An Adaptive C4FM Signal Demodulation Method Based on Median Discreteness

Abstract

This invention provides an adaptive C4FM signal demodulation method based on median discreteness, relating to the field of communication signal processing. The method includes: locating the signal synchronization head and calculating the sampling start point; sampling using the Gardner algorithm at a preset initial step size; dividing the sampling points into upper and lower bound sequences for synchronization, and calculating the median and absolute median difference for each; dynamically iteratively correcting the timing step size of the Gardner algorithm based on the discrete mean of the absolute median difference to obtain the optimal step size and resampling to update the absolute median difference; dynamically calculating the upper and lower bound decision thresholds by combining the final absolute median difference with a compensation factor for the current signal-to-noise ratio; and using the thresholds to perform symbol decision and output the result. This invention improves demodulation robustness and synchronization accuracy under complex channels and significantly reduces the bit error rate.

Description

Technical Field

[0001] This invention relates to the field of communication signal processing technology, and more specifically, to an adaptive C4FM signal demodulation method based on median discretization. Background Technology

[0002] Continuous 4-Level Frequency Modulation (C4FM) is an important branch of fourth-order frequency shift keying (4FSK) in digital modulation technology. Because C4FM modulated signals possess excellent characteristics such as constant envelope, low distortion, rapid roll-off attenuation, low out-of-band radiation, and high spectral efficiency, they can fully utilize limited spectrum bandwidth to transmit more data. Therefore, they are widely used in current digital trunking communication systems, public safety digital radio systems, and various dedicated radio communication systems.

[0003] However, with the continuous evolution of digital radio technology and the increasing complexity of communication scenarios, the electromagnetic environment for signal transmission at the air interface (AMI) is becoming increasingly harsh. In actual complex operating conditions, communication equipment often faces severe multipath fading, frequency-selective fading, and various sudden impulse noises and co-channel / adjacent-channel interference. These complex channel environments cause significant fluctuations in the signal-to-noise ratio (SNR) at the receiver, leading to severe distortions in the signal envelope and phase. How to effectively improve the system's resistance to abnormal interference and reduce the demodulation error rate of C4FM signals under conditions of drastic SNR fluctuations, mixed interference, and deep fading has become a key technical challenge that urgently needs to be solved in the field of modern communication signal processing.

[0004] Traditional C4FM signal demodulation schemes typically employ a fixed timing synchronization step size (such as the traditional Gardner timing synchronization algorithm) and a fixed symbol decision threshold. This static demodulation architecture performs reasonably well in ideal high signal-to-noise ratio white noise channels, but it exposes significant limitations in complex and variable environments: on the one hand, a fixed timing synchronization step size cannot achieve a balance between convergence speed and steady-state timing sampling accuracy; on the other hand, the traditional single fixed threshold symbol decision scheme has extremely poor channel tolerance and cannot dynamically adjust to changes in actual noise intensity.

[0005] To address the aforementioned issues, several improved demodulation schemes have been proposed in the industry, but all suffer from varying degrees of technical bottlenecks. For example, Chinese patent application 2023118725103 discloses "A 4FSK Demodulation Method Based on Multi-Symbol Joint Estimation." This scheme is based on instantaneous frequency measurement, uses the variance of multiple symbols to jointly estimate the starting position of the symbol, then calculates the symbol frequency estimate based on the starting position, and uses the minimum distance criterion for symbol discrimination. However, this method requires frequency measurement and estimation for each symbol, resulting in extremely high computational overhead. Furthermore, it still uses a fixed sampling step size, making it difficult to achieve dynamic convergence with timed feedback.

[0006] For example, Chinese patent application 2014101941642 discloses a "1-symbol differential 4FSK demodulation method for power wireless private networks," which maps the phase change of a continuous phase carrier modulated signal within one symbol time to the corresponding signal symbol for demodulation. However, this demodulation logic is extremely sensitive to outliers, and the mapping relationship is static and fixed, making it completely impossible to dynamically and adaptively adjust according to fluctuations in the environmental signal-to-noise ratio.

[0007] Furthermore, Chinese patent application 2011104298425 discloses a "Proprietary Protocol Control Method for Digital Fisheries Radios Using 4FSK". Due to its basic architecture design, this scheme does not have adaptive demodulation capability. In Chinese patent application 2011103322893, which discloses an "Efficient Mapping Algorithm from Soft Symbols to Soft Bits", although the received soft symbols are mapped to soft bits and then BPTC soft decoding is performed, its front end still relies on the conventional 4FSK demodulation process and uses a fixed step size for sampling to obtain soft symbol information. It also has the technical defect of not being able to dynamically adjust according to the channel state.

[0008] Further investigation revealed that existing conventional demodulation algorithms often rely heavily on a single ideal Gaussian normal distribution assumption when evaluating the dispersion or noise intensity of sampled signals, and commonly use conventional variance or mean squared error (MSE) for evaluation. Since variance calculation is extremely sensitive to extreme values, the dispersion evaluation results will be severely skewed when the system encounters occasional non-Gaussian outlier interference in complex channels. This causes subsequent timing feedback and threshold settings to completely fail, resulting in a precipitous deterioration in demodulation performance under low signal-to-noise ratio conditions.

[0009] In summary, existing C4FM demodulation methods generally suffer from high computational overhead, severe susceptibility to outliers, poor robustness in complex channels, difficulty in balancing synchronization convergence and timing accuracy, and an inability to adaptively adjust the decision threshold according to environmental signal-to-noise ratio and actual discrete conditions. Therefore, there is an urgent need to propose a novel demodulation method that can overcome the limitations of the single normal distribution assumption and achieve dual dynamic adaptive adjustment of the timing sampling step size and symbol decision domain to ensure decision consistency and demodulation reliability under complex interference conditions. Summary of the Invention

[0010] The present invention aims to solve at least one of the aforementioned technical problems existing in the prior art.

[0011] Therefore, this invention provides an adaptive C4FM signal demodulation method based on median discreteness.

