Self-adaptive multi-band signal-to-noise ratio estimation method and device

By constructing a multi-band parameter configuration framework and combining weighted fusion of front-and-back symbol differential estimation and empty subcarrier estimation, the problems of multi-band adaptability and dynamic channel robustness of signal-to-noise ratio estimation in power line communication are solved, achieving high-precision and low-complexity signal-to-noise ratio estimation and improving the reliability and stability of power line communication.

CN121547078APending Publication Date: 2026-02-17深圳市力合微电子股份有限公司
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Patent Information

Application Number
CN202511878602.1
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2025-12-12
Publication Date
2026-02-17

AI Technical Summary

Technical Problem

In existing power line communication technologies, signal-to-noise ratio estimation methods have poor adaptability to multiple frequency bands, insufficient robustness to dynamic channels, and difficulty in maintaining high accuracy and low complexity in complex noise environments.

Method used

An adaptive multi-band signal-to-noise ratio estimation method is adopted. By constructing a multi-band parameter configuration framework, weighted fusion is performed by combining front and rear symbol differential estimation and empty subcarrier estimation, and the weights are dynamically adjusted to adapt to different channel conditions.

Benefits of technology

It achieves high accuracy and robustness in signal-to-noise ratio estimation under complex and variable power line communication environments, supports versatility and low complexity for multi-frequency band applications, and improves the reliability and stability of communication.

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Abstract

The invention discloses a self-adaptive multi-band signal-to-noise ratio estimation method and device. The method comprises the following steps: S1, acquiring a data subcarrier index set, an empty subcarrier index set and a frequency domain signal; s2, based on the frequency domain signal, obtaining a first noise power estimation value by adopting a front and back symbol difference estimation algorithm; s3, based on the frequency domain signal and the null subcarrier index set, obtaining a second noise power estimation value by adopting a null subcarrier estimation algorithm; s4, based on a preset initial weight, performing weighted fusion on the first noise power estimation value and the second noise power estimation value to obtain a total noise power estimation value; s5, calculating a signal power estimation value based on the frequency domain signal and the data subcarrier index set, and obtaining a preliminary signal-to-noise ratio estimation value in combination with the total noise power estimation value; and S6, performing adaptive adjustment based on the initial signal-to-noise ratio estimation value to obtain a final signal-to-noise ratio estimation value, thereby remarkably improving the SNR estimation precision and robustness in a complex and changeable power line communication environment.
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Description

Technical Field

[0001] This invention relates to the field of power line communication technology, and in particular to a method and apparatus for high-precision and robust signal-to-noise ratio estimation in complex and variable power line channel environments. Background Technology

[0002] Power line communication (PLC) utilizes existing power line networks as a transmission medium, offering advantages such as wide coverage and no need for rewiring, leading to its increasing application in the Internet of Things (IoT) and smart grids. However, the power line channel environment is exceptionally complex, characterized by high noise, strong impulse interference, narrowband interference, and severe frequency-selective fading, all of which severely limit the reliability of communication performance.

[0003] Signal-to-noise ratio (SNR) is a fundamental parameter characterizing channel quality and enabling key technologies such as adaptive modulation and coding, and power control. Existing SNR estimation methods mainly include pilot-assisted estimation methods and blind estimation methods. In power line communication scenarios, these methods face severe challenges: (1) Poor multi-band adaptability: Power line communication standards (such as IEEE 1901) define multiple operating frequency bands (such as 2-12MHz, 2.4-5.6MHz, etc.), and the subcarrier distribution, pilot positions, and other parameters of different frequency bands vary. Traditional methods are mostly designed for specific frequency bands and lack a unified framework, resulting in high complexity and low resource efficiency when deploying multiple frequency bands. (2) Insufficient robustness of dynamic channels: Frequent fluctuations in power line loads lead to strong time-varying channel impedance. Fixed-weight estimation methods (such as fixed-order filtering methods) are difficult to quickly track channel changes, and the estimation accuracy drops significantly when the channel changes abruptly. (3) The contradiction between estimation accuracy and complexity: Algorithms that perform well under the Gaussian white noise assumption (such as the second and fourth moment methods) deteriorate under the impulse noise and narrowband interference unique to PLCs. Algorithms that can resist interference are often computationally complex and difficult to run in real time on resource-constrained PLC equipment.

[0004] Therefore, there is an urgent need in this field for an SNR estimation solution that can adapt to multiple power line communication frequency bands, dynamically respond to channel changes, and maintain high accuracy and low complexity in complex noise environments. Summary of the Invention

[0005] The present invention aims to address the deficiencies in the prior art. Specifically, the technical problem to be solved is: how to provide a signal-to-noise ratio estimation method that can adapt to different operating frequency bands of power line communication, and maintain high accuracy and robustness of the estimation results under drastic changes in channel conditions and complex noise interference, while meeting the constraints of terminal equipment on computational complexity.

[0006] The technical problem of this invention is solved by the following technical solution: In a first aspect, the present invention provides an adaptive multi-band signal-to-noise ratio estimation method, comprising the following steps: S1. Obtain the received time-domain signal and the frequency band identifier of the current communication, and obtain the data subcarrier index set, the empty subcarrier index set and the frequency-domain signal based on the time-domain signal and the frequency band identifier; S2. Based on the frequency domain signal, the first noise power estimate is obtained by using the front and back symbol difference estimation algorithm; S3. Based on the frequency domain signal and the empty subcarrier index set, the second noise power estimate is obtained by using the empty subcarrier estimation algorithm. S4. Based on the preset initial weights, the first noise power estimate and the second noise power estimate are weighted and fused to obtain the total noise power estimate; S5. Based on the frequency domain signal and data subcarrier index set, calculate the signal power estimate and combine it with the total noise power estimate to obtain the preliminary signal-to-noise ratio estimate. S6. Based on the preliminary signal-to-noise ratio estimate, perform adaptive adjustment to obtain the final signal-to-noise ratio estimate.

[0007] In some embodiments, the following technical features are also included: Step S1 specifically includes the following steps: S11. Based on the frequency band identifier, query the pre-stored multi-frequency band parameter configuration table to obtain the data subcarrier index set and empty subcarrier index set corresponding to the current frequency band. S12. Perform time-domain synchronization processing on the time-domain signal to determine the symbol start position; S13. Based on the starting position of the symbol, perform a fast Fourier transform on the time-domain signal to obtain the frequency-domain signal.

