LoRa signal physical layer security method based on fractional domain phase pseudo-randomization

Abstract

The application provides a LoRa signal physical layer security method based on fractional domain phase pseudo-randomization. Step 1: generating a LoRa signal, obtaining a modulated waveform s(t) based on the LoRa signal including a bandwidth B and a spreading factor SF; step 2: sampling the modulated waveform s(t) of step 1 to obtain a discrete signal s(n); step 3: generating a fractional domain signal under an alpha' angle based on the discrete signal s(n) of step 2; step 4: performing phase pseudo-randomization on the fractional domain signal of step 3, and transforming the obtained fractional domain signal into a time domain, so that the amplitude of each point of the time domain FRPLM signal is affected by the pseudo-random phase e jθ Step 5: demodulating the time domain FRPLM signal of step 4 to obtain the original physical layer bit sequence of the LoRa signal. The application reduces the existence detection of the transmission signal by an illegal interception party, and at the same time, without affecting the demodulation performance of a legal receiving party, makes the illegal interception party unable to demodulate effective information.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of communication, and particularly relates to a LoRa signal physical layer security method based on fractional domain phase pseudo-randomization. BACKGROUND

[0002] LoRa technology is based on Chirp signal, and has the advantages of low power consumption, wide transmission, easy networking, low cost, simple deployment, etc., which perfectly meets the needs of the Internet of Things, and is widely used in various Internet of Things fields. In the foreseeable future, LoRa is one of the main core technologies of the development of the Internet of Things. At present, the massive data of the Internet of Things and the information contained in them have become valuable resources, and people have also begun to pay more and more attention to the privacy of the data generation and exchange process, and the secure communication of the Internet of Things has become a research problem with more and more important significance.

[0003] Traditional information security is based on the computational complexity of the upper layer of the network, but with the continuous development of the computing power of modern computers, the time for breaking the key through brute force method is greatly shortened, which makes the information encryption mechanism based on computational complexity face great challenges. Physical layer security is from the perspective of information theory, and the potential threat is defended in the physical layer signal processing stage, so as to realize the transmission of information security and make up for the short board of the upper network information security transmission. The prior art points out that the research on physical layer security algorithm has important theoretical significance and application value for the information security of the Internet of Things.

[0004] Physical layer security does not change the existing communication technology, and can be well combined with different wireless transmission system modulation technologies. The prior art uses channel instantaneous phase to encrypt LoRa signal frequency shift, which improves the physical layer security performance. The prior art designs CloakLoRa physical layer hidden channel, and hides LoRa information by using amplitude modulation technology. The above schemes have good physical layer security performance, but only use the single index of bit error rate when evaluating the performance of the scheme. With the innovation of modern signal processing technology and the continuous enhancement of equipment processing capacity, the signal detection and parameter estimation means of illegal interceptors have been greatly improved. Therefore, after a physical layer security algorithm is proposed, the interception ability of illegal interceptors should be considered comprehensively, and the performance of the security scheme should be measured from multiple angles and multiple aspects.

[0005] Physical layer security is different from the encryption method of information coding, and can utilize the physical characteristics (time-varying, reciprocity, randomness) of the wireless channel to realize information encryption. The prior art extracts the key based on the reciprocity and randomness of the wireless channel, and improves the security of the key extraction. The prior art applies the received signal strength indication (RSSI) of the LoRa terminal to the key generation. The prior art significantly improves the key generation rate by adding a signal processing technology in the key generation link. The prior art proposes a secure key generation technology for FLoRa, which can realize a high key generation rate (KGR), and the extracted key meets the randomness requirement. It can be seen that the research focus of LoRa physical layer information encryption is mostly on the extraction of the key, and the LoRa signal encryption method combining the LoRa fractional domain physical layer characteristics has rarely been involved.