[0012] The adaptive C4FM signal demodulation method based on median discretization proposed in this invention includes: S1. Perform frequency offset correction and instantaneous frequency calculation on the received continuous fourth-order frequency-modulated signal, find the signal synchronization head position through synchronization correlation, and calculate the sampling start point based on the sampling rate and symbol rate; S2. The Gardner algorithm is used to sample the current synchronization symbol according to a preset initial step size, and the sampling points of the current synchronization symbol are output. S3. Based on the distribution characteristics of the synchronization head, the sampling points are divided into a synchronization upper bound point sequence and a synchronization lower bound point sequence. The median of the two sets of sequences is found respectively. The median deviation sequence of the two sets of sequences is calculated. Based on the median deviation sequence, the absolute median difference between the synchronization upper bound point sequence and the synchronization lower bound point sequence is calculated. S4. The median discrete mean is measured based on the upper and lower bounds of the absolute median difference, and the timing step size of the Gardner algorithm is dynamically iteratively corrected to obtain the optimal step size. The algorithm is then resampled according to the optimal step size to update and obtain the final absolute median difference. S5. Establish a decision domain sample fluctuation model, use the median of the two sets of sequences to describe the fluctuation center, use the final absolute median difference to describe the fluctuation degree, and combine it with the compensation factor based on the current signal-to-noise ratio to dynamically calculate the upper and lower decision thresholds of the current optimal symbol. S6. Construct a symbol decision interval using the upper and lower decision thresholds, perform symbol decision on the sample points after the optimal step size correction sampling, and output the demodulation result.

[0013] The adaptive C4FM signal demodulation method based on median discretization according to the above-described technical solution of the present invention may also have the following additional technical features: In the above technical solution, the step of performing frequency offset correction and instantaneous frequency calculation on the received continuous fourth-order frequency-modulated signal, finding the signal synchronization header position through synchronization correlation, and calculating the sampling start point based on the sampling rate and symbol rate includes: Signal frequency offset correction is achieved based on the differential autocorrelation algorithm, wherein a preset symbol length is obtained as the frequency offset correction sample length, and a preset ratio of the symbol duration is used as the differential delay. The instantaneous frequency of the received signal is solved based on the phase difference method; By plotting the cross-correlation spectrum of the synchronous waveform using a sliding window, the position of the synchronous peak point is marked. The sampling interval is calculated based on the sampling rate and symbol rate, and the sampling start point is obtained.

[0014] In the above technical solution, step S3 divides the sampling points into a synchronization upper bound sequence and a synchronization lower bound sequence and calculates the median deviation sequence, including: Based on the characteristic that the synchronization header of the C4FM signal consists of +3 level symbols and -3 level symbols, the sampling points corresponding to the +3 level symbols are selected to form the synchronization upper limit point sequence, and the sampling points corresponding to the -3 level symbols are selected to form the synchronization lower limit point sequence. Find the median of each of the two sets of sequences, and calculate the median deviation between the two sets of sequences. The calculation methods include:

[0015]

[0016] in, This represents the median of the synchronization upper bound sequence or the synchronization lower bound sequence, where up is the index of the synchronization upper bound sequence and down is the index of the synchronization lower bound sequence. This represents the median function; This indicates the upper bound sequence or the lower bound sequence of synchronization points. This represents the median deviation sequence of the synchronization upper bound sequence or the synchronization lower bound sequence.

[0017] In the above technical solution, step S3 calculates the absolute median difference between the upper synchronization bound sequence and the lower synchronization bound sequence based on the median deviation sequence. The calculation method includes:

[0018] in, It represents the absolute median difference between the upper and lower bounds of the current synchronization symbol sequence.

[0019] In the above technical solution, the timing step size of the Gardner algorithm in S4 is dynamically iteratively corrected, including: Calculate the median discrete mean of the upper and lower bounds:

[0020] in, This represents the median discrete mean of the upper and lower bounds; Represents the absolute median difference of the sequence of synchronization upper bounds for the current synchronization symbol; Represents the absolute median difference of the sequence of lower synchronization points of the current synchronization symbol; Set the initial adaptive step size; The next shortening step length and increasing step length are calculated based on the median discrete mean of the upper and lower bounds. The calculation method includes:

[0021] in, Indicates the current step length; This indicates the next step length to be shortened; Indicates the next increment step length; Indicates the degree of discrete correction, and .

[0022] In the above technical solution, after calculating the next shortening step length and increasing step length based on the median discrete mean of the upper and lower bounds in step S4, it further includes: According to the next shortening step length and the next growth step length The corresponding Gardner algorithm is used to resample and calculate a new median discrete mean. and ; To shorten the step length The corresponding median discrete mean; To increase step length The corresponding median discrete mean; Compare , and ,like If the minimum value is found, then the current step length is taken directly. Find the optimal step size and stop iterating; like minimum, take Update to the current step length ; and take Updated to upper and lower bounds, median, and discrete mean. Repeat the calculation of the next shortening step length and increasing step length; like To minimize, take Update to the current step length and take Updated to upper and lower bounds, median, and discrete mean. Repeat the calculation to shorten and increase the step length for the next iteration.

[0023] In the above technical solution, the number of times the steps of calculating the next step length shortening and increasing step length are repeatedly executed is limited. If the number of iterations reaches the set value, the current step length corresponding to the last iteration is taken as the optimal step length.

[0024] In the above technical solution, the calculation method for the compensation factor of the current signal-to-noise ratio in S5 includes:

[0025] in, Indicates the compensation factor; Represents the empirical scale constant, and ; This indicates the current signal-to-noise ratio.

[0026] In the above technical solution, S5 dynamically calculates the upper and lower bound decision thresholds of the current optimal symbol. The calculation method includes:

[0027] in, This represents the upper bound of the optimal decision threshold for the sign; This represents the lower bound sign optimal decision threshold; Represents the absolute median difference of the sequence of synchronization upper bounds for the current synchronization symbol; This represents the absolute median difference of the lower synchronization point sequence of the current synchronization symbol.