[0008] In some embodiments, step S1 specifically includes the following steps: S11. Based on the frequency band identifier, query the pre-stored multi-frequency band parameter configuration table to obtain the data subcarrier index set and empty subcarrier index set corresponding to the current frequency band. S12. Perform time-domain synchronization processing on the time-domain signal to determine the symbol start position; S13. Based on the starting position of the symbol, perform a fast Fourier transform on the time-domain signal to obtain the frequency-domain signal.

[0009] In some embodiments, the multi-band parameter configuration table in step S11 pre-stores parameter sets for multiple power line communication standard frequency bands, and the parameter sets include at least a data subcarrier index set and a null subcarrier index set.

[0010] In some embodiments, the time-domain synchronization process in step S12 specifically includes the following steps: Generate a preamble template that matches the current frequency band; calculate the cross-correlation value between the time-domain signal and the preamble template; determine the symbol start position based on the peak position of the cross-correlation value, and judge the synchronization quality based on the ratio of the main peak to the secondary peak; if the synchronization quality is lower than a preset threshold, then in step S6, the weights used for the empty subcarrier estimation algorithm are adjusted to be greater than the weights used for the front and rear symbol differential estimation algorithm.

[0011] In some embodiments, the calculation of the second noise power estimate using the empty subcarrier estimation algorithm in step S3 specifically includes the following steps: Calculate the power on each subcarrier in the empty subcarrier index set; sort the calculated power and remove abnormal power values ​​that exceed a preset threshold; average the remaining power after removing abnormal values ​​to obtain the second noise power estimate.

[0012] In some embodiments, the adaptive adjustment in step S6 specifically includes the following steps: S61. Based on the range of the preliminary signal-to-noise ratio estimate, adaptively adjust the weights corresponding to the first noise power estimate and the second noise power estimate, respectively. S62. Using the adjusted weights, re-execute steps S4 and S5 to obtain the final signal-to-noise ratio estimate.

[0013] In some embodiments, step S61, which adaptively adjusts the weights based on the range of the preliminary signal-to-noise ratio estimate, specifically includes the following steps: If the preliminary signal-to-noise ratio estimate is lower than the first threshold, the weight of the second noise power estimate is increased; if the preliminary signal-to-noise ratio estimate is higher than the second threshold, the weight of the first noise power estimate is increased; if the preliminary signal-to-noise ratio estimate is between the first threshold and the second threshold, the weights of the first noise power estimate and the second noise power estimate are kept similar.

[0014] In a second aspect, the present invention provides an adaptive multi-band signal-to-noise ratio estimation device for power line communication, comprising: The signal acquisition module is used to acquire the received time-domain signal and the identifier of the current communication frequency band; The configuration query module is used to query the pre-stored multi-band parameter configuration table based on the frequency band identifier, and obtain the data subcarrier index set and empty subcarrier index set corresponding to the current frequency band; The synchronization processing module is used to perform time-domain synchronization processing on the time-domain signal to determine the symbol start position; The transformation module is used to perform a fast Fourier transform on the time-domain signal according to the symbol start position to obtain a frequency-domain signal; The first noise power estimation module is used to calculate the first noise power estimate based on the frequency domain signal using the front and back symbol difference estimation algorithm; The second noise power estimation module is used to calculate the second noise power estimate based on the frequency domain signal and the empty subcarrier index set using an empty subcarrier estimation algorithm. The fusion module is used to perform weighted fusion of the first noise power estimate and the second noise power estimate based on preset initial weights to obtain a total noise power estimate. The signal-to-noise ratio (SNR) estimation module is used to calculate the signal power estimate based on the frequency domain signal and the data subcarrier index set, and to calculate the preliminary SNR estimate by combining the total noise power estimate. The output module is used to adaptively adjust based on the preliminary signal-to-noise ratio estimate and output the final signal-to-noise ratio estimate.

[0015] In some embodiments, the output module further includes an adaptive adjustment submodule, which is used to adaptively adjust the weights corresponding to the first noise power estimate and the second noise power estimate according to the range of the signal-to-noise ratio estimate, and use the adjusted weights to recalculate the final signal-to-noise ratio estimate through the fusion module and the preliminary calculation module.

[0016] Thirdly, the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the above-described method.

[0017] The beneficial effects of this invention compared to the prior art include: The adaptive multi-band signal-to-noise ratio (SNR) estimation method and apparatus provided by this invention constructs a unified multi-band parameter configuration framework and innovatively integrates two complementary noise estimation methods, namely, front-to-back symbol differential estimation and empty subcarrier estimation, through adaptive weighted fusion. This achieves the following beneficial effects at the top level: significantly improving the SNR estimation accuracy and robustness in complex and variable power line communication environments, while ensuring versatility and low complexity in multi-band applications.

[0018] This top-level effect is derived through the synergistic effect of the following intermediate effects: First, by querying a pre-stored multi-band parameter configuration table, this invention can automatically adapt to different power line communication standard frequency bands (such as bands 0, 1, 2, and 3), obtain accurate data and empty subcarrier indices, solve the adaptability problem of multi-band deployment, and achieve a highly versatile and simple deployment intermediate effect. Second, by using the empty subcarrier estimation method to directly measure the power of subcarriers not used for data transmission, the influence of signal leakage is avoided. Furthermore, by using a mechanism to sort and eliminate outliers (such as impulse interference), it achieves a highly anti-interference and statistically stable intermediate effect under low SNR and strong interference conditions. Then, by utilizing the characteristic of the front-and-back symbol difference estimation method to effectively cancel out common frequency errors and phase noise between symbols, it achieves a high noise separation purity and high estimation sensitivity under high SNR and channel stability conditions. Finally, the fusion weights of the two methods are dynamically adjusted based on the preliminary SNR estimate (e.g., emphasizing empty subcarrier estimation at low SNR and symbol differential estimation at high SNR), and auxiliary weight adjustments can be made according to the time-domain synchronization quality, so that the fusion strategy can intelligently adapt to the dynamic changes of the channel.

[0019] The four intermediate effects mentioned above do not exist in isolation. Universality provides an accurate input basis for both estimation methods; anti-interference capability and high sensitivity ensure that each has a reliable estimation basis under adverse and favorable channel conditions, respectively; the adaptive adjustment mechanism, as the core of intelligent scheduling, dynamically allocates the contribution of the two reliable estimation bases according to the real-time channel state (reflected by the initial SNR and synchronization quality), and ultimately achieves the top-level beneficial effect of maintaining high accuracy and high robustness across the entire SNR range and various channel conditions.