[0006] The present application is directed to the physical layer characteristics of LoRa signals in the fractional domain, and proposes a physical layer security method for enhancing the security of LoRa signal information transmission based on the fractional domain phase pseudo-randomization transform domain signal processing idea. The method not only can realize the secure encryption of communication information, but also can realize the hiding of the transmission signal. SUMMARY

[0007] The present application provides a LoRa signal physical layer security method based on fractional domain phase pseudo-randomization, to reduce the existence detection of the transmission signal by an illegal interception party, and at the same time, without affecting the demodulation performance of the legal receiving party, the illegal interception party cannot demodulate the effective information.

[0008] The present application is realized by the following technical solutions:

[0009] A LoRa signal physical layer security method based on fractional domain phase pseudo-randomization, the LoRa signal physical layer security method comprising the following steps:

[0010] Step 1: generating a LoRa signal, based on the LoRa signal including a bandwidth B and a spreading factor SF to obtain a modulated waveform s(t);

[0011] Step 2: sampling the modulated waveform s(t) of step 1 to obtain a discrete signal s(n);

[0012] Step 3: generating a fractional domain signal under an angle of a' based on the discrete signal s(n) of step 2;

[0013] Step 4: performing phase pseudo-randomization on the fractional domain signal of step 3, and transforming the obtained fractional domain signal into the time domain, so that the amplitude of each point of the time domain FRPLM signal is affected by the pseudo-random phase e jθ ;

[0014] Step 5: Demodulate the time domain FRPLM signal of step 4 to get the original bit sequence of LoRa signal physical layer.

[0015] A LoRa signal physical layer security method based on fractional domain phase pseudo-randomization, wherein step 1 is specifically SF∈{7,8,9,10,11,12}. The binary information bit stream d i is converted into a decimal cyclic shift value K, wherein the value of K is {0,1,···N-1}; each transmission symbol of the LoRa symbol is divided into N=2 SF chips, and the chip period T c =1 / B, the symbol period T s =N·T c , the frequency modulation slope μ=B / T s ; for a baseband transmission system, the frequency of the symbol rises from f0 to B in the time period [0,T s ], returns to 0 at T0=(N-K) / B, and then rises from 0 to f0 again;

[0016] The specific mathematical expression can be described as:

[0017]

[0018] Wherein, u(t) is a step function;

[0019] And the corresponding modulated waveform can be represented as:

[0020]

[0021] A LoRa signal physical layer security method based on fractional domain phase pseudo-randomization, wherein step 2 is specifically sampling the LoRa signal s(t) to obtain a discrete signal s(n), if f s represents the sampling frequency, then the discrete baseband equivalent equation of s(t) can be represented as:

[0022]

[0023] LoRa signal only needs f s =B to realize demodulation,

[0024] Therefore, by single sampling, data samples equivalent to B as the sampling frequency can be obtained, the sampling interval is T sample =1 / B, the length of the sampled sequence is N, and the discrete signal expression can be simplified as:

[0025]

[0026] A LoRa signal physical layer security method based on fractional domain phase pseudo-randomization, wherein step 3 is specifically: performing N-point discrete fractional Fourier transform on s(n) to obtain S α (k) :

[0027]

[0028] Then The above formula is expressed as:

[0029]

[0030] At this time, the energy of the LoRa signal is most dispersed in the fractional domain, and the phase pseudo-randomization operation on the signal can maximize the influence of the pseudo-random phase on the time domain signal amplitude.

[0031] A LoRa signal physical layer security method based on fractional domain phase pseudo-randomization, wherein step 4 is specifically: using r (r≥SF) bits of data in the pseudo-random sequence to map the pseudo-random phase value, a k is the decimal conversion result of the r-bit binary sequence; and the generated pseudo-random phase is:

[0032]

[0033] The generated pseudo-random phase is multiplied by the fractional domain signal S α' (k) to obtain a fractional domain FRPLM signal:

[0034] F(k) = S α' (k)·e jθ(k) , k = 0, 1,..., N-1 (43)

[0035] Since the inverse discrete fractional Fourier transform to the time domain can be expressed as:

[0036]

[0037] Therefore, the time domain of the FRPLM signal with a fractional domain transform angle of a' is:

[0038]

[0039] From the above formula, since the signal phase pseudo-randomization operation is performed at the angle a' in the fractional domain, the amplitude of each point of the time domain FRPLM signal is affected by the pseudo-random phase e jθ , which is irrelevant to the original LoRa signal time domain waveform and has a noise-like characteristic, thereby increasing the difficulty of signal existence detection for an illegal interception party and improving the physical layer security of the signal waveform.