[0028] In the above technical solution, step S6 performs sign determination on the sample points after the optimal step size correction sampling and outputs the demodulation result. The determination logic includes: like If so, the demodulation symbol is determined to be +3; like If so, the demodulation symbol is determined to be +1; like If so, the demodulation symbol is determined to be -1; like If so, the demodulation symbol is determined to be -3; Where "point" represents the sampling point after the corrected sampling.

[0029] In summary, due to the adoption of the above-mentioned technical features, the beneficial effects of the present invention are: This invention effectively improves the demodulation robustness of the system in complex channel environments and significantly reduces the bit error rate caused by sudden abnormal interference. Traditional demodulation methods often rely heavily on a single ideal normal distribution assumption when assessing noise intensity. This invention innovatively introduces absolute median difference (MAD) to estimate the discreteness of the synchronization waveform's own characteristics, establishing a universal discreteness-noise intensity mapping relationship. Since absolute median difference is statistically insensitive to extreme values, this invention exhibits more stable discreteness assessment results and is less affected by occasional abnormal data when facing frequent multipath fading and sporadic abnormal data (outlier) interference in complex operating conditions. It also demonstrates superior overall anti-interference performance under low signal-to-noise ratio conditions.

[0030] This invention achieves an optimal balance between timing synchronization convergence speed and steady-state timing accuracy. Breaking through the limitation of traditional timing synchronization algorithms using a fixed step size, this invention proposes an adaptive iterative mechanism based on the median dispersion feedback of the upper and lower bounds of the synchronization head sampling points. This mechanism can objectively evaluate whether the timing step size is optimal based on the median dispersion of the current synchronization symbol sampling points, and dynamically explore and correct the timing step size of the Gardner algorithm using a bidirectional step size iteration formula. This completely overcomes the technical contradiction of traditional fixed step size algorithms, where long step sizes are prone to divergence and short step sizes result in extremely slow convergence, achieving a perfect combination of fast convergence and extremely high timing sampling accuracy under current signal-to-noise ratio conditions.

[0031] This invention significantly enhances the channel inclusiveness and adaptability of the symbol decision-making process. Referring to the central limit theorem and the mean-variance relationship, this invention establishes a sample fluctuation model for the decision domain, combining the absolute median difference, representing the degree of fluctuation, with a compensation factor based on the current signal-to-noise ratio as weights to dynamically calculate the optimal symbol decision domain under the current channel conditions. Compared to the fixed threshold decision scheme of traditional methods, the decision threshold of this invention can adaptively float and adjust according to the median dispersion of the actual signal and the fluctuation of the environmental signal-to-noise ratio. This dynamic threshold strategy is more flexible and can still ensure a high degree of consistency in system decisions even under extreme conditions such as deep fading and frequency-selective interference, fundamentally avoiding synchronization misadjustment and symbol misjudgment.

[0032] The demodulation performance of this invention has achieved a significant quantitative improvement in practical engineering applications. Simulation data shows that, under the same and varying signal-to-noise ratio (SNR) conditions, the bit error rate of the algorithm proposed in this invention is consistently lower than that of traditional demodulation algorithms, and it can more fully benefit from the SNR gain. Especially under extreme conditions, thanks to the dynamic iterative timing synchronization sampling method and the decision method that dynamically floats with the SNR, the bit error rate performance limit of this invention is significantly better than that of traditional algorithms. The traditional C4FM demodulation algorithm reaches its bit error rate limit (producing a bit error rate plateau) at an SNR of 13dB, while the algorithm proposed in this invention only reaches its bit error rate limit at an SNR as high as 20dB, resulting in an overall improvement in bit error rate performance of an order of magnitude. It has extremely high engineering practical value and broad application prospects.

[0033] Additional aspects and advantages of the invention will become apparent in the following description or may be learned by practice of the invention. Attached Figure Description

[0034] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the description of the embodiments taken in conjunction with the following drawings, in which: Figure 1 This is a flowchart of an embodiment of the adaptive C4FM signal demodulation method based on median discreteness according to the present invention; Figure 2 This is a schematic diagram of the initial step size Gardner synchronization symbol sampling results in an adaptive C4FM signal demodulation method based on median discreteness according to an embodiment of the present invention; Figure 3 This is a flowchart of the optimal timing synchronization step size calculation in an adaptive C4FM signal demodulation method based on median discreteness according to an embodiment of the present invention. Figure 4 This is a schematic diagram of the sampling effect and decision domain of the algorithm proposed in this invention when SNR=2dB in one embodiment of the invention; Figure 5 This is a schematic diagram of the sampling effect and decision domain of the algorithm proposed in this invention when SNR=10dB in one embodiment of the invention; Figure 6 This is a schematic diagram comparing the performance of the traditional algorithm and the algorithm proposed in this invention under different signal-to-noise ratios in one embodiment of the present invention. Detailed Implementation

[0035] To better understand the above-mentioned objectives, features, and advantages of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that, unless otherwise specified, the embodiments and features described in these embodiments can be combined with each other.

[0036] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and therefore the scope of protection of the invention is not limited to the specific embodiments disclosed below.

[0037] The following reference Figures 1 to 6 This describes an adaptive C4FM signal demodulation method based on median discreteness provided according to some embodiments of the present invention.

[0038] Some embodiments of this application provide an adaptive C4FM signal demodulation method based on median discreteness. This invention addresses the problem of degraded demodulation performance caused by large signal-to-noise ratio (SNR) fluctuations in complex channel environments by proposing an adaptive C4FM signal demodulation method based on median discreteness. Traditional demodulation methods, due to their fixed decision threshold and fixed timing step size, cannot dynamically adjust with SNR and noise intensity, resulting in poor adaptability in complex channels and mixed interference environments, and significant susceptibility to outliers. Therefore, this invention primarily relies on the characteristics of the signal synchronization waveform itself to estimate and evaluate the discreteness of the actual signal, establishing a universal discreteness-noise intensity mapping relationship. It no longer relies on the assumption of a single normal noise distribution, and is less affected by occasional abnormal data. In selecting the optimal sampling point, this invention relies on the median dispersion of the synchronization header sampling point to evaluate whether the current timing step size is optimal, and dynamically iterates and corrects it to obtain the optimal balanced step size for convergence speed and timing accuracy. In symbol decision, this invention calculates the absolute median difference between the upper and lower bounds of the optimal sampling points of the synchronization symbol, and dynamically calculates the symbol decision domain in combination with the signal-to-noise ratio, adaptively adjusting the decision threshold, thereby effectively improving the robustness of demodulation processing under varying signal-to-noise ratio conditions and reducing the demodulation bit error rate.

