OFDM (Orthogonal Frequency Division Multiplexing) subcarrier number estimation method and system based on statistical characteristic test

Abstract

The invention discloses an OFDM (Orthogonal Frequency Division Multiplexing) subcarrier number estimation method and system based on statistical characteristic test, and belongs to the technical field of wireless communication, and the method comprises the following steps: segmenting OFDM received signals with different lengths, and carrying out fast Fourier transform of different points on each segmented signal to obtain a corresponding frequency domain sample set; respectively extracting a real part and an imaginary part of the frequency domain sample, respectively fitting normal distribution of the real part and the imaginary part, and calculating an empirical probability density function and a theoretical probability density function; various statistical distances between the empirical probability density function and the theoretical probability density function are calculated; and carrying out peak value detection on the change result of each statistical magnitude along with the fast Fourier transform length, and taking the fast Fourier transform point number corresponding to the peak value as the estimated subcarrier number. According to the method, the statistical distribution characteristics of the frequency domain samples of the received signals are analyzed under different FFT lengths, and characteristic judgment is carried out by utilizing various statistical distance measurement criteria, so that high-precision estimation of the number of subcarriers is realized.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of wireless communication, in particular to an OFDM subcarrier number estimation method and system based on statistical feature test, which can be used in cognitive radio, non-cooperative signal detection, electronic reconnaissance and the like scenes. BACKGROUND

[0002] Orthogonal Frequency Division Multiplexing (OFDM) technology is widely used in modern wireless communication systems due to its high spectral efficiency and anti-multipath fading capability. In non-cooperative communication scenarios such as cognitive radio or signal reconnaissance, the receiving end often lacks prior information of the transmitting end (such as subcarrier number, cyclic prefix length, modulation mode, etc.), so blind parameter estimation of the received signal is needed. Among them, the subcarrier number as a key parameter of OFDM signal, its accurate estimation is crucial for subsequent signal demodulation and identification.

[0003] In the prior art, OFDM subcarrier number estimation methods are mainly based on the autocorrelation characteristics, cyclic prefix features or frequency domain feature analysis of the signal. For example, the method based on Kolmogorov-Smirnov (KS) test estimates by comparing the difference between the empirical distribution and the theoretical distribution, but the estimation accuracy significantly decreases in low signal-to-noise ratio (SNR) environment. In addition, most of the existing methods rely on known symbol structure or pilot information, and it is difficult to accurately estimate the subcarrier number under unknown parameter conditions, which limits its applicability in completely blind signal conditions.

[0004] Therefore, there is an urgent need for an OFDM subcarrier number estimation method without prior information, low computational complexity, and still maintaining high estimation accuracy in low signal-to-noise ratio environment. SUMMARY

[0005] The present application aims to solve the problem that the OFDM signal in the prior art is difficult to accurately estimate its subcarrier number under unknown parameter conditions, and provides an OFDM subcarrier number estimation method and system based on statistical feature test, which analyzes the statistical distribution characteristics of the received signal frequency domain samples under different Fast Fourier Transform (FFT) lengths (point numbers), and uses multiple statistical distance measurement criteria for feature judgment, thereby realizing high-precision estimation of the subcarrier number.

[0006] The purpose of the present application is achieved by the following technical solutions: In a first aspect, an OFDM subcarrier number estimation method based on statistical feature test is provided, as shown in Figure 1 The method comprises the following steps: Signal generation and acquisition: generate an OFDM received signal; Frequency domain segmentation and fast Fourier transform: segmenting the OFDM received signal with different lengths, and performing fast Fourier transform on each segmented signal with different point numbers to obtain corresponding frequency domain sample sets; Statistical feature extraction: extracting the real part and the imaginary part of the frequency domain sample respectively, fitting the normal distribution of the real part and the imaginary part respectively to obtain the mean and standard deviation parameters, and calculating the empirical probability density function and the theoretical probability density function; Statistical distance calculation: calculating the statistical distance between the empirical probability density function and the theoretical probability density function; Feature peak decision and subcarrier number estimation: performing peak detection on the result of each statistical quantity varying with the fast Fourier transform length, and taking the fast Fourier transform point number corresponding to the peak as the estimated subcarrier number.

[0007] In some embodiments, the method further comprises the steps of: Performance evaluation and result output: statistically evaluating the subcarrier number estimation accuracy of each statistical index under different signal-to-noise ratios.