[0040] A LoRa signal physical layer security method based on fractional domain phase pseudo-randomization, and the step 5 specifically comprises the following steps:

[0041] Step 5.1: Discrete data sample extraction

[0042] Step 5.2: Fractional domain phase adjustment

[0043] Step 5.3: Optimal angle fractional domain transformation

[0044] Step 5.4: Spectrum peak search

[0045] Step 5.5: Radix conversion.

[0046] A LoRa signal physical layer security method based on fractional domain phase pseudo-randomization, and the step 5.1 discrete data sample extraction specifically is,

[0047] When the transmitted signal passes through an AWGN channel, the receiving party performs T sample =1 / B single sampling processing on the continuous signal, and then the received signal r(n) can be obtained:

[0048] r(n) = f(n) + w(n), n = 0, 1, ···, N-1 (46)

[0049] where w(n) represents a discrete complex AWGN sequence with a mean of zero and a variance of σ 2 .

[0050] A LoRa signal physical layer security method based on fractional domain phase pseudo-randomization, and the step 5.2 fractional domain phase adjustment specifically is,

[0051] The N-point DFRFT transformation is performed on r(n) to obtain a fractional domain signal under the angle of α':

[0052]

[0053] where F α' (k) and W α' (k) represent the fractional domain forms of the discrete signals f(n) and w(n), respectively;

[0054] The signal R α' (k) is multiplied by e -jθ(k) to obtain:

[0055]

[0056] where

[0057] A LoRa signal physical layer security method based on fractional domain phase pseudo-randomization, and the step 5.3 optimal angle fractional domain transformation specifically is,

[0058] According to the rotation additivity of DFRFT The N-point DFRFT transformation of R(k) is made in the order of α-α':

[0059]

[0060] When α = -arccot (2πB 2 / N), the signal fractional spectrum energy is gathered, at this time, α is the optimal transformation angle, and then:

[0061]

[0062] Wherein

[0063] In the fractional domain of the optimal angle of energy gathering, the envelope of the fractional spectrum is a sinc function, the fractional domain signal presents the characteristics of an approximate impulse function, and there is a spectrum peak at v = Ksinα.

[0064] A LoRa signal physical layer security method based on fractional domain phase pseudo-randomization, and the step 5.4 spectrum peak search is specifically,

[0065] The center of the sinc function is obtained by using the spectrum peak search Restoration parameters

[0066]

[0067] Wherein Indicates rounding down.

[0068] The step 5.5 conversion is specifically,

[0069] The decimal Is converted into binary, and then the original bit sequence can be recovered

[0070] The present application has the beneficial effects that:

[0071] The present application starts from the fractional domain characteristics of the LoRa signal, gives and deduces the fractional domain transformation angle of the most dispersed energy distribution of the LoRa signal, and the fractional domain transformation angle is called α' below.

[0072] The present application carries out fractional domain phase pseudo-randomization processing on the fractional domain LoRa signal of a specific angle α', transforms the processed signal back to the time domain, and obtains a new time domain waveform with the FRPLM physical layer security encryption signal with the noise-like characteristics. Considering the FRPLM signal constellation point and the spectrum peak search method, it is illustrated that the algorithm has the effect of dispersing signal energy.

[0073] The present application comprehensively considers the demodulation process of the legal receiver and the illegal interception party: for the legal receiver with known fractional field phase pseudo-randomization, a fractional field phase adjustment link is set to ensure smooth demodulation; the illegal interception party cannot correctly recover the transmission information due to the lack of the demodulation link.