[0020] In addition, some embodiments also have the following beneficial effects: By adjusting the weights based on synchronization quality (primary / secondary peak ratio), the empty subcarrier estimation method, which is insensitive to synchronization errors, is preferentially used when synchronization is poor, further enhancing the estimation success rate under adverse channel initial conditions.

[0021] By setting weight adjustment thresholds (e.g., a low SNR threshold of 0 dB and a high SNR threshold of 10 dB) and setting empirical adjustment ranges for the weights, a clear and reliable adjustment basis is provided for the adaptive algorithm, avoiding weight oscillations and ensuring the stability of the estimation process.

[0022] By sorting the empty subcarrier power and removing outliers, the impact of impulse noise and narrowband interference on noise power estimation is effectively suppressed, thus improving the accuracy of the empty subcarrier estimation method in typical power line environments.

[0023] Other beneficial effects of the embodiments of the present invention will be further described below. Attached Figure Description

[0024] Figure 1 This is a flowchart of an adaptive multi-band signal-to-noise ratio estimation method in an embodiment of the present invention.

[0025] Figure 2 This is a flowchart of an adaptive multi-band signal-to-noise ratio estimation method in another embodiment of the present invention.

[0026] Figure 3 This is a flowchart of multi-band processing in an embodiment of the present invention.

[0027] Figure 4 This is a time-domain schematic diagram of the OFDM symbol block structure in an embodiment of the present invention.

[0028] Figure 5 This is a frequency domain schematic diagram of the OFDM symbol block structure in an embodiment of the present invention.

[0029] Figure 6 This is a schematic diagram of the empty subcarrier selection for calculating noise power using the empty subcarrier estimation method in an embodiment of the present invention.

[0030] Figure 7 These are weight optimization curves for three SNR scenarios in this embodiment of the invention.

[0031] Figure 8 This is a comparison chart of the absolute performance of the three methods in the embodiments of the present invention. Detailed Implementation

[0032] The present invention will be further described below with reference to the accompanying drawings and preferred embodiments. It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other.

[0033] It should be noted that the directional terms such as left, right, up, down, top, and bottom used in this embodiment are only relative concepts or are based on the normal use of the product, and should not be considered as restrictive.

[0034] Implementation Concept The core of this invention lies in providing a high-precision, robust SNR estimation scheme that can adapt to the multi-band and dynamic channels of power line communication. The basic concept is as follows: frequency band adaptation is achieved through a pre-stored multi-band parameter configuration table; two noise estimation methods are employed: front-and-back symbol differential and empty subcarrier; the fusion weights of the two methods are dynamically adjusted based on the preliminary SNR estimation results to fully utilize their respective advantages; and finally, a calibrated high-precision SNR estimate is output.

[0035] Example 1 This embodiment provides an adaptive multi-band signal-to-noise ratio estimation method, such as Figure 1As shown, it includes the following steps: S1. Obtain the received time-domain signal and the current communication frequency band identifier, and obtain the data subcarrier index set, the empty subcarrier index set, and the frequency-domain signal based on the time-domain signal and the frequency band identifier. Step S1 specifically includes the following steps: S11. Obtain the time domain signal and frequency band identifier. Based on the frequency band identifier, configure the frequency band parameters using a multi-band parameterized configuration framework. Query the pre-stored multi-band parameter configuration table. Automatically obtain the current frequency band configuration parameters in the configuration framework based on the frequency band identifier. If the frequency band changes, dynamically obtain the current frequency band configuration parameters based on the multi-band parameterized configuration framework to obtain the data subcarrier index set and empty subcarrier index set corresponding to the current frequency band.

[0036] S12. Perform time-domain synchronization processing on the time-domain signal to determine the symbol start position, and select an SNR estimation strategy based on the synchronization result.

[0037] S13. Based on the symbol start position and the time-domain signal synchronization processing result, perform FFT transformation on the time-domain signal to obtain the frequency-domain signal.

[0038] S2. Based on the frequency domain signal, the first noise power estimate is obtained by using the front and back symbol difference estimation algorithm.

[0039] S3. Based on the frequency domain signal and the empty subcarrier index set, the second noise power estimate is obtained by using the empty subcarrier estimation algorithm.

[0040] S4. Based on the preset initial weights, the first noise power estimate and the second noise power estimate are weighted and fused to obtain the total noise power estimate.

[0041] Specifically, step S3, which uses the empty subcarrier estimation algorithm to calculate the second noise power estimate, includes the following steps: Calculate the power on each subcarrier in the empty subcarrier index set; sort the calculated power and remove abnormal power values ​​that exceed a preset threshold; average the remaining power after removing abnormal values ​​to obtain the second noise power estimate.

[0042] In this embodiment, the principle of steps S2-S4 is as follows: combining the differential estimation method of adjacent OFDM symbols and the empty subcarrier estimation method, the noise power of the corresponding subcarrier is calculated respectively. For the empty subcarrier estimation method, the noise power is filtered to determine the final noise power. According to the initial preset different weight values ​​of the two methods, the total noise power estimate is obtained by weighted calculation.

[0043] S5. Based on the frequency domain signal and data subcarrier index set, calculate the signal power estimate, and combine it with the total noise power estimate to obtain the preliminary signal-to-noise ratio estimate. In this embodiment, the signal power estimate is the subcarrier signal power. The corresponding subcarrier signal power is calculated based on the data subcarriers within the OFDM symbol, and the preliminary signal-to-noise ratio estimate (i.e., the preliminary estimated SNR value) is calculated.

[0044] S6. Based on the preliminary signal-to-noise ratio (SNR) estimate, perform adaptive adjustment to obtain the final SNR estimate. The adaptive adjustment specifically includes the following steps: S61. Based on the range of the preliminary signal-to-noise ratio (SNR) estimate obtained in step S5, adaptively and dynamically adjust the weight values ​​corresponding to the first and second noise power estimates in step S4, and adaptively select the weight values ​​according to the range of the estimated SNR values. ).

[0045] S62. Based on the adjusted weight values, select either the front-to-back symbol difference estimation method or the empty subcarrier estimation method to dynamically adapt to different channel scenarios. Re-execute steps S4 and S5 to recalculate the total noise power estimate and obtain the final signal-to-noise ratio estimate.

