A LoRa signal blind estimation method based on linear frequency modulation characteristics

Abstract

The present invention belongs to the technical field of signal detection and estimation, and more specifically relates to a method for blindly estimating LoRa signals based on linear frequency modulation characteristics. The method of the present invention mainly uses the carrier frequency to down-convert the intercepted LoRa signal, utilizes the linear spread spectrum modulation characteristics of the LoRa signal to estimate the frequency modulation slope parameters of the LoRa signal, and uses the estimated parameters to further estimate the remaining parameters of the signal. Finally, by limiting the parameters of the LoRa signal, a more accurate estimate is obtained, thereby achieving the purpose of blindly estimating the LoRa signal parameters.

Description

Technical Field

[0001] The present invention belongs to the technical field of signal detection and estimation, and in particular relates to a LoRa signal blind estimation method based on linear frequency modulation characteristics. Background Art

[0002] With the advent of the Internet of Everything (IoE) concept, the networking of smart devices has become a major focus. Currently, IoT technologies are primarily categorized into two types. Short-range communication technologies, such as Wi-Fi, Bluetooth, and ZigBee, are limited in range and power consumption, making them unsuitable for industrial and agricultural applications requiring large-scale deployment and low-cost maintenance. Therefore, to address the challenges encountered in the development of the IoT, Low Power Wide Area Network (LPWAN) technology has gradually gained traction.

[0003] LoRa is a type of low-power wide area network (LPWAN) communication technology. Currently, major LPWAN technologies include LoRa, SigFox, LTE, Cat-m, and NB-IoT. Compared to other LPWAN technologies, LoRa offers not only low cost and flexible deployment, but also excellent Doppler immunity. More importantly, LoRa can flexibly adjust transmission distance, receiver sensitivity, and transmission rate by increasing or decreasing the spreading factor (SF). Precisely because of these advantages, LoRa has gradually gained attention and has become one of the most promising and popular LPWAN technologies.

[0004] LoRa signal refers to the signal type that can be used for long-distance communication 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 spread spectrum technology. The curve of its frequency change over time is shown in the figure below. Each code element in LoRa modulation can be expressed as a sinusoidal signal, f c is the center frequency of the frequency range swept by the center signal, BW is the signal bandwidth, and the frequency band range is [f c -BW / 2,f c +BW / 2], the LoRa symbol duration is T s , starting from a certain initial frequency in the frequency range and rising to the highest frequency f c +BW / 2, then falls back to the lowest frequency f c -BW / 2, continues to rise until the duration of the symbol T s So in a T s Within the time, the frequency of the LoRa code element will definitely sweep the entire frequency band range, such as Figure 1shown.

[0005] For a typical single code element baseband signal of a LoRa signal, the model expression of the signal s(t) is shown in formula (1).

[0006]

[0007] where f init is the starting frequency of the LoRa signal, t1 is the time of frequency hopping, k is the frequency modulation slope of the signal, is the instantaneous phase of the signal, t is the time scale, and e is the natural base.

[0008] The LoRa signal obtains the gain effect of the spread spectrum signal through linear spread spectrum modulation. According to the Shannon formula given by formula (2), it can be obtained that when the channel capacity is certain, increasing the bandwidth can achieve the effect of working under lower signal-to-noise ratio conditions. In the case of LoRa signals, since the maximum spread spectrum factor can reach 2 12 , that is, a spread spectrum gain of 36dB, which enables the LoRa signal to operate at a signal-to-noise ratio below -10dB under special circumstances, which makes general detection and estimation of the LoRa signal difficult to achieve.

[0009]

[0010] Where C is the channel capacity, B is the signal bandwidth, and S / N is the signal-to-noise ratio.

[0011] Figure 2 The power spectrum of the LoRa signal under the condition of -10dB signal-to-noise ratio, which can work normally, is given. It can be seen that the signal has been completely submerged in the noise. It can be seen that it is difficult to detect and estimate the LoRa signal under this signal-to-noise ratio condition using traditional means. Summary of the Invention

[0012] In response to the above problems, the present invention proposes a blind estimation method for LoRa signals based on linear frequency modulation characteristics.

[0013] The technical solution of the present invention is:

[0014] A blind estimation method for LoRa signals based on linear frequency modulation characteristics includes the following steps:

[0015] S1. Down-convert the signal received by the receiver to baseband.

[0016] S2. Multiply the baseband signal by its own time-shifted conjugate signal.

[0017] S3. Obtain the peak position through Fourier transform, and calculate the estimated value of the frequency modulation slope k.

[0018] S4. Use the calculated frequency modulation slope value to generate an LFM signal with a decreasing slope. Use the LFM signal to convolve with it to obtain the peak interval. Use this data to estimate the bandwidth of the LoRa signal, and make a relatively accurate estimate by using the spreading factor, which is only an exponential multiple of 2.