[0039] like Figure 1 As shown, the first embodiment of the present invention proposes an adaptive C4FM signal demodulation method based on median discreteness, including the following steps S1 to S6.

[0040] S1. Perform frequency offset correction and instantaneous frequency calculation on the received continuous fourth-order frequency-modulated signal, find the signal synchronization head position through synchronization correlation, and calculate the sampling start point based on the sampling rate and symbol rate; S2. The Gardner algorithm is used to sample the current synchronization symbol according to a preset initial step size, and the sampling points of the current synchronization symbol are output. S3. Based on the distribution characteristics of the synchronization head, the sampling points are divided into a synchronization upper bound point sequence and a synchronization lower bound point sequence. The median of the two sets of sequences is found respectively. The median deviation sequence of the two sets of sequences is calculated. Based on the median deviation sequence, the absolute median difference between the synchronization upper bound point sequence and the synchronization lower bound point sequence is calculated. S4. The median discrete mean is measured based on the upper and lower bounds of the absolute median difference, and the timing step size of the Gardner algorithm is dynamically iteratively corrected to obtain the optimal step size. The algorithm is then resampled according to the optimal step size to update and obtain the final absolute median difference. S5. Establish a decision domain sample fluctuation model, use the median of the two sets of sequences to describe the fluctuation center, use the final absolute median difference to describe the fluctuation degree, and combine it with the compensation factor based on the current signal-to-noise ratio to dynamically calculate the upper and lower decision thresholds of the current optimal symbol. S6. Construct a symbol decision interval using the upper and lower decision thresholds, perform symbol decision on the sample points after the optimal step size correction sampling, and output the demodulation result.

[0041] Next, combine Figure 1 This paper provides a detailed description of the implementation details of each core step of the adaptive C4FM signal demodulation method based on median discretization proposed in this invention.

[0042] First, regarding step S1 (performing frequency offset correction and instantaneous frequency calculation on the received C4FM signal, finding the signal synchronization head position through synchronization correlation, and calculating the sampling start point based on the sampling rate and symbol rate), its main purpose is to complete the early-stage acquisition and coarse synchronization processing of the signal, laying the foundation for subsequent fine-tuned timing sampling.

[0043] In one specific embodiment, frequency offset correction of the signal can be achieved based on a differential autocorrelation algorithm. In actual wireless communication environments, the local oscillator frequencies of the transmitter and receiver often deviate, and the Doppler effect also introduces frequency offset, causing the baseband signal phase to rotate continuously. To eliminate this effect, in this embodiment, a preset symbol length (e.g., 2000 symbols in a typical scenario; the specific value can be adjusted according to the frame structure and frequency offset tolerance of the actual communication system) is selected as the sample length for frequency offset correction. Simultaneously, a preset proportion of the symbol duration (e.g., 10% of the symbol duration) is selected as the differential delay. By calculating the phase angle of the conjugate product of this sample sequence and its own delay, the carrier frequency offset of the signal can be estimated, and frequency compensation of the received signal can be performed accordingly. Those skilled in the art will understand that, in addition to the differential autocorrelation algorithm, other well-known methods such as FFT frequency measurement can also be used for frequency offset estimation, all of which are within the scope of protection of this invention.

[0044] After completing the frequency offset correction, the instantaneous frequency of the received signal is further solved based on the phase difference method. Specifically, the phase difference between adjacent sampling points is calculated and combined with the sampling period to convert it into an instantaneous frequency value, thereby converting the received complex baseband signal into an instantaneous frequency sequence of the frequency-modulated signal to reflect the symbol information carried by different frequencies in the C4FM signal.

[0045] After acquiring the instantaneous frequency sequence, the synchronization header needs to be accurately located because the data stream contains a large amount of valid information and synchronization sequence. In some embodiments, a sliding correlation method is used to search for and locate the synchronization header. The receiver pre-stores a standard synchronization waveform (e.g., a waveform composed of ideal alternating +3 and -3 symbols). Using this local synchronization waveform, a sliding window cross-correlation operation is performed with the instantaneous frequency sequence of the received signal to generate a cross-correlation spectrum. Due to the good autocorrelation characteristics of the synchronization header, a significant peak will appear in the cross-correlation spectrum. By marking the position of this synchronization peak, the physical interval where the synchronization header is located in the signal can be determined.

[0046] Subsequently, based on the system's set sampling rate and symbol rate, the sampling interval corresponding to a single symbol (i.e., the number of samples contained in each symbol) is calculated. Combining the previously marked synchronization peak point positions and sampling intervals, the initial sampling starting point can be deduced and calculated. This sampling starting point will serve as the reference position for the subsequent Gardner timing synchronization algorithm to start.

[0047] Step S2 mainly aims to use the Gardner timing synchronization algorithm to perform preliminary sampling of the current synchronization symbol at the determined synchronization header position according to the preset initial step size, thereby correcting and outputting the sampling point set of the current synchronization symbol.

[0048] In the field of digital communications, the Gardner timing synchronization algorithm is a well-known and typical non-data-aided timing error detection algorithm. It is insensitive to carrier phase offset and is well-suited for multi-level digital modulation systems such as Continuous Fourth-Order Frequency Modulation (C4FM). In one specific embodiment, for the received signal whose sampling start point has been determined in step S1, the system initiates the Gardner loop. The Gardner loop typically includes a timing error detector (TED), a loop filter, and a numerically controlled oscillator (or interpolator). The system uses the loop to extract two specific samples within one symbol period (usually the symbol decision point and the transition point between two adjacent symbols), and calculates the current timing error based on the amplitude relationship between these two points, thereby driving the loop filter to adjust the resampling timing point.

