differentially calculated to estimate the Doppler frequency of each pulse. The Doppler frequency estimation results from multiple pulses are averaged to achieve coherent estimation of the Doppler frequency. Using the coherent estimation results of the Doppler frequency and the Doppler phase estimation results of the synchronization sequence following each pulse, the fitted Doppler phase of the preceding synchronization sequence for each pulse is obtained through linear backtracking. The Doppler phase of the preceding synchronization sequence for each pulse and the fitted Doppler phase of the preceding synchronization sequence are averaged to achieve coherent estimation of the Doppler phase of the preceding synchronization sequence for each pulse. Finally, the Doppler phase change of each pulse data segment is fitted using the coherent estimation results of the Doppler frequency and the coherent estimation results of the Doppler phase of the preceding synchronization sequence to obtain the channel fading response. Specifically, the moment with the minimum inter-symbol interference within the GMSK symbol time is taken as the optimal sampling point. The receiver extracts the optimal sampling point for each pulse timing synchronization signal at the moment with the minimum inter-symbol interference.

[0073] In this embodiment, channel estimation includes two parts: Doppler frequency coherent estimation and Doppler phase coherent estimation, as detailed below:

[0074] (1) Doppler frequency coherent estimation

[0075] ① Extract the pre-synchronization sequence and post-synchronization sequence of each pulse signal, multiply them by their conjugates with the local sequence, sum them, and take the phase to obtain the Doppler phase estimate of the pre-synchronization sequence and post-synchronization sequence of that pulse. Take the m-th pulse as an example.

[0076] Doppler phase estimation of the presynchronization sequence within the m-th pulse θ m,pre :

[0077]

[0078] Where atan(·) is the phase take operation, (·)* is the conjugate take operation, len is the symbol length of the synchronization sequence, and y m(k) represents the signal observation at the k-th optimal sampling time within the m-th pulse after resampling, and c(k) is the value of the k-th symbol in the local sequence, i.e.:

[0079]

[0080] Where, d i It is the i-th original bit within the pulse and takes a value of ±1.

[0081] Doppler phase estimation of the post-synchronization sequence within the m-th pulse θ m,back :

[0082]

[0083] In the formula, (·)* represents the conjugate operation, and T interval This is the time interval between the start time of the presynchronization sequence and the start time of the postsynchronization sequence.

[0084] ② The Doppler frequency estimation is completed by using the difference between the Doppler phase estimates of the pre-synchronization sequence and the post-synchronization sequence, i.e.:

[0085]

[0086] ③ The Doppler frequencies estimated from multiple pulses are averaged to increase the processing gain and complete the coherent estimation of the Doppler frequencies. That is:

[0087]

[0088] In the formula, Num represents the number of pulses within a frame.

[0089] (2) Doppler phase coherent estimation

[0090] ① Taking the m-th pulse as an example, based on the Doppler phase estimation θ of the post-synchronization sequence within the m-th pulse. m,back And Doppler frequency estimation Obtain the fitted presynchronous sequence Doppler phase θest m,pre ,Right now:

[0091]

[0092] In the formula, T interval This is the time interval between the start time of the presynchronization sequence and the start time of the postsynchronization sequence.

[0093] ② The fitted presynchronous sequence Doppler phase θest m,pre Doppler phase estimation θ of presynchronous sequence m,pre Meaning is applied to increase the processing gain, resulting in a Doppler phase coherent estimate of the presynchronous sequence. That is:

[0094]

[0095] ③ Based on Doppler frequency coherent estimation Doppler phase coherent estimation of presynchronous sequences The channel fading response of the m-th pulse is fitted, i.e.:

[0096]

[0097] In the formula, For the floor function, len is the length of the synchronization sequence, T is the symbol time, and Np is the number of pulse symbols.

[0098] Using the same method, the channel fading response of the received pulse signal can be fitted.

[0099] Step S9: Channel equalization. In this embodiment, the channel fading response of the received signal pulse is directly canceled by the zero-forcing algorithm based on the obtained channel fading response to obtain an equalized signal.

[0100] Step S10, GMSK Demodulation. The equalized signal is demodulated using GMSK and hard-decision processing to recover the service data. The specific process includes:

[0101] ① After suppressing channel fading response through channel equalization, the received equalized signal is extracted. The sampling time is the optimal sampling time, and the sampling rate is 1 / T, where T is the symbol time.

[0102] Dem=[dem(0),dem(1),dem(2),…,dem(Np-1)]

[0103] Where Np is the number of pulse symbols, and dem(k) is the observation of the kth symbol of the mth pulse after equalization.