[0074] For the illegal interception party, the Neyman-Pearson criterion is used, and the existence detection of signals on the time domain, the frequency domain, the optimal transform angle fractional field and the non-optimal transform angle fractional field is fully considered, and the security and reliability of the proposed algorithm are verified through detection probability.

[0075] For the illegal interception party, the fourth-order cumulant and the signal bit error rate are used to illustrate the improvement of fractional field phase pseudo-randomization on information security from the information hiding aspect. BRIEF DESCRIPTION OF DRAWINGS

[0076] Figure 1 It is a LoRa modulation and demodulation principle block diagram based on the LoRa signal physical layer security method proposed in the present application.

[0077] Figure 2 It is a pseudo-random phase mapping schematic diagram.

[0078] Figure 3 It is a LoRa signal and FRPLM signal time domain signal diagram.

[0079] Figure 4 It is a schematic diagram of each fractional field LoRa signal and FRPLM signal.

[0080] Figure 5 It is a LoRa signal and FRPLM signal constellation diagram.

[0081] Figure 6 It is a demodulation diagram of the legal receiver and the illegal interception party when SNR is-10dB.

[0082] Figure 7 It is a signal detection probability diagram of each domain.

[0083] Figure 8 It is a fourth-order cumulant diagram of the LoRa signal without noise.

[0084] Figure 9 It is a fourth-order cumulant diagram of the FRPLM signal without noise.

[0085] Figure 10 It is a signal instantaneous frequency rate estimation accuracy diagram under different SNRs.

[0086] Figure 11 It is a BER performance comparison diagram of the legal receiver and the illegal interception party. DETAILED DESCRIPTION

[0087] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by a person of ordinary skill in the art without creative effort belong to the protection scope of the present application.

[0088] The present application relates to a LoRa signal physical layer security technology in the field of communication, which is used for enhancing the information transmission security of LoRa wireless communication system. Specifically, the LoRa signal is transformed into a fractional domain with the most dispersed energy distribution, and then the LoRa signal is subjected to phase pseudo-randomization operation in the fractional domain and is transformed back to time domain, so that a new time domain waveform of the fractional pseudo-random phase LoRa modulation (FRPLM) signal has a noise-like characteristic, so that an illegal interception party cannot correctly demodulate the original information, thereby improving the physical layer security performance of the LoRa signal. Through signal constellation comparison, signal existence detection, communication parameter estimation, legal receiver and illegal interception party demodulation and bit error rate performance comparison, it is shown that the method can well improve the physical layer security performance of the LoRa signal.

[0089] Specifically, it includes generating a LoRa signal; single-bandwidth sampling; generating a fractional domain signal under an angle of α'; fractional domain phase pseudo-randomization; and legal receiver demodulation. The overall block diagram of the method of the present application is shown in Figure 1 .

[0090] First, the principles used in the implementation of the present application are described:

[0091] Principle 1: Fractional Fourier transform of LoRa signal with the most dispersed energy

[0092] The LoRa signal c(t) can be expressed as:

[0093]

[0094] Wherein, μ is the frequency modulation slope of the LoRa signal, f0 is the initial frequency, and T is the signal duration.

[0095] The fractional Fourier transform (FRFT) of the signal c(t) is defined as:

[0096]

[0097] Wherein, the u-axis is the fractional Fourier transform domain, the variable u is called the fractional frequency, and

[0098] denotes the operator of fractional Fourier transform, and a is the rotation angle of fractional Fourier transform, and the integral kernel function K α (u, t) satisfies:

[0099]

[0100] where k is an integer, and

[0101] The fractional Fourier transform of c(t) can be obtained from the definition of fractional Fourier transform as:

[0102]

[0103] From the above formula, the optimal transform angle of the signal c(t) is a = -arccot(2pim), and at this time:

[0104]

[0105] The LoRa signal is concentrated in the fractional domain at this angle, and the fractional domain amplitude is:

[0106]

[0107] At this time, the LoRa signal in the fractional domain presents the characteristics of an approximate impulse function, and the fractional domain spectrum envelope is a sinc function, with the center at u = 2pif0sin a.