[0049] In some embodiments, considering the drastic changes in signal-to-noise ratio in actual communication environments, in order to ensure that the system loop can quickly enter the working state at the initial startup and to provide a benchmark dispersion test sample for subsequent adaptive evaluation, the system pre-sets an initial adaptive step size (denoted as the preset initial step size). At this stage, the Gardner algorithm uses the aforementioned preset initial step size. The system operates by periodically resampling and correcting the synchronization waveform in the synchronization head.

[0050] Combined with appendix Figure 2 Explanation provided, attached Figure 2 A waveform diagram illustrating the Gardner synchronization symbol sampling results with a preset initial step size is shown. In one specific embodiment, a preset initial step size is set. .from Figure 2 As can be seen intuitively, the continuous solid line represents the analog synchronization waveform of the C4FM signal after front-end processing, while the discrete dots on the waveform represent the system following the initial step size. Resample and correct the timing synchronization sampling points of the output.

[0051] Those skilled in the art should understand that, in complex and variable signal-to-noise ratio environments, relying solely on a single fixed initial step size is insufficient. Often, it is impossible to directly converge to the optimal steady-state sampling accuracy. If the fixed step size is too short, the timing synchronization algorithm will have an excessively long convergence time and will be unable to track the rapid phase distortion of the channel; if the fixed step size is too long, the algorithm may diverge in the loop, resulting in a severe reduction in timing accuracy. Therefore, the current synchronization symbol sampling points output by the preset initial step size in step S2 are essentially used as the initial evaluation sample data for the adaptive iterative mechanism of this invention. This batch of sample data will then be input into subsequent processing steps to measure the quality of the initial sampling effect, and based on this, the dynamic step size optimization process in steps S3 to S4 will be initiated.

[0052] The core purpose of step S3 is to calculate the median dispersion of the upper and lower bounds of the current synchronization symbol point, thereby providing a quantitative indicator with strong anti-interference capability for the subsequent evaluation and adjustment of the adaptive step size.

[0053] In one specific embodiment, those skilled in the art know that C4FM modulated signals contain four discrete levels, namely, four symbols: {+3, +1, -1, -3}. In order to ensure accurate signal acquisition at the receiving end and obtain a high cross-correlation peak, the protocol specifications of the communication system usually use extreme levels (i.e., +3 and -3 symbols) to form a synchronization sequence (synchronization header).

[0054] Based on this characteristic, the system first groups the sampling points extracted in step S2. Specifically, according to the characteristic that the synchronization header of the C4FM signal consists of +3 level symbols and -3 level symbols, the system performs threshold prediction to select the sampling points corresponding to the +3 level symbols to form a synchronization upper bound point sequence (using a set). Similarly, the sampling points corresponding to the -3 level symbol are selected to form a sequence of synchronization lower bound points (using a set). (Represented). Through the above screening, the originally intertwined sampling points are separated into two independent clusters representing positive and negative maxima.

[0055] In some embodiments, after the sequence partitioning is completed, the system finds the median of each of the two sets of sequences. The median is a fundamental concept in robust statistics, referring to the value in the middle of a set of data arranged in ascending order. Compared to the traditional arithmetic mean, the median is extremely insensitive to extreme outliers (outliers). The specific calculation formula is as follows:

[0056] Subsequently, the system calculates the median deviation of the two sets of sequences. Median deviation refers to the absolute distance of each actual sampling point in the sequence from its center of fluctuation (i.e., the median). The calculation method is as follows:

[0057] in, This represents the median of the synchronization upper bound sequence or the synchronization lower bound sequence, where up is the index of the synchronization upper bound sequence and down is the index of the synchronization lower bound sequence. This represents the median function; This indicates the upper bound sequence or the lower bound sequence of synchronization points. This represents the median deviation sequence of the synchronization upper bound sequence or the synchronization lower bound sequence.

[0058] By taking the absolute value here, we ensure that all deviations are positive scalars, laying a mathematical foundation for subsequent dispersion evaluation.

[0059] In one specific embodiment, based on the median deviation sequence obtained above, the system further calculates the absolute median difference (MAD) between the upper synchronization bound sequence and the lower synchronization bound sequence. The calculation formula is as follows:

[0060] in, It represents the absolute median difference between the upper and lower bounds of the current synchronization symbol sequence.

[0061] Those skilled in the art should understand the deeper physical meaning of introducing absolute median difference (MAD) in this step: from a statistical perspective, MAD represents the true dispersion of the sampling points. A larger MAD value indicates poorer consistency and more drastic fluctuations in the sampling points, suggesting a poorer sampling effect of the Gardner loop (potentially deviating from the optimal eye diagram opening point); conversely, a smaller MAD value indicates better sampling performance. This invention abandons the traditional variance evaluation method based on the Gaussian distribution assumption and instead uses MAD as a metric, fundamentally eliminating the catastrophic impact of occasional large impulse noise in complex channels on dispersion evaluation, fully satisfying the core concept of improving robustness in this invention.

[0062] Step S4 aims to break free from the constraints of traditional fixed-step-size algorithms. Based on the absolute median difference between the upper and lower bounds calculated in step S3, a closed-loop adaptive feedback optimization mechanism is constructed. By dynamically iteratively correcting the timing step size of the Gardner algorithm, a better balance between timing convergence speed and steady-state timing accuracy is ultimately achieved.

[0063] In one specific embodiment, combined with Figure 3 As shown, the dynamic optimization process in step S4 specifically includes the following execution stages: First, the initial discrete baseline is calculated. The system calculates the median discrete mean of the absolute median difference between the upper and lower bounds of the current synchronization symbol point. The calculation formula is as follows:

[0064] in, This represents the median discrete mean of the upper and lower bounds; Represents the absolute median difference of the sequence of synchronization upper bounds for the current synchronization symbol; This represents the absolute median difference of the lower bound sequence of the current synchronization symbol; simultaneously, an initial adaptive step size is set (such as 0.01 in the aforementioned embodiment). Assigning this initial step size at the beginning of the optimization phase ensures that the system has a very high convergence speed.