[0008] In some embodiments, the generating OFDM received signal specifically comprises: Building an OFDM modulator, setting the fast Fourier transform length, the cyclic prefix length, and the guard interval; Generating OFDM signal waveform through constellation mapping of random bit stream; Adding additive white Gaussian noise to the OFDM signal waveform under different signal-to-noise ratios to obtain the OFDM received signal.

[0009] In some embodiments, in the statistical feature extraction step, further comprising: After extracting the real part and the imaginary part of the frequency domain sample, the sample is subjected to centering and standardization processing.

[0010] In some embodiments, the plurality of statistical distances include Hellinger distance, total variation distance, Kullback-Leibler divergence, and Jensen-Shannon divergence.

[0011] In some embodiments, the peak detection comprises: Comparing the values of the statistical distances under different fast Fourier transform point numbers, and selecting the fast Fourier transform point number corresponding to the maximum value as the subcarrier number estimation result.

[0012] In some embodiments, the theoretical probability density function is a standard Gaussian probability density function.

[0013] The second aspect provides an OFDM subcarrier number estimation system based on statistical feature inspection, comprising: A signal generation and collection module is configured to generate an OFDM receiving signal. A frequency domain segmentation and fast Fourier transform module is configured to segment the OFDM receiving signal into segments of different lengths, and perform fast Fourier transform on each segment signal to obtain a corresponding frequency domain sample set. A statistical feature extraction module is configured to extract real and imaginary parts of the frequency domain sample, respectively, fit a normal distribution to the real and imaginary parts, respectively, obtain mean and standard deviation parameters, and calculate an empirical probability density function and a theoretical probability density function. A statistical distance calculation module is configured to calculate a plurality of statistical distances between the empirical probability density function and the theoretical probability density function. A feature peak value decision and subcarrier number estimation module is configured to perform peak value detection on the result of each statistical quantity varying with the fast Fourier transform length, and take the fast Fourier transform point number corresponding to the peak value as the estimated subcarrier number.

[0014] In some embodiments, the system further comprises: A performance evaluation and result output module is configured to statistically evaluate the subcarrier number estimation accuracy of each statistical index under different signal-to-noise ratios.

[0015] It should be further noted that the technical features corresponding to the above-mentioned option embodiments can be combined or replaced with each other to form new technical solutions without conflict.

[0016] Compared with the prior art, the present application has the following advantages: 1. No prior information is needed: The present application only relies on the statistical feature distribution of the receiving signal, without the need for known pilots, symbol structure or modulation method parameters, and is suitable for completely blind signal conditions.

[0017] 2. Low computational complexity: The present application is based on FFT transform and basic statistical distance calculation, and the algorithm is simple and easy to realize in real time in embedded devices or communication reconnaissance systems.

[0018] 3. High estimation accuracy: The present application uses multiple statistical distance joint decision, and can still maintain a high estimation accuracy in a low signal-to-noise ratio environment (such as 0 dB), which is significantly better than the OFDM subcarrier number estimation method based on KS distance.

[0019] 4. Wide applicability: It can be applied to cognitive radio, non-cooperative signal detection, electronic reconnaissance and other scenarios, and provides key parameter support for OFDM signal recognition and demodulation.

[0020] 5. Strong robustness: The present application uses multiple statistical quantity fusion decision to improve the stability and reliability of the estimation, and is suitable for complex channel environments. BRIEF DESCRIPTION OF DRAWINGS

[0021] Figure 1 A flow chart of an OFDM subcarrier number estimation method based on statistical characteristic inspection according to the present application; Figure 2 An IDFT schematic diagram of a receiving end according to the present application; Figure 3 A TV distance schematic diagram of an empirical probability density function and a theoretical probability density function under different FFT point numbers of a transceiving end according to the present application; Figure 4 An EPDF and PDF comparison schematic diagram when the FFT point number is 64 according to the present application; Figure 5 A comparison schematic diagram of different statistical quantity estimations of OFDM subcarrier numbers according to the present application; Figure 6 A system work flow chart of an OFDM subcarrier number estimation method based on statistical characteristic inspection according to the present application. DETAILED DESCRIPTION

[0022] The technical solutions of the present application will be described clearly and completely below in conjunction with the accompanying drawings. Obviously, the described embodiments are only some of the embodiments of the present application, rather than all the embodiments. The components of the embodiments of the present application described and shown in the accompanying drawings can be arranged and designed in various different configurations. Based on the embodiments in the present application, all the other embodiments obtained by those skilled in the art without creative efforts belong to the scope of protection of the present application.

