A glrt-based loRa signal detection method

Abstract

This invention belongs to the field of non-cooperative signal detection technology, specifically relating to a LoRa signal detection method based on GLRT. Based on the principle of GLRT testing and the LoRa preamble signal, this invention determines the detector model for this method and establishes a local template signal library based on prior conditions. Under the null hypothesis, the distribution of the test statistic is statistically analyzed, and the false alarm rate of the detector is determined, thus establishing the test threshold. The received signal is then processed to obtain the observed signal used for testing. If the test statistic of the observed signal is greater than the set threshold, a LoRa signal is detected; otherwise, no LoRa signal is detected. Finally, Monte Carlo simulation analysis is used to analyze the change of the test rate with signal-to-noise ratio under different conditions with a 0.1% false alarm rate. This method can achieve relatively good LoRa signal detection.

Description

Technical Field

[0001] This invention belongs to the field of non-cooperative signal detection, specifically relating to a LoRa signal detection method based on GLRT. Background Technology

[0002] LoRa signal refers to the signal type that can be used for long-distance communication by using spread spectrum technology in LoRa communication technology. Its main modulation method is frequency shift chirp modulation (FSCM) technology, which is a modulation method based on linear frequency modulation technology.

[0003] LoRa preamble symbols are commonly used for verification and synchronization at the receiver. Their main function is to help the receiver complete signal detection, timing synchronization, and frequency synchronization at the beginning of communication. A single LoRa preamble symbol in the baseband... The signal expression is shown in equation (1).

[0004] (1)

[0005] in, The signal amplitude, The initial phase of the signal, For signal bandwidth parameters, For signal spreading factor parameters, The imaginary unit, The duration of the signal. A schematic diagram of the time-domain waveform of a single LoRa preamble symbol in baseband is shown below. Figure 1 As shown. Signal duration Spreading factor and bandwidth The decision is made, and the expression is shown in equation (2).

[0006] (2)

[0007] As shown in equation (1), the LoRa preamble symbol is determined by parameters such as spreading factor, bandwidth, amplitude, and initial phase, and its signal form has a clear mathematical expression. Therefore, when the signal structure is known but some parameters are unknown, it can be described by a parameterized model.

[0008] The Generalized Likelihood Ratio Test (GLRT) is a statistical test method commonly used to detect signals with a defined structure but some unknown parameters. Its basic principle is to construct two hypotheses within the hypothesis testing framework: the null hypothesis and the zero hypothesis. This indicates that the observed signal contains only noise, while the alternative hypothesis... This indicates that the observed signal contains both the target signal and noise. When some parameters in the signal are unknown, GLRT constructs a generalized likelihood ratio statistic by performing maximum likelihood estimation on these unknown parameters and replacing them with parameter values ​​that maximize the likelihood function. Specifically, GLRT calculates the likelihood ratio statistic in the signal. and The ratio of the likelihood function of the observed data under the given conditions is compared with a set detection threshold: if the ratio is greater than the threshold, the signal is determined to exist; otherwise, it is determined to be noise.

[0009] Because the LoRa preamble signal has a known structural form, but its parameters (such as...) , In practical detection scenarios, parameters such as the signal structure information (e.g., the preamble) are often unknown. Therefore, the GLRT method can be used to search for or estimate these parameters and construct corresponding test statistics to achieve effective detection of LoRa preamble signals. This method can fully utilize signal structure information under unknown parameter conditions, improving the reliability and accuracy of detection. Summary of the Invention

[0010] To address the aforementioned problems, this invention provides a method for detecting preamble symbols in non-cooperative LoRa signals using GLRT.

[0011] The technical solution adopted in this invention is:

[0012] The GLRT method was used to detect non-cooperative LoRa signals, and the detection performance of the detector was evaluated through Monte Carlo simulation experiments at different signal-to-noise ratios.

[0013] Specifically, the following steps are included:

[0014] S1. Establish a GLRT checker model for LoRa preamble symbols and generate a local template signal library.

[0015] The LoRa preamble symbol can be regarded as a deterministic signal with unknown parameters. A checker model is constructed based on the GLRT check principle and the LoRa preamble symbol signal expression.

[0016] S2. Generate a local template signal library required for GLRT testing based on prior conditions.

[0017] S3, in Under the given conditions, statistical analysis of GLRT test values ​​and determination of detection thresholds were performed.