[0046] In step S11, the multi-band parameter configuration table pre-stores parameter sets for multiple power line communication standard frequency bands. These parameter sets include at least a data subcarrier index set and a null subcarrier index set. The multi-band parameterized configuration framework, as described in this embodiment, implements different scenario parameters using configuration tables. This means that parameter sets for different frequency band types are predefined. Frequency band types include band 0 (2-12MHz), band 1 (2.4-5.6MHz), band 2 (0.7-2.9MHz), and band 3 (1.7-2.9MHz). The parameter set represents the data subcarrier position and null subcarrier position for the corresponding frequency band. Determining the frequency band type determines the parameter set, supporting seamless multi-band switching. The step of obtaining the current frequency band configuration parameters based on the frequency band identifier specifically includes: Data subcarrier position: Subcarrier index used for signal power calculation; Empty subcarrier position: Subcarrier index used for noise power estimation; If a frequency band switch occurs, the current frequency band configuration parameters are dynamically obtained according to the multi-band parameterized configuration framework, specifically: If the current frequency band type is configured as frequency band 0, then the data subcarrier position and empty subcarrier position are the data subcarrier position and empty subcarrier position of frequency band 0. If the current frequency band changes from frequency band 0 to frequency band 1, that is, the frequency band type changes, then the data subcarrier position and empty subcarrier position are dynamically changed to the data subcarrier position and empty subcarrier position of frequency band 1 according to the multi-band parameterized configuration framework. The time-domain synchronization process in step S12 specifically includes the following steps: The time-domain synchronization processing involves performing correlation detection on the received signal and calculating the synchronization point, specifically including: Generate a preamble template matching the current frequency band; calculate the cross-correlation value between the time-domain signal and the preamble template; determine the symbol start position based on the peak position of the cross-correlation value, and judge the synchronization quality based on the ratio of the main peak to the secondary peak; if the synchronization quality is lower than a preset threshold, in step S6, the weights used for the empty subcarrier estimation algorithm are adjusted to be greater than the weights used for the front-to-back symbol difference estimation algorithm. Specific details are as follows: Generate preamble template: Use the long preamble sequence defined by the IEEE 1901 / HomePlug AV standard as the template LocPream to adapt to different frequency bands; Downsampling and cross-correlation calculation: Cross-correlation calculation uses the formula R = IFFT( FFT(Y) * conj(FFT(LocPream)) ), where FFT is the FFT transform, IFFT is the IFFT transform, conj is the conjugate processing, Y is the received time-domain signal, and the maximum amplitude point of R is found as a candidate synchronization point.

[0047] Synchronization point evaluation based on the ratio of the main peak to the largest secondary peak: Calculate the ratio of the main peak to the largest secondary peak. If the ratio is greater than the empirical threshold set for synchronization, the synchronization is confirmed to be successful. If the ratio is found to be lower than the empirical threshold set for synchronization, it indicates that the current channel environment is poor, and the more robust empty subcarrier estimation method for the current scenario can be used directly.

[0048] In this implementation, the first noise power estimate in step S2 is the differential noise power between the preceding and following symbols, and the second noise power estimate in step S3 is the empty subcarrier noise power. The differential noise power estimation between the preceding and following symbols specifically includes the following steps: The preceding and following symbol differential noise power estimation uses the symbol difference between adjacent OFDM symbols to estimate the noise power, thus obtaining the first noise power estimate. Assign weights ,in The noise power is estimated using empty subcarriers to obtain the second noise power estimate. Assign weights ,in , Through extensive channel simulations, it was determined that under typical power line channel conditions, the initial weights should be set to... = = 0.5 indicates good starting performance. Therefore, the estimated total noise power is... The estimation process for the difference noise power between the front and back symbols is as follows: In OFDM communication systems, there are typically two or more OFDM symbols with the same structure, or one OFDM symbol containing many identical blocks. Therefore, noise power can be estimated based on consecutive OFDM symbols with the same structure or consecutive blocks within an OFDM symbol.

[0049] The m-th and (m+1)-th received OFDM symbols as follows: For the m-th OFDM symbol, the modulated signal of the k-th subcarrier, Let m be the channel frequency domain response of the m-th OFDM symbol and k-th subcarrier, assuming... , Given a Gaussian white noise signal with a mean of 0 and a variance of 1, when Then: in, For the channel frequency domain response of the k-th subcarrier, when Then: Subtracting the OFDM symbols from the beginning and end, we have: but: After FFT transformation to the frequency domain, the first noise power estimate is: The estimation of empty subcarrier noise power specifically includes the following steps: Calculate the power on each subcarrier within the empty subcarrier index set; sort the calculated power and remove abnormal power values ​​exceeding a preset threshold; average the remaining power after removing abnormal values ​​to obtain the second noise power estimate (i.e., empty subcarrier noise power). The specific process of empty subcarrier noise power estimation is as follows: This method divides OFDM symbols into blocks. Assuming the symbol length is N, dividing the OFDM symbol into Q blocks results in each block having a length of... ,in The time-domain construction after OFDM block partitioning is as follows Figure 4 As shown, Figure 4 The OFDM symbol is divided into Q-block subcarriers. The empty subcarrier noise power estimation method is implemented in the frequency domain. Figure 4 The time-domain construction is converted to the frequency domain for implementation, as shown in the frequency domain construction. Figure 5 As shown.

[0050] like Figure 6 As shown, combined with Figure 5 The frequency domain segmentation diagram illustrates how OFDM symbol data subcarriers are segmented based on the index addresses of data subcarriers and empty subcarriers within the frequency band. After segmentation, the first to Q-th blocks contain signals as follows: , The remaining undivided subcarriers are The remaining undivided portion is an empty subcarrier. The signal on the nth subcarrier is represented as: The signal received by the nth symbol is: The signal energy is obtained by performing a second-order matrix calculation on the data on the effective subcarriers in the block: This method performs joint processing on consecutive subcarriers within each block, effectively smoothing random noise and suppressing narrowband interference and transient pulse effects in the subband through frequency domain energy averaging. This makes the estimated signal energy closer to the true value. Individual subcarrier estimation, on the other hand, is completely exposed to random noise fluctuations. Given the severe frequency selectivity of power line channels, some subcarriers may be at deep fading points with very low received power. The block-based approach reduces estimation bias and improves robustness. Second-order matrix calculations are performed on the data on empty subcarriers to obtain the noise energy. Since the empty subcarrier estimation method may be contaminated by narrowband interference, the energy of each subcarrier calculated on the empty subcarriers is sorted, and outliers significantly exceeding a set energy threshold are removed to enhance robustness. A schematic diagram of the empty subcarrier used for noise power estimation is shown below. Figure 6 As shown, according to Figure 6 The second noise power estimate obtained from the empty subcarrier calculation is as follows: The noise energy threshold for empty subcarriers is determined based on the average noise energy value, and the noise energy threshold TH is set as follows: in, It is represented as a constant.