[0023] It should be noted that the defects of the above prior art solutions are the results obtained by the inventors after practice and careful study. Therefore, the discovery process of the above problems and the solutions proposed by the embodiments of the present application to the above problems should be the contributions made by the inventors to the present application, and should not be understood as the technical content known to those skilled in the art.

[0024] In view of the technical problems pointed out in the background art, the embodiments provided by the present application are as follows: In an exemplary embodiment, an OFDM subcarrier number estimation method based on statistical characteristic inspection is provided, comprising the following steps: (1) Signal generation and collection An OFDM modulator is constructed, and parameters such as FFT length, cyclic prefix length, guard interval, etc. are set. An OFDM signal waveform is generated after random bit stream is mapped through a constellation. The waveform is added with additive white Gaussian noise (AWGN) under different signal-to-noise ratio (SNR) conditions to obtain a received signal.

[0025] (2) Frequency domain segmentation and fast Fourier transform The received signal is segmented into segments of different lengths; Perform Fast Fourier Transform (FFT) on each segment of the signal with different numbers of points (lengths) to obtain the corresponding frequency domain sample set.

[0026] (3) Statistical feature extraction The real and imaginary parts of the frequency domain samples are extracted separately, and the samples are then centered and standardized. Normal distributions are fitted to the real and imaginary samples respectively to obtain their mean and standard deviation parameters; The empirical probability density (EPDF) and theoretical distribution function (PDF) are calculated based on the fitted distribution.

[0027] (4) Statistical distance calculation Calculate various statistical distances between EPDF and PDF, including: Hellinger distance; Total Variation (TV) distance; Kullback–Leibler divergence (KL divergence); Jensen–Shannon divergence (JS divergence).

[0028] (5) Characteristic peak decision and subcarrier number estimation Peak detection is performed on the results of each statistic changing with the FFT length; The FFT length corresponding to the maximum value of the statistical distance curve is taken as the estimated number of subcarriers; The estimation accuracy of different methods was statistically analyzed after multiple experiments.

[0029] (6) Performance evaluation and result output The accuracy of subcarrier number estimation for various statistical indicators of the design under different signal-to-noise ratios was statistically analyzed. Output the estimation accuracy curves for different statistical methods to evaluate the algorithm performance.

[0030] Specifically, the principle behind this method is as follows: Assume the number of IDFT points of the OFDM signal at the transmitting end is . The number of DFT points at the receiving end is , If the number is positive, the expression for the transmitting signal is: (1) in, It is the first The symbol of the first The output of each IDFT, It is the first The first symbol Each constellation mapping symbol, at the receiving end, is processed... Point DFT yields the signal: (2) According to formula (2), if the number of DFT points at the receiver is greater than the number of transform points at the transmitter, a single DFT transform at the receiver will contain multiple OFDM symbols, such as... Figure 2 As shown.

[0031] Case 1: If It is a positive integer, and Equation (2) can be simplified to: (3) That is, at this time The DFT output of the point is The sum of the constellation mapping symbols, after estimating the number of OFDM subcarriers, is generally... The value will not be particularly large. The distribution exhibits non-Gaussianity.

[0032] Scenario 2: If If it is not an integer, then... (4) Substituting formula (4) into formula (2), we get: (5) therefore When the value is not an integer, then the output of the receiving end... It is the sum of the constellation mapping symbols within an OFDM symbol and the constellation mapping symbols of the OFDM symbol at each point, and the sum of multiple independent and identically distributed random variables exhibits Gaussianity.

[0033] set up It is the overall A set of sample observations, sorted from smallest to largest as follows: , Let be any real number, then the function is called: (6) Let be the empirical distribution function, whose graph is a step curve for any real number . , The value is equal to the sample observations that do not exceed The frequency. With the number of sample observations... The increase, Approximately close to the total Distribution function For any real number ,when hour It converges to with probability 1 That is, (7) Kolmogorov-Smirnov test is used to determine whether the empirical distribution of a sample conforms to a certain theoretical distribution, after receiving a group of signal samples, ordering them from small to large, constructing KS test statistics (8) Wherein, is the empirical distribution function of the signal sample, is the parameter estimation vector of the signal sample is Theoretical distribution, assuming that the signal theoretical distribution is normal distribution, the parameter estimation vector is the sample mean and standard deviation, that is At this time, by calculating the maximum distance between And Compare with the critical value of normal distribution, reject or accept the original hypothesis at the significance level

[0034] On this basis, the KS distance is used to estimate the OFDM subcarrier number, the OFDM receiving signal is subjected to DFT of different point numbers, the output is obtained, and the KS test is performed on the output, so that the value of the KS test statistics is the subcarrier number of the OFDM signal.