[0018] Will The noise signal under the given conditions is substituted into the GLRT test metric, and statistical analysis is performed using Monte Carlo simulation experiments. The distribution of test quantities under certain conditions is determined, and the GLRT test threshold is determined based on the false alarm rate.

[0019] S4. Process the received signal to obtain the observation signal of the GLRT tester.

[0020] If the received signal contains an RF LoRa data packet, down-converting it will yield a baseband LoRa data packet. The LoRa data packet header contains several repeated LoRa preamble symbols, which the GLRT detector will then detect as LoRa signals.

[0021] S5. Calculate the test value for the observed signal and determine whether a LoRa signal is detected based on the threshold.

[0022] Perform a GLRT test on the observed signal obtained in step three. Compare the GLRT test result with the threshold set in step two. If the test result is greater than the threshold, it is determined that a LoRa signal has been detected; otherwise, a LoRa signal has not been detected.

[0023] The beneficial effect of this invention is that, under certain conditions, this method can effectively detect LoRa signals. This method can make full use of signal structure information under unknown parameter conditions, thereby improving the reliability and accuracy of detection. Attached Figure Description

[0024] Figure 1 Time-domain waveform of LoRa preamble symbol;

[0025] Figure 2 Solution flowchart;

[0026] Figure 3 Distribution of GLRT test cases under the null hypothesis;

[0027] Figure 4 The test rate of the GLRT tester varies with the signal-to-noise ratio. Detailed Implementation

[0028] The technical principles and solutions of this invention are described in detail below with reference to the accompanying drawings and simulation examples:

[0029] The proposed solution involves establishing a GLRT detector model for LoRa preamble symbols, pre-generating a local template signal library, and defining the detector threshold under noise conditions. Subsequently, the received and processed observation signal is tested, and the relationship between the test result and the threshold is used to determine whether a LoRa signal has been detected. The solution process is as follows: Figure 2 As shown, the specific method of the present invention is as follows:

[0030] S1. Establish a GLRT checker model for LoRa preamble symbols and generate a local template signal library.

[0031] First, a checker model for the LoRa preamble symbol is established based on the GLRT check theory. Then, according to the LoRa preamble symbol expression (1), the receiver uses a sampling rate of... The discrete expression after sampling is shown in equation (3).

[0032] (3)

[0033] in, Under complex Gaussian white noise conditions, the signal expression observed by the detector is shown in equation (4).

[0034] (4)

[0035] in, , Let Variance be the variance of the complex Gaussian white noise. Let the amplitude... and phase As mentioned earlier, equation (4) can be written in vector form as shown in equation (5).

[0036] (5)

[0037] in, and All Vector. Define unknown parameters. ,in , .

[0038] Therefore, the equivalent parameter test of a single LoRa preamble symbol of the baseband is shown in Equation (6).

[0039] (6)

[0040] Under the complex Gaussian noise assumption, the observation vector is subject to two assumptions: the null hypothesis and the zero hypothesis. and alternative hypotheses The likelihood functions are shown in equations (7) and (8), respectively.

[0041] (7)

[0042] (8)

[0043] amplitude and phase The maximum likelihood estimates are shown in equations (9) and (10).

[0044] (9)

[0045] (10)

[0046] The GLRT test statistic for the LoRa preamble symbol is shown in equation (11).

[0047] (11)

[0048] As can be seen from the above formula, GLRT testing of LoRa signals requires a reasonable... The search is performed within the parameter space, and the maximum value of the corresponding test statistic is taken.

[0049] S2, based on The prior conditions of the parameters generate the template signal vector. Specifically, different values ​​are substituted into equation (12). parameter.

[0050] (12)

[0051] S3, in Under these conditions, statistical analysis of the test statistic based on GLRT was conducted, and the detection threshold was determined.

[0052] exist The observed signal under the given conditions contains only noise. Substituting into equation (11) yields Inspection quantity under the condition As shown in equation (13).

[0053] (13)

[0054] Calculations were performed using Monte Carlo simulation experiments. and statistics The distribution of the false alarm rate is determined, and the GLRT test threshold is determined based on the false alarm rate. False alarm rate and threshold The relationship is shown in equation (14).

[0055] (14)

[0056] S4. Process the received signal to obtain the observed signal vector of the input detector. .

[0057] The received signal is down-converted to obtain the baseband signal. If the received signal contains RF LoRa data packets, down-converting it will yield the baseband LoRa data packets. If the LoRa data packet header contains several repeated LoRa preamble symbols, the GLRT checker can calculate the checksum and determine the presence of a LoRa signal in the received signal based on a threshold; this is called LoRa signal detection.