[0019] The beneficial effect of the present invention is that the method of the present invention mainly uses the carrier frequency to down-convert the intercepted LoRa signal, uses the characteristics of the linear spread spectrum modulation of the LoRa signal to estimate the frequency modulation slope parameters of the LoRa signal, uses the estimated parameters to further estimate the remaining parameters of the signal, and finally obtains a more accurate estimation value by limiting the parameters of the LoRa signal, thereby achieving the purpose of blind estimation of the LoRa signal parameters. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 This is the time-frequency characteristic diagram of LoRa signal.

[0021] Figure 2 This is the power spectrum density diagram of the LoRa signal under the condition of -10dB signal-to-noise ratio.

[0022] Figure 3 This is the flow chart of blind detection and estimation of LoRa signal parameters.

[0023] Figure 4 This is the LoRa signal detection effect diagram.

[0024] Figure 5 This is the RRMSE effect diagram for LoRa signal parameter estimation. DETAILED DESCRIPTION

[0025] The technical principles and solutions of the present invention are described in detail below with reference to the accompanying drawings and simulation examples:

[0026] The present invention is divided into four parts, namely signal down-conversion, signal time-shift conjugate multiplication, frequency modulation slope acquisition, and signal bandwidth estimation. Figure 3 As shown, the specific method of the present invention is:

[0027] S1, the original signal received by the receiver is used Down-convert and down-sample, the down-conversion method is shown in formula (3).

[0028]

[0029] where s s (t) is the original signal received, f c is the signal carrier frequency.

[0030] The downsampling method is to extract the original high sampling rate signal, and obtain a signal with a lower sampling rate by evenly extracting the locations in the original signal, so as to make the calculation rate of the method faster.

[0031] S2, the LoRa signal s(t) after down-conversion is shown in formula (4).

[0032]

[0033] Where BW is the signal bandwidth, f init is the starting frequency of the LoRa signal, t1 is the time of frequency hopping, T s is the duration of a single symbol of the signal, k is the frequency modulation slope of the signal, is the instantaneous phase of the signal.

[0034] The original LoRa signal received by the receiver is time-shifted and conjugated to obtain the time-shifted conjugated LoRa signal s T The expression of (t) is shown in formula (5).

[0035]

[0036] Where T is the length of the time shift.

[0037] Multiply the two to get the processed signal s t (t) is shown in formula (6).

[0038]

[0039] S2, the processed signal s t (t) is subjected to Fourier transform, and the spectrum expression obtained by the transformation is shown in formula (7).

[0040] S(ω)=A1δ(ω-kT)+A2δ(ω-(kT-BW))+A3δ(ω)(7)

[0041] Where δ is the impulse function, A1 is the spectrum amplitude of the upper half of equation (5), A2 is the spectrum amplitude of the lower half of equation (5), and A3 is s t The amplitude of the time-independent component in (t) is removed by removing the DC component in subsequent processing to avoid interference from this part on the result.

[0042] The largest component in equation (7) is the spectrum line at kT. By finding the peak position, the frequency modulation slope information of the original LoRa signal can be obtained. The size of this peak can be increased by increasing the time length of the received original LoRa signal, while the time-shifted conjugate multiplication result of the Gaussian white noise itself is still Gaussian white noise. At the same time, the increase in time length does not change the variance of its Gaussian distribution, which makes the main components of the accumulation all signal components that support parameter estimation, thereby achieving parameter estimation under low signal-to-noise ratio conditions.

[0043] S4. Generate an LFM signal with a decreasing slope using the estimated frequency modulation slope parameter. The expression of this signal is shown in formula (8).

[0044]

[0045] Where f0 is the center frequency of the signal, which can be set to 0 here.

[0046] Convolve the LFM signal with the down-converted LoRa signal to obtain the processed signal as shown in formula (9).

[0047] s c =s(t)*s L (t) = T s Sa(πkT s t)(9)

[0048] This envelope is approximately a Sinque function (Sa), with a pulse width (zero-point spacing) of 2 / B and a peak at the end of each rising FM slope signal.

[0049] Equation (9) only gives the result for a single symbol. For multiple symbols, multiple peaks are obtained, separated by distances between 0 and two symbols. By calculating the mean of the peaks, a rough estimate of the length of a single symbol can be obtained. The formula for calculating the signal bandwidth and symbol length is shown in Equation (10).

[0050]

[0051] 2 of them SF SF is the spreading factor, which is generally an integer between 5 and 12.

[0052] Since the spreading factor of the LoRa signal is only an exponential multiple of 2, the calculation formulas for the spreading factor, signal frequency modulation slope, and signal bandwidth are shown in formula (11).

[0053]

[0054] By using these two equations and the limitation of the spreading factor, a more accurate estimation of the signal bandwidth can be obtained.

[0055] From this, we can get the estimated values ​​of the bandwidth, spreading factor, and frequency modulation slope of the LoRa signal.