[0065] Secondly, a two-way step-size exploratory calculation is performed. A step size that is too short will result in extremely slow convergence, while a step size that is too long may lead to divergence. Therefore, this embodiment adopts a trial-and-error strategy similar to gradient descent. The system is based on the current upper and lower bounds and the median discrete mean. As a measure of error, the next step size (shortening or increasing) is calculated using the following formula:

[0066] in, Indicates the current step length; This indicates the next step length to be shortened; Indicates the next increment step length; Indicates the degree of discrete correction, and (In a preferred embodiment, it may be set) =0.5).

[0067] Those skilled in the art will understand that, in the above formula, when the discrete mean When the sample size is large (i.e., the current sampling points are very scattered and the effect is poor), the adjustment range of the step size will also be increased accordingly to accelerate the escape from the local disadvantage zone; when When the step size is relatively small (i.e., the sampling points are relatively concentrated), the adjustment range of the step size automatically decreases, entering a fine-tuning state, thereby preventing oscillations near the optimal point.

[0068] Next, perform exploratory resampling and optimal update. Calculate... and Subsequently, the system resamples the synchronization symbols using the Gardner algorithm with both trial step sizes, and calculates the corresponding new absolute median difference according to the logic in step S3, thereby obtaining the corresponding... The new median discrete mean and corresponding The new median discrete mean .

[0069] Subsequently, the system compared , and The magnitudes of these three values: If the current The minimum step size indicates that increasing or decreasing the step size will lead to a larger sampling dispersion (i.e., worse sampling), meaning that the current step size is already in an optimal state. In this case, the current step size is directly taken. Find the optimal step size and stop iterating.

[0070] like or The existence of a minimum value indicates that a better sampling concentration can be obtained by following the corresponding direction (shortening or lengthening). In this case, the system selects the value that produced the minimum. or Update to the current step length and the smallest or Updated to the current upper and lower bounds, median, and discrete mean. Then, with the updated parameters, return to the previous step and repeat the process of calculating the next shortening / increasing step length.

[0071] Finally, the iteration termination condition is applied and the final parameters are output. In some embodiments, to prevent the algorithm from getting stuck in an infinite loop under extremely poor channel conditions and consuming excessive hardware computing resources, the system limits the number of iterations that are repeatedly executed. If the number of iterations reaches a set threshold (for example, 5 times in a specific embodiment; those skilled in the art can flexibly adjust this setting value according to the processor's computing power), the optimization loop is forcibly exited, and the current step length corresponding to the last iteration is taken. This is the optimal step size.

[0072] After obtaining the optimal step size, the system follows that optimal step size. Perform a final resampling to update and derive the final absolute median difference. and These two sets of extremely precise dispersion parameters will be directly passed to the next step S5 to construct the dynamic decision threshold.

[0073] Next, the implementation details of step S5 will be described in detail. The core of step S5 lies in dynamically calculating the current optimal symbol decision threshold based on the final absolute median difference obtained from the previous steps and the signal-to-noise ratio of the current environment, thereby providing an adaptive scale for the final symbol decision.

[0074] In signal processing theory, according to the central limit theorem, the sequence of synchro head sampling points subjected to independent random noise interference approximately follows a normal distribution. Traditional decision models often use the arithmetic mean μs to describe the center of signal fluctuations and the variance (θs) to describe the degree of signal fluctuations. However, as mentioned in the background section, the variance is extremely sensitive to extreme outliers, which can easily lead to model failure.

[0075] Therefore, in one specific embodiment, this invention innovatively establishes a decision domain sample point fluctuation model based on robust statistics, referring to the traditional mean-variance relationship: that is, using the median of the two sets of sequences ( and The center of the fluctuation is described by , and the final absolute median difference output after the optimal step size iteration in step S4 is used. and The degree of fluctuation is described by ().

[0076] To further enhance the adaptive capability of the decision threshold under different channel conditions, the system introduces a compensation factor based on the current signal-to-noise ratio (SNR) as a weight. In some embodiments, the compensation factor f based on the current SNR is calculated as follows:

[0077] in, Indicates the compensation factor; This represents an empirical scale constant used to control the basic proportion of compensation intensity, and For example, in specific engineering simulation and debugging, K=0.6 can be preferably set; This indicates the current signal-to-noise ratio, expressed in decibels (dB).

[0078] It should be noted that, regarding the current signal-to-noise ratio... The acquisition method of the signal-to-noise ratio (SNR) parameter adopts an open architecture and is not strictly limited. In some embodiments, the SNR parameter can be a known environmental parameter directly output by the receiver's underlying RF hardware; in other embodiments, it can also be obtained by the baseband digital processing module through real-time evaluation of the preamble using a well-known SNR estimation algorithm before demodulation. These all fall within the scope of what those skilled in the art can achieve using conventional technical means.

[0079] After calculating the compensation factor f, in a specific embodiment, the system dynamically calculates the upper and lower bound decision thresholds for the current optimal symbol by combining the fluctuation center, fluctuation degree, and compensation weight. The calculation formula is as follows:

[0080] in, This represents the upper bound of the optimal decision threshold for the sign; This represents the lower bound sign optimal decision threshold; Represents the absolute median difference of the sequence of synchronization upper bounds for the current synchronization symbol; This represents the absolute median difference of the lower synchronization point sequence of the current synchronization symbol.

[0081] Combination Figure 4 (Sampling performance and decision region of the proposed algorithm when SNR=2dB) and Figure 5 (The sampling effect and decision domain of the algorithm proposed in this invention when SNR=10dB) can very intuitively illustrate the implementation effect of the above dynamic threshold. Among them, Figure 4 and Figure 5 To analyze the results of the algorithm simulation using simulation software, the simulation values ​​are β=0.5, ξ0=0.01, K=0.6, and the simulation signal is a digital trunking signal.