[0104] ② Based on the equalized signal Dem, the demodulation information of the k-th symbol of the m-th pulse is calculated using orthogonal demodulation, i.e.:

[0105]

[0106] Here, imag(·) is the imaginary part operation, and real(·) is the real part operation.

[0107] ③ Finally, the business data is recovered through a hard decision. The hard decision criteria are as follows:

[0108]

[0109] Where OutSig(k) is the service data corresponding to the kth symbol, and DemSig(k) is the demodulation information corresponding to the kth symbol.

[0110] This invention can effectively reduce the length of the sampled signal processing and decrease the processing delay. The phase estimation range of this method is improved to -π to π, and the frequency estimation range is improved to -1 / 2T. interval ~1 / 2T interval It has strong resistance to Doppler frequency and phase shift.

[0111] It should be noted that this embodiment does not necessarily include all content and operations / steps, nor does it necessarily have to be executed in the described order. For example, some operations / steps can be broken down, while others can be combined or partially combined. Therefore, the actual execution order may change depending on the actual situation.

[0112] Appendix Figure 2 , 3 4. Additional explanations are needed regarding what each figure represents and what results are obtained after comparison.

[0113] See Figure 2 Simulations were conducted using GMSK modulation with B×T = 0.3, where the optimal sampling point was at the half-symbol time, the interval between preceding and following synchronization sequences was 20µs, and the synchronization segment duration was 2µs. The frequency estimation range of the frequency doubling method was -6.25kHz to 6.25kHz, while the proposed algorithm's frequency estimation range was -25kHz to 25kHz. As shown in the figure, when the Doppler frequency was 5kHz, the frequency estimation accuracy of the proposed algorithm was superior to the frequency doubling method at low signal-to-noise ratios (SNR), while the accuracy of both methods was comparable at high SNRs. When the Doppler frequency was 20kHz, it exceeded the estimation range of the frequency doubling method, resulting in a relatively large frequency offset error; however, the frequency estimation accuracy of the proposed algorithm remained at a high level. Therefore, the proposed algorithm can improve the Doppler frequency range and estimation accuracy, and possesses strong resistance to Doppler frequency and phase offset.

[0114] See Figure 3 (a)~ Figure 3 (d) The simulation sets GMSK modulation with B×T=0.3, and its optimal sampling point time is half a symbol time. As shown in the figure, the received signal constellation points are relatively concentrated when there is no sampling time deviation. When there is a 0.2 symbol deviation between the sampling time and the symbol time, the received signal constellation points are distorted, causing phase distortion of the received signal and resulting in a loss of system reception performance. When there is a 0.2 symbol deviation between the sampling time and the symbol time, after processing by the correlation curve fitting algorithm of the resampling module proposed in this invention, the sampling time of the resampled signal can approach the optimal sampling point time. The distorted received signal constellation points will re-aggregate and converge, effectively suppressing the phase distortion of the received signal introduced by the sampling error. Its reception performance is comparable to that under no sampling time deviation, suppressing the reception performance loss caused by the sampling time error.

[0115] See Figure 4(a) Simulation setting of GMSK modulation with B×T=0.3, the optimal sampling point time is half-symbol time. Under ideal synchronization, the coherent receiving algorithm of the GMSK demodulation module proposed in this invention has comparable performance to the optimal demodulation algorithm, but the receiving complexity is significantly reduced. The optimal demodulation algorithm requires 2 L-1 One filter and 4×2 L-1 Maximum likelihood sequence detection is performed on each phase state, but the demodulation module of this invention is not limited by the correlation length L, does not require oversampling, and processes each symbol only at the optimal sampling time. Please refer to [reference needed]. Figure 4 (b) In this embodiment, coherent demodulation can be achieved using two delay units and two adders, effectively reducing hardware overhead and processing latency, and making it easy to implement in engineering. Furthermore, when a 20kHz Doppler frequency is present, the coherent demodulation performance processed by the channel estimation module and channel equalization module of this invention exhibits negligible performance degradation compared to ideal synchronization performance.

[0116] In particular, according to embodiments of this application, the processes described above can be implemented as computer software programs. For example, embodiments of this application include a computer program product comprising a computer program carried on a computer-readable medium, the computer program containing program code for performing the methods shown in the flowchart.