[0035] On this basis, the present application proposes an OFDM subcarrier number verification method based on probability density fitting, the amplitude of I / Q component is subjected to probability density fitting to obtain an empirical probability density function , compare it with the theoretical probability density function of the signal sample parameter estimation vector Since the I / Q component has been preprocessed, here That is (9) By calculating the statistical distance between the empirical probability density and the unit Gaussian probability density, the FFT point number that makes the statistical distance maximum is the estimated OFDM subcarrier number. Several statistical distance definitions used are as follows: Hellinger distance: (10) TV distance: (11) KL divergence: (12) JS divergence: (13) ​ (14) where is the value of the standard Gaussian probability density at is the value of the empirical distribution at

[0036] The advantages of the present application can be illustrated by the following simulation performance: 1. OFDM subcarrier number estimation using TV distance (1a) Simulation conditions and contents The simulation OFDM signal subcarrier number is 64, the cyclic prefix length is 64, the constellation mapping used is 4QAM, the OFDM symbol number used for OFDM subcarrier number estimation is 1, the signal-to-noise ratio SNR = 15 dB, and the preset FFT point number range is 50-200.

[0037] The OFDM subcarrier number is estimated according to the method described in step (4), and the estimation accuracy is used to measure the estimation performance under the AWGN channel.

[0038] (1b) Simulation results The statistical distance used is the TV distance, and the TV distance under different FFT point numbers is as follows: Figure 3 The maximum value is obtained when the FFT point number is 64, that is, the accurate OFDM subcarrier number estimation is obtained. Figure 4 is the EPDF and PDF when the FFT point number is 64.

[0039] 2. Comparison of OFDM subcarrier number estimation performance under different statistical distances (2a) Simulation conditions and contents The simulation OFDM signal subcarrier number is 64, the cyclic prefix length is 64, the constellation mapping used is 4QAM, the OFDM symbol number used for OFDM subcarrier number estimation is 10, the signal-to-noise ratio SNR = 0-10 dB, the preset FFT point number range is 50-200, and the Monte Carlo simulation number is 100.

[0040] (2b) Simulation results The OFDM subcarrier number estimation accuracy of each statistical distance under the AWGN channel is shown in the following figure: Figure 5 From the simulation results of Figure 5 It can be seen from the simulation results that the OFDM subcarrier number estimation accuracy of the method using the TV distance is much higher than that of the OFDM subcarrier number estimation method using the KS distance under low signal-to-noise ratio, and the estimation accuracy is 56% at 0 dB, and the estimation accuracy is above 95% when the signal-to-noise ratio is higher than 2 dB.

[0041] ​​Based on the inventive concept of the above method, in another exemplary embodiment, an OFDM subcarrier number estimation system based on statistical characteristic tests is provided, comprising: The signal generation and acquisition module is used to generate OFDM received signals; The frequency domain segmentation and fast Fourier transform module is used to segment the OFDM received signal into segments of different lengths and perform fast Fourier transforms on each segment with different numbers of points to obtain the corresponding frequency domain sample set. The statistical feature extraction module is used to extract the real and imaginary parts of the frequency domain samples respectively, fit normal distributions to the real and imaginary parts respectively, obtain their mean and standard deviation parameters, and calculate the empirical probability density function and the theoretical probability density function. The statistical distance calculation module is used to calculate various statistical distances between the empirical probability density function and the theoretical probability density function. The characteristic peak decision and subcarrier number estimation module is used to perform peak detection on the results of each statistic as the length of the Fast Fourier Transform changes, and use the number of Fast Fourier Transform points corresponding to the peak as the estimated number of subcarriers.

[0042] like Figure 6 As shown, the system's workflow mainly includes OFDM signal generation and OFDM subcarrier number estimation. OFDM signal generation is performed by the signal generation and acquisition module, which sequentially performs bitstream generation, constellation mapping, serial-to-parallel conversion, IFFT, adding a cyclic prefix, signal windowing, and parallel-to-serial conversion. Then, at the receiving end, the OFDM signal after passing through the AWGN channel is received. The frequency domain segmentation and Fast Fourier Transform module performs serial-to-parallel conversion on the signal, performs FFT on the signal with different numbers of points within a preset range, and extracts the IQ components of the FFT-enhanced signal. The statistical feature extraction module performs preprocessing on the IQ components, such as mean removal and normalization, and fits the probability density of the IQ components to a standard Gaussian distribution. The statistical distance calculation module calculates the statistical distance between the fitted PDF and the standard Gaussian probability density under different FFT point numbers. The feature peak decision and subcarrier number estimation module performs peak detection to obtain the number of FFT points that maximizes the statistical distance between the fitted PDF and the standard Gaussian probability density, i.e., the OFDM subcarrier number.