[0082] The red dashed line in the figure represents the decision threshold calculated in this step (including the lower limit, i.e., the upper limit, of the +3 sign). And the upper limit, i.e. the lower limit, of the -3 sign. Comparing the two figures reveals that when the signal-to-noise ratio (SNR) is extremely low (e.g., 2dB), the absolute median difference increases due to the high noise intensity, and the compensation factor f brought about by the low SNR also increases. The system automatically widens the decision threshold to accommodate the severely discrete sampling points under poor channel conditions. However, when the SNR improves (e.g., 10dB), the signal dispersion decreases, and the decision threshold is correspondingly tightened intelligently, thus effectively avoiding the risk of out-of-bounds misjudgment that is unavoidable in traditional fixed threshold schemes.

[0083] Step S6 is the final output stage of the demodulation method of the present invention. Its main task is to use the dynamic decision scale obtained in the preceding steps to perform accurate symbol mapping and hard decision on the actual received service data payload.

[0084] In one specific embodiment, the system utilizes the upper bound symbol optimal decision threshold calculated in step S5. and the lower bound sign optimal decision threshold By combining the zero-level baseline of the signal, the entire demodulation mapping space is precisely divided into four independent symbol decision intervals.

[0085] Subsequently, the system performs four-level symbol decision on the samples after the sampling has been corrected by the optimal step size (i.e., the optimal timing step size determined in the final iteration in step S4) and outputs the demodulation result. The specific decision logic is as follows: like If so, the demodulation symbol is determined to be +3; like If so, the demodulation symbol is determined to be +1; like If so, the demodulation symbol is determined to be -1; like If so, the demodulation symbol is determined to be -3; Where "point" represents the sampling point after the corrected sampling.

[0086] In some embodiments, those skilled in the art will understand that, since the Continuous Fourth-Order Frequency Modulation (C4FM) signal employs a fourth-order frequency shift keying modulation mechanism, the four decision intervals strictly correspond to the four discrete baseband states of the signal during over-the-air transmission. When the sampling points of the effective data payload fall into the corresponding intervals one by one, the system determines them as the corresponding discrete digital symbols (+3, +1, -1, or -3). After completing the hard decision at the symbol level, the system can then directly interface with the symbol-to-bit inverse mapping operation known in the art, ultimately restoring these discrete symbols to the original binary bit stream, thereby completing the entire baseband demodulation service flow at the receiving end.

[0087] To further verify the effectiveness and advancement of the method proposed in this invention, the following is combined with... Figure 6 The demodulation performance of this invention and traditional demodulation methods is compared and explained through simulation.

[0088] Figure 6 The figure shows a comparison of the bit error rate (BER) performance of the traditional C4FM demodulation algorithm and the adaptive C4FM signal demodulation method based on median discreteness proposed in this invention under different signal-to-noise ratio (SNR) conditions. Figure 6 In the graph, the horizontal axis represents the signal-to-noise ratio (in dB), and the vertical axis represents the demodulation bit error rate (displayed in a logarithmic coordinate system). The red curve with a circular marker represents the traditional C4FM demodulation algorithm with a fixed step size and fixed threshold, while the blue curve represents the method proposed in this invention.

[0089] Depend on Figure 6 The simulation trend clearly shows that the proposed solution has significant advantages in demodulation performance, specifically in the following two aspects: On the one hand, this invention exhibits superior global demodulation accuracy. Across all signal-to-noise ratio (SNR) ranges covered in the simulation (e.g., from -2dB to 22dB), the bit error rate of the proposed algorithm is consistently significantly lower than that of traditional demodulation algorithms. This indicates that this invention is no longer limited to a single fixed decision system; it accurately evaluates the dispersion using the median absolute difference (MAD), enabling the system to more fully benefit from the SNR gain.

[0090] On the other hand, this invention significantly improves the system's bit error rate performance threshold. In complex digital communication, demodulation algorithms often get stuck at a certain high signal-to-noise ratio (SNR) point due to their own architectural flaws, resulting in a "bit error rate plateau" (i.e., no matter how much the SNR increases, the bit error rate cannot continue to decrease). Figure 6 As shown, traditional demodulation algorithms tend to flatten out their bit error rate curve when the signal-to-noise ratio (SNR) climbs to approximately 13 dB, reaching their performance limit prematurely. In contrast, thanks to the dynamically iterative timing-synchronous sampling method in step S4 and the dynamically fluctuating decision method based on the SNR in step S5, the algorithm proposed in this invention effectively delays this plateau. Specifically, the algorithm proposed in this invention only reaches its performance limit when the SNR reaches approximately 20 dB, and the steady-state bit error rate under this limit is reduced by about an order of magnitude compared to traditional algorithms.

[0091] In summary, the simulation experiments demonstrate that the adaptive C4FM signal demodulation method based on median discretization proposed in this invention can effectively overcome the performance bottleneck of traditional demodulation algorithms in environments with varying signal-to-noise ratios. It possesses excellent channel adaptability and robustness, making it extremely suitable for deployment and application in complex working conditions with harsh electromagnetic environments.

[0092] In this specification, the illustrative expressions of the terms used do not necessarily refer to the same embodiments or examples. Moreover, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0093] Any modifications, equivalent substitutions, or improvements made within the spirit and principles of this invention shall be included within the scope of protection of this invention.