[0117] It should be noted that the computer-readable medium shown in the embodiments of this application can be a computer-readable signal medium or a computer-readable storage medium, or any combination of the two. A computer-readable storage medium can be, for example,—but not limited to—an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples of a computer-readable storage medium may include, but are not limited to: an electrical connection having one or more wires, a portable computer disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM), flash memory, optical fiber, portable compact disc read-only memory (CD-ROM), optical storage device, magnetic storage device, or any suitable combination thereof. In this application, a computer-readable storage medium can be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system, apparatus, or device. In this application, a computer-readable signal medium can include a data signal propagated in baseband or as part of a carrier wave, carrying computer-readable program code. Such transmitted data signals can take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. The computer-readable signal medium can also be any computer-readable medium other than a computer-readable storage medium, which can send, propagate, or transmit a program for use by or in connection with an instruction execution system, apparatus, or device. The program code contained on the computer-readable medium can be transmitted using any suitable medium, including but not limited to wireless, wired, etc., or any suitable combination thereof.

[0118] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of this application. Each block in a flowchart or block diagram may represent a module, segment, or portion of code, which contains one or more executable instructions for implementing a specified logical function. It should also be noted that in some alternative implementations, the functions indicated in the blocks may occur in a different order than those indicated in the drawings. For example, two consecutively indicated blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in a block diagram or flowchart, and combinations of blocks in a block diagram or flowchart, can be implemented using a dedicated hardware-based system that performs the specified function or operation, or using a combination of dedicated hardware and computer instructions.

[0119] The units described in the embodiments of this application can be implemented in software or hardware, and the described units can also be located in a processor. The names of these units do not necessarily limit the specific unit itself.

[0120] In another aspect, this application also provides a computer program product or computer program including computer instructions stored in a computer-readable storage medium. A processor of a computer device reads the computer instructions from the computer-readable storage medium and executes the computer instructions, causing the computer device to perform the GMSK coherent reception method based on optimal sampling points as described in the above embodiments.

[0121] In another aspect, this application also provides a computer-readable medium, which may be included in the electronic device described in the above embodiments; or it may exist independently and not assembled into the electronic device. The computer-readable medium carries one or more programs, which, when executed by the electronic device, cause the electronic device to implement the GMSK coherent reception method based on optimal sampling points as described in the above embodiments.

[0122] It should be noted that although several modules or units for the device used to perform actions have been mentioned in the detailed description above, this division is not mandatory. In fact, according to the embodiments of this application, the features and functions of two or more modules or units described above can be embodied in one module or unit. Conversely, the features and functions of one module or unit described above can be further divided and embodied by multiple modules or units.

[0123] Through the above description of the embodiments, those skilled in the art will readily understand that the exemplary embodiments described herein can be implemented by software or by combining software with necessary hardware. Therefore, the technical solutions according to the embodiments of this application can be embodied in the form of a software product, which can be stored in a non-volatile storage medium (such as a CD-ROM, USB flash drive, external hard drive, etc.) or on a network, including several instructions to cause a computing device (such as a personal computer, server, touch terminal, or network device, etc.) to execute the method according to the embodiments of this application.

[0124] For those skilled in the art, the specific meanings of the above terms in this invention can be understood according to the specific circumstances; the accompanying drawings in the embodiments are used to clearly and completely describe the technical solutions in the embodiments of this invention. Obviously, the described embodiments are some embodiments of this invention, but not all embodiments. Generally, the components of the embodiments of this invention described and shown in the accompanying drawings can be arranged and designed in various different configurations.

[0125] Although embodiments of this application have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting this application. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of this application.

Claims

1. A GMSK coherent reception method based on optimal sampling points, characterized in that, include: Transmitter: The service data is split into multiple data segments. Orthogonal synchronization sequences are inserted before and after each data segment to form pulse signals. Each pulse signal is pre-coded and then GMSK modulated. Phase decoupling and π / 2 phase rotation between GMSK symbols are completed to obtain GMSK modulated signals. Each pulse GMSK modulated signal is converted from digital to analog and then up-converted to analog before being radiated out, ultimately forming multiple burst pulse stream signals. Receiver: The received baseband signal is obtained by analog down-conversion and analog-to-digital conversion of multiple burst pulse stream signals. The received baseband signal is detected and each pulse signal is extracted, and then resampled to obtain a timing synchronization signal; The moment with the minimum inter-symbol interference within the GMSK symbol time is taken as the optimal sampling point. The receiver extracts the optimal sampling point for each pulse timing synchronization signal at the moment with the minimum inter-symbol interference, performs Doppler phase estimation of the two synchronization sequences before and after each pulse, performs differential operation on the estimated Doppler phase to achieve Doppler frequency estimation for each pulse, and obtains the coherent estimation of the Doppler frequency by combining the Doppler frequency estimation results of multiple pulses. Coherent estimation of the Doppler phase of the pre-pulse synchronization sequence is achieved by using the coherent estimation results of the Doppler frequency and the Doppler phase estimation results of the two synchronization sequences before and after each pulse. The channel fading response is obtained by fitting the Doppler phase change of each pulse data segment using the coherent estimation results of the Doppler frequency and the coherent estimation results of the Doppler phase of each pulse pre-synchronization sequence. After equalizing the channel fading response of each received pulse signal, GMSK demodulation and hard decision are performed. The hard decision results of multiple pulses are framed to recover the service data.