[0051] In step S5, the subcarrier signal power S is the signal energy calculated in step S4. The calculation yields a preliminary estimated SNR value, specifically including: In step S61, the weights are adaptively adjusted according to the range of the preliminary signal-to-noise ratio estimate, which specifically includes the following steps: If the preliminary signal-to-noise ratio (SNR) estimate is lower than the first threshold, the weight of the second noise power estimate is increased; if the preliminary SNR estimate is higher than the second threshold, the weight of the first noise power estimate is increased; if the preliminary SNR estimate is between the first and second thresholds, the weights of the first and second noise power estimates are kept similar. The specific process is as follows: Based on the calculated preliminary estimated SNR value, the weight values ​​in step S4 are adaptively and dynamically adjusted. The adaptive adjustment threshold is set based on the confidence interval of the noise variance estimation. The weight adjustment threshold (e.g., 0dB, 10dB) and the initial weight (e.g., 0.5) can be optimized according to the actual application scenario and specific communication standard. In the field of power line communication, low SNR is considered to be below 0dB, and high SNR is considered to be above 10dB. Specifically, this includes: If the initial estimated SNR value is small, i.e., low SNR, then the weights should be reallocated. = , = ,in > , + =1, this scenario focuses more on empty subcarrier noise power estimation; If the initial estimated SNR value is appropriate, then the weight values ​​for the symbol differential noise power estimate and the empty subcarrier noise power estimate should be assigned relatively equal values, i.e. = , = ,in + =1, .

[0052] If the initial estimated SNR value is large, i.e., high SNR, then the weights should be reallocated. = , = ,in > , + =1, this scenario focuses more on the estimation of the power difference noise between the front and rear symbols; After adaptively adjusting the weight values ​​based on the above judgments, steps S4 and S5 are executed to obtain the adjusted and calibrated SNR value. ; The preset number of calibration cycles in step S62 is adjusted according to the received signal quality and hardware characteristics. When the calibration cycle ends, the output SNR value is the final estimated SNR value.

[0053] When the estimated value is under low SNR conditions, the signal power is close to or lower than the noise power, and the channel environment is complex, such as deep fading and strong interference, the empty subcarrier estimation method estimates the noise by directly measuring the power of subcarriers not used for data transmission in the frequency domain. It has the following advantages: Strong anti-interference capability: The empty subcarrier is not affected by signal modulation, providing clean noise sampling points and avoiding estimation errors caused by signal leakage; Statistical stability: The number of empty subcarriers is usually large, accounting for 10%-20% of a symbol in an OFDM system. By averaging, random noise fluctuations can be effectively reduced, providing a more stable noise estimate. Insensitive to frequency offset and phase noise: Empty subcarrier estimation does not depend on the phase continuity of the symbol line, and can still work reliably under low SNR conditions when the effects of frequency offset and phase noise are significant; However, the sign difference method has the following disadvantages under low SNR conditions: Amplified noise error: The differential estimation method introduces additional noise gain at low SNR, leading to an increase in estimation variance; Sensitive to frequency offset: In addition, differential processing may not completely eliminate signal components, and residual signals will contaminate noise power estimation; High symbol synchronization requirements: The probability of synchronization error increases at low SNR. Differential methods rely on precise symbol alignment, and synchronization deviations can lead to misestimation failure. Therefore, under low SNR conditions, empty subcarrier estimation becomes a more reliable choice due to its stability and robustness, and the adaptive fusion mechanism will assign it a higher weight value. Under high SNR conditions, the signal power is much higher than the noise, the channel conditions are better, which aligns with the advantages of the differential method, specifically: Eliminating common signal components: Differential processing can effectively cancel common frequency errors and phase noise between symbols, purify noise samples, and reduce estimation bias caused by channel residues; High sensitivity: At high SNR, the noise power is low, and the difference method is more sensitive to noise, which can capture subtle noise statistical effects and provide high-precision noise estimation. Utilizing symbol correlation: OFDM symbols have continuous phase, and differential methods use this characteristic to enhance noise separation efficiency, making them suitable for scenarios with small multipath propagation. Empty subcarrier estimation has the following drawbacks at high SNR: Resource waste: Empty subcarriers do not fully utilize frequency domain information, resulting in lower estimation efficiency than differential methods. Sensitive to narrowband interference: At high SNR, empty subcarriers may be contaminated by narrowband interference such as adjacent channel leakage, while differential methods can partially suppress this interference through inter-symbol differential.

[0054] Therefore, under high SNR conditions, empty subcarrier estimation becomes a more reliable choice due to its anti-interference and high accuracy characteristics, and the adaptive fusion mechanism will assign it a higher weight value.