[0056] Simulation Example

[0057] In terms of detection performance, the detection probability was obtained through 1000 Monte Carlo experiments as a basis for judgment. Half of the theoretical peak value was selected for the setting of the detection threshold. When the number of peaks is more than one, it is considered a false alarm and is not counted in the number of successful detections. The original LoRa signal parameters selected in the experiment are BW=500kHz, SF=6, signal carrier frequency fc=915MHz, signal sampling rate of 40MHz, and sampling rate fs=1MHz after downsampling. According to the code value, it is divided into two cases: code signal with all 0s and code signal with random values. The time-shifted conjugate multiplication method with different accumulation lengths is tested against the traditional energy detection method. The threshold in energy detection is calculated based on the false alarm probability of 1%. The experimental results are as follows under different signal-to-noise ratio conditions: Figure 4 shown.

[0058] Depend on Figure 4 It can be seen that when the accumulation length is long enough, a high detection probability can still be obtained under extremely low signal-to-noise ratio conditions. At the same time, the detection performance of general random code element signals and special 0 code element signals is not much different. However, the detection performance of traditional methods drops sharply under conditions of signal-to-noise ratio below 0dB, and is only close to the time-shifted conjugate multiplication method with 10 code element accumulation. At the same time, the energy detection method is difficult to obtain the parameters of the original LoRa signal, while the time-shifted conjugate multiplication method can estimate the signal parameters while detecting.

[0059] In terms of the effect of parameter estimation, the relative root mean square error (RRMSE) of the signal frequency modulation slope estimation is obtained through 1000 Monte Carlo experiments to judge the performance of parameter estimation. The calculation formula of RRMSE is shown in formula (12).

[0060]

[0061] where y i is the true value of the ith experiment, is the estimated value of the ith experiment, m is the total number of experiments, is the average value of the actual experimental value.

[0062] Since the bandwidth estimation accuracy depends entirely on the estimation accuracy of the FM slope, it is only necessary to obtain the estimation effect of the signal FM slope to determine the bandwidth estimation effect. The original LoRa signal parameters selected in the experiment are BW = 500kHz, SF = 7, signal carrier frequency fc = 915MHz, signal sampling rate 40MHz, sampling rate after downsampling fs = 1MHz, and code element signal is a random code element. The RRMSE curves for different signal-to-noise ratios under the conditions of accumulation lengths of 10000, 1000, and 100 are shown as follows. Figure 5 shown.

[0063] Depend on Figure 5 It can be seen that as the accumulation length increases, the limit at which the error increases with decreasing signal-to-noise ratio decreases. When the accumulation length is 10,000, parameter estimation can be achieved under -12dB signal-to-noise ratio conditions. The maximum accuracy of parameter estimation is determined by the length of the time shift. Under high signal-to-noise ratio conditions, the RRMSE reaches 0.0077, an error of less than 1%. This error is due to methodological error and cannot be removed, but it is small enough not to affect subsequent parameter estimation. It can achieve LoRa signal parameter detection and estimation under extremely low signal-to-noise ratio conditions.

Claims

1. A LoRa signal blind estimation method based on linear frequency modulation characteristics is used for signal parameter detection and estimation of the LoRa communication system. The communication signal bandwidth used by the communication system is defined as BW, the spreading factor is SF, and the carrier frequency of the transmitted signal is , the frequency modulation slope of the signal is k; it is characterized in that, The method comprises the following steps: S1. Down-convert the signal received by the receiver to the baseband and downsample it. After down-conversion, we get: ， in is the original signal received, e is the natural base; The downsampling method is to extract the original high sampling rate signal and obtain a signal with a lower sampling rate by evenly extracting points in the original signal; S2, time-shift conjugate the original LoRa signal received by the receiver to obtain the time-shift conjugate LoRa signal : ， in is the length of the time shift; Will and Multiply them to get the processed sinusoidal signal with the required parameter as the main frequency: ， in, is the starting frequency of the LoRa signal, is the frequency hopping time, is the duration of a single symbol of the signal, is the frequency modulation slope of the signal, is the instantaneous phase of the signal; S3, obtain the peak position through Fourier transform, and calculate the estimated value of the frequency modulation slope k. Specifically, first convert the processed signal Perform Fourier transform, and the spectrum expression obtained by transformation is : ， in is the impulse function, for The spectrum amplitude in the upper half, for The spectrum amplitude in the lower half, for The amplitude of the time-independent component of The largest component is located at The spectrum line at , by finding the peak position, the estimated value of the frequency modulation slope k is obtained; S4. Generate an LFM signal with a decreasing slope using the calculated FM slope value: ， in is the signal center frequency; The peak interval is obtained by convolving the LFM signal with the down-converted LoRa signal: ， in is the Sinque function, and its pulse width is , a peak appears at the end of each rising frequency modulation slope signal; The relationship between signal bandwidth, spreading factor, and signal frequency modulation slope is: ， in is the spreading factor, SF is an integer between 5 and 12. The spreading factor is only an exponential multiple of 2 to make a relatively accurate estimate, and then the estimated value of each parameter is obtained through the relationship between the parameters.

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