2. The GMSK coherent reception method based on optimal sampling points according to claim 1, characterized in that, The specific method of precoding is as follows: Where N is the set of natural numbers, d i a is the i-th original bit within the pulse, and its value is ±1. i It represents the i-th precoded bit within the pulse.

3. The GMSK coherent reception method based on optimal sampling points according to claim 1, characterized in that, In the process of obtaining the received baseband signal by analog down-conversion and analog-to-digital conversion of the received GMSK modulated signal, the sampling rate is twice the symbol rate.

4. The GMSK coherent reception method based on optimal sampling points according to claim 1, characterized in that, The specific method for resampling is as follows: The peak time incoherent processing result, the previous incoherent processing result, and the next incoherent processing result of the peak time are obtained after incoherent detection of multiple pulse signal synchronization sequences. The sampling time deviation is estimated by the correlation curve fitting method. Construct interpolation filter coefficients based on sampling time deviation; The received baseband signal is interpolated based on the interpolation filter coefficients to obtain a timing precision synchronization pulse signal after the sampling time is synchronized with the minimum time of inter-symbol interference.

5. The GMSK coherent reception method based on optimal sampling points according to claim 1, characterized in that, The coherent estimation method for the Doppler frequency is as follows: Extract the presynchronization sequence and postsynchronization sequence from the timing precision synchronization pulse signal, multiply them by the conjugate of the local sequence, sum them, and take the phase to obtain the Doppler phase estimate of the presynchronization sequence and postsynchronization sequence of the pulse; Doppler frequency estimation is performed using the difference between the Doppler phase estimates of the pre-synchronization sequence and the post-synchronization sequence. The Doppler frequencies estimated from multiple pulses are averaged to complete the coherent estimation of Doppler frequencies.

6. The GMSK coherent reception method based on optimal sampling points according to claim 1, characterized in that, The Doppler phase coherent estimation method for each pulse pre-synchronization sequence is as follows: Based on the Doppler frequency coherent estimation results and the Doppler phase estimation results of the post-synchronization sequence within each pulse, the Doppler phase of the pre-synchronization sequence fitted for each pulse is obtained by linear backtracking. The Doppler phase of the presynchronous sequence within each pulse and the fitted Doppler phase estimation results of the presynchronous sequence are averaged to obtain the coherent estimation of the Doppler phase of the presynchronous sequence within each pulse.

7. The GMSK coherent reception method based on optimal sampling points according to claim 1, characterized in that, The channel fading response acquisition method is as follows: the channel fading response of the pulse is obtained by fitting the results of the intra-pulse Doppler frequency coherent estimation and the Doppler phase coherent estimation of each pulse pre-synchronization sequence; The channel fading response for each received pulse signal is obtained using the same method.

8. The GMSK coherent reception method based on optimal sampling points according to claim 1, characterized in that, The equalization processing method is as follows: based on the obtained channel fading response, the zero-forcing algorithm is used to directly cancel the channel fading response of the received pulse signal.

9. The GMSK coherent reception method based on optimal sampling points according to claim 1, characterized in that, The specific methods for recovering business data include: Extract the equalized signal obtained after channel equalization processing, and the sampling time is the optimal sampling point time with the minimum inter-symbol crosstalk of GMSK symbols. GMSK demodulation is performed on the channel equalization signal to obtain the demodulation soft information for each symbol of each pulse: Where imag(·) is the imaginary part operation, real(·) is the real part operation, dem(k) is the observation of the kth symbol of the equalized signal within the pulse, and DemSig(k) is the demodulation soft information corresponding to the kth symbol within the pulse; Hard decision is made on the demodulated soft information of each symbol in each pulse to recover the service data.

10. The GMSK coherent reception method based on optimal sampling points according to claim 9, characterized in that, The specific method for the hard decision is as follows: Where OutSig(k) is the service data corresponding to the kth symbol, and DemSig(k) is the demodulation information corresponding to the kth symbol.

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