[0055] This embodiment combines front-and-back symbol differential noise estimation and empty subcarrier noise estimation methods, assigning different noise power weights to the two methods and employing a dynamic weight adjustment strategy to achieve high-accuracy and robust SNR estimation. The specific design method includes: frequency band identification and configuration parameter acquisition, time-domain synchronization processing, FFT transformation, noise power estimation, adaptive weight adjustment fusion, and SNR estimation output. This embodiment effectively solves the challenges of complex noise, diverse frequency bands, and dynamic channel changes in power line communication systems, improving communication reliability and stability; and effectively addresses the core problems of poor frequency band adaptability and dynamic channel challenges inherent in traditional methods. Specifically: (1) Through dynamic weight adjustment and multi-level compensation, noise fluctuations and channel distortion are effectively suppressed, and estimation accuracy is improved; (2) In low SNR environments, the focus is on empty subcarrier estimation to resist impulse noise and interference and ensure reliability under harsh channel conditions. (3) In high SNR environments, the focus is on symbol difference estimation to eliminate frequency offset, improve accuracy, and support high-speed data transmission; (4) It adopts a parameterized configuration framework to support seamless switching between multiple frequency bands. It manages specific parameters of frequency bands through configuration tables, reducing deployment complexity. (5) Strong dynamic channel robustness: The weight value is dynamically adjusted based on the real-time SNR estimate, which effectively copes with real-time channel conditions such as power line impedance changes and load fluctuations, and improves the estimation stability. The advantages of the embodiments of the present invention include: (1) Low SNR Environment Optimization: When the estimated value is low SNR, the weight value focuses on empty subcarrier estimation to resist impulse noise and interference and ensure reliability under harsh channel conditions. At low SNR, empty subcarrier estimation has the following advantages: Strong anti-interference capability: The empty subcarrier is not affected by signal modulation, providing clean noise sampling points and avoiding estimation errors caused by signal leakage; Statistical stability: The number of empty subcarriers is usually large, accounting for 10%-20% of a symbol in an OFDM system. By averaging, random noise fluctuations can be effectively reduced, providing a more stable noise estimate. Insensitive to frequency offset and phase noise: Empty subcarrier estimation does not depend on the phase continuity of the symbol line and can still work reliably under low SNR conditions when the effects of frequency offset and phase noise are significant.

[0056] (2) Enhancement in high SNR environments: When the estimated value is at a high SNR, the weight value focuses on symbol difference estimation to eliminate frequency offset and phase noise, and supports high-speed data transmission. At high SNR, the difference estimation method has the following advantages: Eliminating common signal components: Differential processing can effectively cancel common frequency errors and phase noise between symbols, purify noise samples, and reduce estimation bias caused by channel residues; High sensitivity: At high SNR, the noise power is low, and the difference method is more sensitive to noise, which can capture subtle noise statistical effects and provide high-precision noise estimation. Utilizing symbol correlation: OFDM symbols have continuous phase, and differential methods use this characteristic to enhance noise separation efficiency, making them suitable for scenarios with small multipath paths.

[0057] (3) Architecture universality: It adopts a multi-band parameterized configuration framework to support seamless switching of multiple bands, including band 0, band 1, band 2 and band 3. It manages specific parameters of the band through configuration table, avoiding the development of independent algorithms for each band and reducing deployment complexity.

[0058] (4) Adaptive weight adjustment: The fusion weights are dynamically adjusted based on the real-time SNR estimate (e.g., spatiotemporal subcarrier dominance in low SNR, differential dominance in high SNR) to effectively cope with time-varying channel conditions such as power line impedance changes and load fluctuations. The estimation stability is improved in impedance mutation tests.

[0059] (5) Multi-level calibration: integrate multi-level calibration (synchronization quality calibration, SNR estimation calibration) to compensate for channel dynamics.

[0060] Example 2 See Figure 2 This invention provides a high-precision and robust adaptive multi-band SNR estimation method for power line communication systems, applied to an adaptive multi-band signal-to-noise ratio estimation device for power line communication, the device comprising: The signal acquisition module is used to acquire the received time-domain signal and the identifier of the current communication frequency band; The configuration query module is used to query the pre-stored multi-band parameter configuration table based on the frequency band identifier, and obtain the data subcarrier index set and empty subcarrier index set corresponding to the current frequency band; The synchronization processing module is used to perform time-domain synchronization processing on the time-domain signal to determine the symbol start position; The transformation module is used to perform a fast Fourier transform on the time-domain signal according to the symbol start position to obtain a frequency-domain signal; The first noise power estimation module is used to calculate the first noise power estimate based on the frequency domain signal using the front and back symbol difference estimation algorithm; The second noise power estimation module is used to calculate the second noise power estimate based on the frequency domain signal and the empty subcarrier index set using an empty subcarrier estimation algorithm. The fusion module is used to perform weighted fusion of the first noise power estimate and the second noise power estimate based on preset initial weights to obtain a total noise power estimate. The signal-to-noise ratio (SNR) estimation module is used to calculate the signal power estimate based on the frequency domain signal and the data subcarrier index set, and to calculate the preliminary SNR estimate by combining the total noise power estimate. The output module is used to adaptively adjust based on the preliminary signal-to-noise ratio estimate and output the final signal-to-noise ratio estimate.

[0061] The output module further includes an adaptive adjustment submodule, which is used to adaptively adjust the weights corresponding to the first noise power estimate and the second noise power estimate according to the range of the signal-to-noise ratio estimate, and use the adjusted weights to recalculate the final signal-to-noise ratio estimate through the fusion module and the preliminary calculation module.