[0043] The above detailed embodiments are a description of the present invention. It should not be considered that the specific embodiments of the present invention are limited to these descriptions. For those skilled in the art, several simple deductions and substitutions can be made without departing from the concept of the present invention, and all of these should be considered to fall within the protection scope of the present invention.

Claims

1. A method for estimating the number of OFDM subcarriers based on statistical characteristic tests, characterized in that, Includes the following steps: Signal generation and acquisition: Generate OFDM received signals; Frequency domain segmentation and fast Fourier transform: The OFDM received signal is segmented into segments of different lengths, and fast Fourier transforms with different numbers of points are performed on each segment to obtain the corresponding frequency domain sample set. Statistical feature extraction: Extract the real and imaginary parts of the frequency domain samples respectively, fit normal distributions to the real and imaginary parts respectively, obtain their mean and standard deviation parameters, and calculate the empirical probability density function and the theoretical probability density function; Statistical distance calculation: Calculate various statistical distances between the empirical probability density function and the theoretical probability density function; Characteristic peak decision and subcarrier number estimation: Peak detection is performed on the results of each statistic as the length of the Fast Fourier Transform, and the number of Fast Fourier Transform points corresponding to the peak is used as the estimated number of subcarriers.

2. The OFDM subcarrier number estimation method based on statistical characteristic tests according to claim 1, characterized in that, It also includes the following steps: Performance evaluation and results output: Statistical analysis of subcarrier number estimation accuracy for various statistical indicators under different signal-to-noise ratios.

3. The OFDM subcarrier number estimation method based on statistical characteristic tests according to claim 1, characterized in that, The generation of the OFDM received signal specifically includes: Construct an OFDM modulator and set the fast Fourier transform length, cyclic prefix length, and guard interval; OFDM signal waveforms are generated by mapping a random bit stream through a constellation. Additive white Gaussian noise is added to the OFDM signal waveform under different signal-to-noise ratio conditions to obtain the OFDM received signal.

4. The OFDM subcarrier number estimation method based on statistical characteristic tests according to claim 1, characterized in that, The statistical feature extraction step also includes: After extracting the real and imaginary parts of the frequency domain samples, the samples are decentered and standardized.

5. The OFDM subcarrier number estimation method based on statistical characteristic tests according to claim 1, characterized in that, The various statistical distances include Hellinger distance, total variation distance, Kullback-Leibler divergence, and Jensen-Shannon divergence.

6. The OFDM subcarrier number estimation method based on statistical characteristic tests according to claim 1, characterized in that, The peak detection includes: Compare the statistical distance values ​​under different numbers of Fast Fourier Transform (FFT) points, and select the FFT point number corresponding to the maximum value as the subcarrier number estimation result.

7. The OFDM subcarrier number estimation method based on statistical characteristic tests according to claim 1, characterized in that, The theoretical probability density function is a standard Gaussian probability density function.

8. An OFDM subcarrier number estimation system based on statistical characteristic tests, characterized in that, include: The signal generation and acquisition module is used to generate OFDM received signals; The frequency domain segmentation and fast Fourier transform module is used to segment the OFDM received signal into segments of different lengths and perform fast Fourier transforms on each segment with different numbers of points to obtain the corresponding frequency domain sample set. The statistical feature extraction module is used to extract the real and imaginary parts of the frequency domain samples respectively, fit normal distributions to the real and imaginary parts respectively, obtain their mean and standard deviation parameters, and calculate the empirical probability density function and the theoretical probability density function. The statistical distance calculation module is used to calculate various statistical distances between the empirical probability density function and the theoretical probability density function. The characteristic peak decision and subcarrier number estimation module is used to perform peak detection on the results of each statistic as the length of the Fast Fourier Transform changes, and use the number of Fast Fourier Transform points corresponding to the peak as the estimated number of subcarriers.

9. The OFDM subcarrier number estimation system based on statistical characteristic test according to claim 8, characterized in that, Also includes: The performance evaluation and result output module is used to calculate the subcarrier number estimation accuracy of various statistical indicators under different signal-to-noise ratios.

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