[0058] S5. Calculate the GLRT test value under the observed signal conditions, and determine whether LoRa signal is detected based on the threshold.

[0059] The observation signal vector obtained in step three Performing the GLRT test yields the following results: The GLRT test quantile under the given conditions is shown in Equation (15).

[0060] (15)

[0061] in This is the conjugate transpose of the local template signal vector generated in step one.

[0062] And compare the GLRT test quantity with the threshold defined in step two. The comparison is performed. If the test value is greater than the threshold, the LoRa signal is detected; otherwise, the LoRa signal is not detected.

[0063] The performance of this invention is tested and described in detail using simulation examples:

[0064] The LoRa signal parameters selected for simulation were: bandwidth 500kHz, spreading factor 9, amplitude 1, initial phase 0, and signal sampling rate 2MHz. The search range of the bandwidth (BW) parameter of the local template signal was set to 50kHz to 2MHz with an accuracy of 10kHz, and the search range of the spreading factor (SF) parameter was set to 4 to 12 with an accuracy of 1. 1764 local template signals were generated according to these parameters.

[0065] Under the null hypothesis The simulation was performed using randomly generated additive white Gaussian noise with unit variance, running 20,000 Monte Carlo experiments. The final simulation results of the statistical test are as follows: Figure 3 As shown.

[0066] The false alarm rate for the GLRT test is set at 0.1%. Figure 3 The threshold corresponding to a false alarm rate of 0.1% is plotted in the figure, with a threshold value of 13.7.

[0067] Alternative hypotheses at different signal-to-noise ratios Under the given conditions, Monte Carlo experiments were conducted 5000 times, with a signal-to-noise ratio (SNR) range of -30 dB to -10 dB and a precision of 1 dB. For each SNR condition, the number of times the test case exceeded the threshold was counted, and the percentage of times exceeding the threshold out of the total number of counts was calculated as the test rate for that SNR condition. The curve showing the test rate of the GLRT tester as a function of SNR with a false alarm rate of 0.1% is shown below. Figure 4 As shown.

[0068] As can be seen from the figure, from -25dB to -17dB, the success rate increases continuously with the increase of signal-to-noise ratio; after the signal-to-noise ratio is greater than -16dB, the success rate is 1.

[0069] In summary, the detection method proposed in this invention is effective.

Claims

1. A LoRa signal detection method based on GLRT, using a single LoRa preamble symbol in the baseband. The signal expression is: ， in, The signal amplitude, The initial phase of the signal, For signal bandwidth parameters, For signal spreading factor parameters, The imaginary unit, The duration of the signal; characterized in that the method includes: S1. Establish a detector model for GLRT to check the LoRa preamble symbol. Under complex Gaussian white noise conditions, the signal expression observed by the detector is set as follows: ， in, The receiver uses a sampling rate It is obtained by sampling a single LoRa preamble symbol. , Let Variance be the variance of complex Gaussian white noise. Writing it in vector form, we get: ， in, and The corresponding parameters are in vector form, all of which are vector; Define the unknown parameter as ,in , The equivalent parameter check formula for a single LoRa preamble symbol in the baseband is: ， Observation vector under the null hypothesis and alternative hypotheses The likelihood functions are as follows: ， ， in, Indicates the presence of unknown parameters and of vector; The GLRT test statistic for the LoRa preamble symbol is obtained as follows: ； S2. Construct based on requirements Prior conditions for parameters, generating template signal vectors : ； S3, in Under the condition, Substitution From Inspection quantity under the condition : ， Calculations were performed using Monte Carlo simulation experiments. and statistics The distribution of the false alarm rate is used to determine the GLRT test threshold. and threshold The relation is: ； S4. Process the received signal to obtain the observation signal vector of the GLRT tester. ; S5. Calculate the GLRT test value under the observed signal conditions, and determine whether a LoRa signal is detected based on the threshold, specifically: The observation signal vector obtained in S4 Performing the GLRT test yields the following results: GLRT test quantifier under the given conditions: ， in This is the conjugate transpose of the template signal vector generated in S2; The test value of GLRT is compared with the threshold defined in S3. The comparison is performed. If the test value is greater than the threshold, the LoRa signal is detected; otherwise, the LoRa signal is not detected.

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