[0062] The method includes the following steps: Step 1: Obtain the received time-domain signal, denoted as Y, and the frequency band type, denoted as Band, such as... Figure 2 The signal acquisition module acquires the signal and frequency band identifier, and automatically obtains the frequency band configuration parameters in the parameterized configuration architecture based on the frequency band type (Band). Figure 2 The configuration query module retrieves the current frequency band parameter configuration. The multi-frequency band processing flow is as follows: Figure 3 If a frequency band switch occurs, such as from frequency band 0 to frequency band 1, according to the parameterized configuration architecture, the frequency band type changes to frequency band 1, and the parameter set changes to the configuration parameters for frequency band 1. The frequency band configuration parameters for null subcarriers are set to NullSubCarrier, and the index for data subcarriers is set to DataSubCarrier. Taking frequency band 0 as an example, the band size is 0, and the total number of subcarriers N within the frequency band is 512. Based on the parameterized configuration framework configuration table, the current frequency band type is determined to be frequency band 0, and the number of data subcarriers... The value of the DataSubCarrier index is 411, with a range of (80, 490). The value range of the NullSubCarrier index is (0, 79) and (491, 511). The index starts counting from 0. If the frequency band changes from frequency band 0 to frequency band 1, then the Band becomes 1. At this time, the frequency band type in the parameterized configuration framework configuration table becomes frequency band 1, and the parameter set becomes the parameter set of frequency band 1, which is the number of data subcarriers. The value is 131, the range of the data subcarrier index DataSubCarrier is (100, 230), and the range of the null subcarrier index NullSubCarrier is (0, 99) and (231, 511). Step 2: Perform time-domain synchronization processing on the received signal Y, such as... Figure 2 The intermediate synchronization processing module performs time-domain synchronization to obtain the synchronization point, including generating the preamble template LocPream, calculating the cross-correlation to obtain the synchronization point CorrPos, and obtaining complete and valid data based on the synchronization point CorrPos. In this example, the synchronization threshold is set to 3, and synchronization is successful. Step 3: Based on the time-domain synchronization processing results Perform a 1024-point FFT transformation, such as Figure 2 The intermediate transform module implements the FFT transform to the frequency domain, specifically as follows: FreqData = fft( .* ); Where fft performs the FFT transformation operation, and conj(.) performs conjugate processing; Step 4: Calculate the noise power using the difference method between adjacent OFDM symbols. and assign initial weight values. The noise power is calculated using the empty subcarrier method. In this example, the empty subcarrier noise power threshold TH=3* After sorting and filtering, the final noise power was determined. Assign initial weight values ,like Figure 2 The first noise power estimation module performs front-and-back symbol difference estimation, and the second noise power estimation module performs empty subcarrier estimation. The total noise power is then calculated by weighted calculation. ,like Figure 2 The fusion module obtains the total noise power, of which and The initial weights can all be set to 0.5, indicating that the initial state is unbiased for both methods. The specific implementation is as follows: =(abs(FreqData(m+1,DataSubCarrier)-FreqData(m,DataSubCarrier) )^2) / 2 = =abs(FreqData(m,NullSubCarrier))^2; m=0,1,...,13; k =0,1,...,511; = = * + * Where abs() is the modulo operation and mean() is the averaging operation, the mean is calculated twice to average the symbol and subcarrier dimensions respectively; Step 5: Calculate the corresponding subcarrier signal power based on the data subcarriers within the OFDM symbol. ,like Figure 2 The signal-to-noise ratio (SNR) estimation module calculates the signal power based on the data subcarriers, specifically as follows: (abs(FreqData(m,DataSubCarrier )^2)) The preliminary estimated SNR value is calculated, such as Figure 2 The signal-to-noise ratio (SNR) estimation module calculates a preliminary estimate of the SNR value, specifically as follows: Step 6: Based on the preliminary estimated SNR value obtained in Step 5, adaptively and dynamically adjust the weight values ​​in Step 4, recalculate the total noise power, and execute Step 5 to calculate the calibrated SNR value, as shown below. Figure 2 The adaptive adjustment submodule performs SNR determination and weight allocation, specifically as follows: If (SNR < 0) = = ; Else If( ) = = ; Else If( >10) = = ; End Step 7: Based on the weight values ​​determined in Step 6, continue executing Steps 4 and 5. If the preset number of calibrations is exceeded, output the final calibration value. This is the estimated SNR value, such as... Figure 2 The output module including an adaptive adjustment sub-module outputs the final SNR value, and the specific implementation is as follows = * + * ; To better illustrate the performance of the SNR estimation method of the invention, in this embodiment, the total number of subcarriers is 512, the FFT length is 1024, the length of one OFDM symbol in the frequency domain is 512. When SNR < 0, The allocation value range of is 70% - 80%, and The allocation range of + = 100%. When SNR < 0, considering that under low signal-to-noise ratio conditions, the error of the symbol difference method will increase, and the error of the null subcarrier estimation method mainly comes from the statistical fluctuation of finite samples and possible minor interference. Therefore, at this time, the weight values are reallocated, and more emphasis is placed on the null subcarrier noise power estimation method. If the time synchronization is very accurate, the weight of the symbol difference method can be appropriately increased. If the channel estimation feedback shows that the current channel is stable, the weight of the null subcarrier estimation can be appropriately increased; on the contrary, when 0 < SNR < 10 and SNR > 10, if the synchronization is accurate, the weight of the symbol difference method can be appropriately increased. If there is a slight error in synchronization, the weight of the null subcarrier estimation method can be appropriately increased. That is, when 0 < SNR < 10, the weight values are reallocated and the weight values of the two methods are quite evenly distributed; when SNR > 10, the weight values are reallocated, and more emphasis is placed on the front and back symbol difference noise power estimation method. The determination of the weight value range is optimized with the goal of minimizing the estimated mean square error (MSE) by combining the actual system synchronization results and a large number of offline channel measurements and simulation experiments. To better describe the weight value range, the following gives the simulation analysis of this implementation example. When the actual SNR = [-5dB, 5dB, 15dB], the MSE curve graphs of the estimation performance when different weights are assigned to the symbol difference estimation method and the null subcarrier estimation method are as Figure 7As shown, under successful synchronization, the MSE (mean square error) curves of the simulated symbol differential method and the empty subcarrier estimation method under different weight values ​​are plotted at SNR=-5dB, SNR=5dB, and SNR=15dB. By observing the changes in the MSE curves through the changes in the allocated empty subcarrier weight values, it can be clearly seen that at SNR=15dB, when the weight value of the empty subcarrier estimation method is 25%, that is, when the weight value of the symbol differential estimation method is 75%, the MSE value is the smallest. At SNR=-5dB, when the weight value of the empty subcarrier is 80%, that is, when the weight value of the symbol differential estimation method is 20%, the MSE value is the smallest. At SNR=5dB, when the weight value of the empty subcarrier is 55%, that is, when the weight value of the symbol differential estimation method is 45%, the MSE value is the smallest.

[0063] When the actual SNR is [-5dB, 5dB, 15dB], the performance MSE curves of the combined symbol differential estimation method and the empty subcarrier estimation method are compared as shown in the figure. Figure 8 As shown. Figure 8 This demonstrates the performance changes of MSE curves when using only the empty subcarrier estimation method, only the symbol differential estimation method, and a fusion method (i.e., jointly using the empty subcarrier estimation method and the symbol differential estimation method) for SNR values ​​of (-5dB, 5dB, 15dB). Figure 8 As can be seen, the fusion method outperforms the empty subcarrier estimation method and the symbol difference estimation method in low SNR, moderate SNR and high SNR scenarios. This verifies that the embodiments of the present invention can significantly improve the SNR estimation accuracy and robustness in complex and variable power line communication environments, while ensuring versatility and low complexity in multi-band applications.

[0064] The aforementioned parameters, such as the synchronization quality judgment threshold, the empty subcarrier power outlier elimination coefficient, and the thresholds for the low SNR range, moderate SNR range, and high SNR range for adaptive weight adjustment, were determined through extensive offline Monte Carlo simulations of the channel model specified in the IEEE 1901 / HomePlug AV standard, with the goal of minimizing the mean square error (MSE) of the signal-to-noise ratio estimation. In practical applications, these parameters can be pre-stored in the device's configuration file.