Claims

1. An adaptive C4FM signal demodulation method based on median discretization, characterized in that, include: S1. Perform frequency offset correction and instantaneous frequency calculation on the received continuous fourth-order frequency-modulated signal, find the signal synchronization head position through synchronization correlation, and calculate the sampling start point based on the sampling rate and symbol rate; S2. The Gardner algorithm is used to sample the current synchronization symbol according to a preset initial step size, and the sampling points of the current synchronization symbol are output. S3. Based on the distribution characteristics of the synchronization head, the sampling points are divided into a synchronization upper bound point sequence and a synchronization lower bound point sequence. The median of the two sets of sequences is found respectively. The median deviation sequence of the two sets of sequences is calculated. Based on the median deviation sequence, the absolute median difference between the synchronization upper bound point sequence and the synchronization lower bound point sequence is calculated. S4. The median discrete mean is measured based on the upper and lower bounds of the absolute median difference, and the timing step size of the Gardner algorithm is dynamically iteratively corrected to obtain the optimal step size. The algorithm is then resampled according to the optimal step size to update and obtain the final absolute median difference. S5. Establish a decision domain sample fluctuation model, use the median of the two sets of sequences to describe the fluctuation center, use the final absolute median difference to describe the fluctuation degree, and combine it with the compensation factor based on the current signal-to-noise ratio to dynamically calculate the upper and lower decision thresholds of the current optimal symbol. S6. Construct a symbol decision interval using the upper and lower decision thresholds, perform symbol decision on the sample points after the optimal step size correction sampling, and output the demodulation result. The calculation method for the compensation factor of the current signal-to-noise ratio in S5 includes: in, Indicates the compensation factor; Represents the empirical scale constant, and ; Indicates the current signal-to-noise ratio; S5 dynamically calculates the upper and lower bound decision thresholds for the current best symbol. The calculation methods include: in, This represents the upper bound of the optimal decision threshold for the sign; This represents the lower bound sign optimal decision threshold; Represents the absolute median difference of the sequence of synchronization upper bounds for the current synchronization symbol; Represents the absolute median difference of the sequence of lower synchronization points of the current synchronization symbol; This represents the median of the sequence of points at the upper limit of synchronization. This represents the median of the lower bound sequence of synchronization points.

2. The adaptive C4FM signal demodulation method based on median discretization according to claim 1, characterized in that, The process of frequency offset correction and instantaneous frequency calculation for the received continuous fourth-order frequency-modulated signals, finding the signal synchronization header position through synchronization correlation, and calculating the sampling start point based on the sampling rate and symbol rate includes: Signal frequency offset correction is achieved based on the differential autocorrelation algorithm, wherein a preset symbol length is obtained as the frequency offset correction sample length, and a preset ratio of the symbol duration is used as the differential delay. The instantaneous frequency of the received signal is solved based on the phase difference method; By plotting the cross-correlation spectrum of the synchronous waveform using a sliding window, the position of the synchronous peak point is marked. The sampling interval is calculated based on the sampling rate and symbol rate, and the sampling start point is obtained.

3. The adaptive C4FM signal demodulation method based on median discretization according to claim 1, characterized in that, S3 divides the sampling points into a synchronization upper bound sequence and a synchronization lower bound sequence and calculates the median deviation sequence, including: Based on the characteristic that the synchronization header of the C4FM signal consists of +3 level symbols and -3 level symbols, the sampling points corresponding to the +3 level symbols are selected to form the synchronization upper limit point sequence, and the sampling points corresponding to the -3 level symbols are selected to form the synchronization lower limit point sequence. Find the median of each of the two sets of sequences, and calculate the median deviation between the two sets of sequences. The calculation methods include: in, This represents the median of the synchronization upper bound sequence or the synchronization lower bound sequence, where up is the index of the synchronization upper bound sequence and down is the index of the synchronization lower bound sequence. This represents the median function; This indicates the upper bound sequence or the lower bound sequence of synchronization points. This represents the median deviation sequence of the synchronization upper bound sequence or the synchronization lower bound sequence.

4. The adaptive C4FM signal demodulation method based on median discretization according to claim 3, characterized in that, In S3, the absolute median difference between the upper synchronization bound sequence and the lower synchronization bound sequence is calculated based on the median deviation sequence. The calculation method includes: in, It represents the absolute median difference between the upper and lower bounds of the current synchronization symbol sequence.

5. The adaptive C4FM signal demodulation method based on median discretization according to claim 4, characterized in that, The timing step size of the Gardner algorithm is dynamically iteratively corrected in S4, including: Calculate the median discrete mean of the upper and lower bounds: in, This represents the median discrete mean of the upper and lower bounds; Represents the absolute median difference of the sequence of synchronization upper bounds for the current synchronization symbol; Represents the absolute median difference of the sequence of lower synchronization points of the current synchronization symbol; Set the initial adaptive step size; The next shortening step length and increasing step length are calculated based on the median discrete mean of the upper and lower bounds. The calculation method includes: in, Indicates the current step length; This indicates the next step length to be shortened; Indicates the next increment step length; Indicates the degree of discrete correction, and .

6. The adaptive C4FM signal demodulation method based on median discretization according to claim 5, characterized in that, After calculating the next shortening step length and increasing step length based on the median discrete mean of the upper and lower bounds in S4, it also includes: According to the next shortening step length and the next growth step length The corresponding Gardner algorithm is used to resample and calculate a new median discrete mean. and ; To shorten the step length The corresponding median discrete mean; To increase step length The corresponding median discrete mean; Compare , and ,like If the minimum value is found, then the current step length is taken directly. Find the optimal step size and stop iterating; like minimum, take Update to the current step length ; and take Updated to upper and lower bounds, median, and discrete mean. Repeat the calculation of the next shortening step length and increasing step length; like To minimize, take Update to the current step length and take Updated to upper and lower bounds, median, and discrete mean. Repeat the calculation to shorten and increase the step length for the next iteration.

7. The adaptive C4FM signal demodulation method based on median discretization according to claim 6, characterized in that, Limit the number of times the step length is repeatedly calculated for the next iteration. If the number of iterations reaches the set value, the current step length corresponding to the last iteration is taken as the optimal step length.

8. The adaptive C4FM signal demodulation method based on median discretization according to claim 4, characterized in that, In S6, the sample points after the optimal step size correction sampling are subjected to sign determination and the demodulation result is output. The determination logic includes: like If so, the demodulation symbol is determined to be +3; like If so, the demodulation symbol is determined to be +1; like If so, the demodulation symbol is determined to be -1; like If so, the demodulation symbol is determined to be -3; Where "point" represents the sampling point after the corrected sampling.

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