[0065] The results of the embodiments of the present invention show that the spatiotemporal subcarrier method is superior in low SNR scenarios and the differential method is superior in high SNR scenarios. The specific principle analysis is as follows: Low SNR favors the empty subcarrier method: the core reason being that the differential method introduces noise enhancement. Subtracting two independent noise signals increases their variance (by twice the variance of a single noise signal). At low SNR, this amplified noise severely contaminates the estimate. The empty subcarrier method, however, is a direct measurement and does not suffer from this drawback.

[0066] High SNR favors differential methods: the core reason being that empty subcarrier methods may be affected by residual narrowband interference or adjacent channel leakage, which can be partially canceled out in differential operations (due to their strong correlation across consecutive symbols). Simultaneously, at high SNR, the noise enhancement effect of differential methods becomes acceptable.

[0067] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, several equivalent substitutions or obvious modifications can be made without departing from the concept of the present invention, and all such modifications, achieving the same performance or purpose, should be considered within the scope of protection of the present invention.

Claims

1. A method of adaptive multi-band signal-to-noise ratio estimation, the method comprising: The method comprises the following steps: S1, obtaining a received time domain signal and a frequency band identifier of a current communication, and obtaining a data subcarrier index set, a null subcarrier index set and a frequency domain signal based on the time domain signal and the frequency band identifier; S2, based on the frequency domain signal, using a front-back symbol difference estimation algorithm to obtain a first noise power estimation value; S3, based on the frequency domain signal and the null subcarrier index set, using a null subcarrier estimation algorithm to obtain a second noise power estimation value; S4, based on a preset initial weight, weighting and fusing the first noise power estimation value and the second noise power estimation value to obtain a total noise power estimation value; S5, based on the frequency domain signal and the data subcarrier index set, calculating a signal power estimation value, and combining the total noise power estimation value to obtain a preliminary signal-to-noise ratio estimation value; S6, based on the preliminary signal-to-noise ratio estimation value, performing adaptive adjustment to obtain a final signal-to-noise ratio estimation value.

2. The method of claim 1, wherein, Step S1 specifically comprises the following steps: S11, according to the frequency band identifier, querying a pre-stored multi-frequency band parameter configuration table to obtain a data subcarrier index set and a null subcarrier index set corresponding to the current frequency band; S12, performing time domain synchronization processing on the time domain signal to determine a symbol starting position; S13, according to the symbol starting position, performing fast Fourier transform on the time domain signal to obtain the frequency domain signal.

3. The method of claim 2, wherein, In step S11, the multi-frequency band parameter configuration table pre-stores parameter sets of multiple power line communication standard frequency bands, and the parameter sets at least include a data subcarrier index set and a null subcarrier index set.

4. The method of claim 2, wherein, In step S12, the time domain synchronization processing specifically comprises the following steps: generating a preamble template matched with the current frequency band; calculating a cross-correlation value of the time domain signal and the preamble template; determining a symbol starting position according to a peak value position of the cross-correlation value, and judging synchronization quality according to a ratio of a main peak to a secondary peak; if the synchronization quality is lower than a preset threshold, in step S6, the weight used for the null subcarrier estimation algorithm is adjusted to be greater than the weight used for the front-back symbol difference estimation algorithm.

5. The method of claim 1, wherein, In step S3, the null subcarrier estimation algorithm is used to calculate the second noise power estimation value, which specifically comprises the following steps: calculating the power on each subcarrier in the null subcarrier index set; sorting the calculated power and eliminating abnormal power values exceeding a preset threshold; averaging the remaining power after eliminating the abnormal values to obtain the second noise power estimation value.

6. The method of claim 1, wherein, In step S6, the adaptive adjustment specifically comprises the following steps: S61, according to the range where the preliminary signal-to-noise ratio estimation value is located, adaptively adjusting the weights corresponding to the first noise power estimation value and the second noise power estimation value respectively; S62, using the adjusted weights, re-executing steps S4 and S5 to obtain the final signal-to-noise ratio estimation value.

7. The method of claim 1, wherein, In step S61, the weights are adaptively adjusted according to the range where the preliminary signal-to-noise ratio estimation value is located, which specifically comprises the following steps: If the preliminary signal-to-noise ratio estimate is lower than a first threshold, the weight of the second noise power estimate is increased; if the preliminary signal-to-noise ratio estimate is higher than a second threshold, the weight of the first noise power estimate is increased; and if the preliminary signal-to-noise ratio estimate is between the first threshold and the second threshold, the weights of the first noise power estimate and the second noise power estimate are kept similar.

8. An adaptive multi-band signal-to-noise ratio estimation apparatus for power line communication, characterized by, The method comprises the steps of: acquiring a received time-domain signal and an identifier of a current communication frequency band; querying a pre-stored multi-frequency band parameter configuration table according to the frequency band identifier to acquire a data subcarrier index set and a null subcarrier index set corresponding to the current frequency band; performing time-domain synchronization processing on the time-domain signal to determine a symbol start position; performing fast Fourier transform on the time-domain signal according to the symbol start position to obtain a frequency-domain signal; calculating a first noise power estimate based on the frequency-domain signal using a front-back symbol difference estimation algorithm; calculating a second noise power estimate based on the frequency-domain signal and the null subcarrier index set using a null subcarrier estimation algorithm; performing weighted fusion on the first noise power estimate and the second noise power estimate based on a pre-set initial weight to obtain a total noise power estimate; calculating a signal power estimate based on the frequency-domain signal and the data subcarrier index set, and combining the total noise power estimate to obtain a preliminary signal-to-noise ratio estimate; outputting a final signal-to-noise ratio estimate based on the preliminary signal-to-noise ratio estimate.

9. The apparatus of claim 8, wherein, The output module further comprises an adaptive adjustment submodule for adaptively adjusting the weights corresponding to the first noise power estimate and the second noise power estimate according to the range of the signal-to-noise ratio estimate, and recalculating the final signal-to-noise ratio estimate using the adjusted weights through the fusion module and the preliminary calculation module.

10. A computer-readable storage medium having stored thereon a computer program, characterized in that, The program is executed by the processor to implement the steps of the method of any one of claims 1 to 7.