[0108] If the fractional domain is not at the optimal transform angle, i.e. a ≠ -arccot(2pim), the fractional spectrum of c(t) is:

[0109]

[0110] where

[0111]

[0112] C(·) and S(·) are Fresnel integrals, which can be expressed as:

[0113]

[0114] Taking the modulus of C α (u) can obtain:

[0115]

[0116] The LoRa signal c(t) is mainly distributed in the fractional domain interval near u = 2pif0sin a in the fractional domain at a ≠ -arccot(2pim) angle, and the interval is:

[0117]

[0118] From the above formula, the LoRa signal has a fractional domain bandwidth of T|cosα+2πμsinα| at an angle α≠-arccot(2πμ), where Then The fractional domain bandwidth reaches a maximum value when That is, the LoRa signal fractional domain energy distribution is most dispersed at an angle α', and α' is a variable related to the frequency modulation slope of the LoRa signal.

[0119] Principle two: communication signal existence detection

[0120] Detection probability P d and false alarm probability P fa are two important interception indicators. Since the loss caused by a missed alarm far exceeds a false alarm, in actual applications, a specific false alarm probability is usually given, and the detection probability is ensured to be large enough. Such a best detection criterion is called the Neyman-Pearson criterion. Assuming that the probability density function (PDF) of the signal detected under the condition H0 can be expressed as p(x|H0), and the condition H1 is p(x|H1), using the likelihood ratio test of binary signal optimal detection, the Neyman-Pearson decision criterion can be expressed as:

[0121]

[0122] where λ(x) is the likelihood ratio function, and η is the threshold value, which is determined by the false alarm probability.

[0123] The real signal echo detection model can be described as:

[0124]

[0125] where w(n) is an additive white Gaussian noise (AWGN) sample with zero mean and variance σ 2 , and S is the amplitude of the echo signal.

[0126] If the mean value of N samples is used to develop a decision rule, that is:

[0127]

[0128] Let Th represent the decision threshold. If the mean value exceeds the threshold, it is determined that a signal exists, and otherwise, it is determined that a signal does not exist. The above detection model can be changed to:

[0129]

[0130] The PDF of the AWGN envelope obeys the Rayleigh distribution, i.e.,

[0131]

[0132] When the detection threshold Th of the given signal is given, the false alarm probability can be expressed as:

[0133]

[0134] Therefore, the detection threshold can be represented by the false alarm probability, i.e.,

[0135]

[0136] The envelope containing both signal and noise obeys the Rice distribution, if there is a useful complex signal and complex Gaussian noise in the intercepted signal, the probability density function at this time can be expressed as:

[0137]

[0138] Where I0(·) represents the first modified zero-order Bessel function, and C represents the signal amplitude.

[0139] Therefore, the detection probability can be obtained as shown below:

[0140]

[0141] Principle three: communication parameter estimation

[0142] In the face of the non-stationary characteristics of LoRa signals, the modulation recognition and parameter estimation methods of traditional stationary signals have great limitations. In addition, LoRa signals can be transmitted in a low SNR environment, and illegal interceptors cannot directly determine the modulation method and modulation parameters from the time domain signal.

[0143] Since the interceptors do not know the modulation method, the multiple-bandwidth sampling method is selected when sampling. According to the multiple-bandwidth sampling signal, the intercepted signal after A / D conversion can be expressed as:

[0144]

[0145] Since the high-order cumulants of the AWGN signal are always zero, only the influence of the communication signal is considered subsequently. In order to facilitate derivation, the above formula is re-expressed as:

[0146] r(n) = exp{j(αn 2 + βn)H1 + j(αn 2 + γn)H2} (24)

[0147] Where the instantaneous frequency change rate α = π / (m 2N), β = 2πK / (mN), γ = 2π(K-N) / (mN),

[0148]

[0149] (1) The fourth moment of LoRa signal

[0150] According to the basic concept of high-order statistics of complex signals, the fourth moment of LoRa signal is represented as:

[0151]

[0152] Substitute the high-order moment calculation formula of discrete data samples into the above formula to obtain:

[0153]

[0154] Let τ1 = 0, τ2 = -τ3 = τ, then the above formula can be simplified as:

[0155]

[0156] (2) The fourth cumulant of LoRa signal

[0157] In actual signal processing, if the non-Gaussian signal satisfies the 2k-order absolute summability, the cumulants of each order can be estimated according to the collected data samples. If x(1), ···, x(N) represent the data samples of x(t), and x(n) = 0 when n≤0 or n>0, then the fourth cumulant formula can be represented as:

[0158]

[0159] The above analysis is based on real signals, and since the LoRa signal studied in the present application is a complex signal, the specific definition of the complex signal needs to be further given. Let {x(n)} represent a zero-mean complex signal, x * (n) represents the complex conjugate of x(n), without loss of generality, the conjugate item is arranged in the front side and the non-conjugate item is arranged in the rear side. Then the fourth cumulant of the discrete signal can be defined as:

[0160] c 4x (τ1,τ2,τ3)=cum{x * (n),x * (n+τ1),x(n+τ2),x(n+τ3)} (29)

[0161] The fourth cumulant calculation formula of LoRa signal can be obtained as:

[0162]

[0163] Substitute the expression of r(n) into it, still let τ1=0, τ2=-τ3=τ, and since the autocorrelation performance of LoRa signal is good, the last three terms in the formula can be ignored, and it is simplified as:

[0164] c 4x (τ1,τ2,τ3)=m 4x (0,τ,-τ)=exp{j(2ατ 2 )} (31)

[0165] The above formula contains the frequency rate of change α of LoRa signal, so the fourth-order cumulant can be used to identify the basic modulation of LoRa signal in the background of additive white Gaussian noise, judge its signal characteristics, and further estimate the instantaneous frequency rate of change of the intercepted signal. The specific method is:

[0166]

[0167] By searching the value of α, the instantaneous frequency rate of change of the intercepted signal can be estimated.

[0168] Principle four: approximate closed-form expression of signal bit error rate

[0169] Information bit demodulation is the last step for the illegal interception party to obtain the transmission information, and the bit error rate (BER) is the most intuitive manifestation of whether the demodulation is successful or not. The existing technology gives an approximate formula of BER:

[0170]

[0171] where Q(·) represents the Q function, Γ is the signal-to-noise ratio (SNR), and H N-1 N-1 represents the N-1 order harmonic number. Further, when N-1 is large, the harmonic number H

[0172]

[0173] where 0.57722 is the gamma constant.

[0174] Considering that the spreading factor SF≥7, it can be assumed that (H N-1 ) 2 ≥π 2 / 12, and by approximating ln(N-1) as lnN, a more simplified approximate expression of BER can be obtained:

[0175]

[0176] The modulation and demodulation mode of the FRPLM signal is based on the optimal transform angle FRFT, and the BER is used to measure the information bit demodulation capability, and the closer the BER of the illegal interception party to 0.5, the better the performance of the physical layer security algorithm of the application.

[0177] A LoRa signal physical layer security method based on fractional domain phase pseudo-randomization, the LoRa signal physical layer security method comprising the following steps:

[0178] Step 1: generating a LoRa signal, based on the LoRa signal including a bandwidth B and a spreading factor SF to obtain a modulated waveform s(t);

[0179] Step 2: sampling the modulated waveform s(t) of step 1 to obtain a discrete signal s(n);

[0180] Step 3: generating a fractional domain signal under an angle of a' based on the discrete signal s(n) of step 2;

[0181] Step 4: performing phase pseudo-randomization on the fractional domain signal of step 3, and transforming the obtained fractional domain signal into a time domain, so that the amplitude of each point of the time domain FRPLM signal is affected by the pseudo-random phase e jθ ;

[0182] Step 5: demodulating the time domain FRPLM signal of step 4 to obtain the original physical layer bit sequence of the LoRa signal.

[0183] A LoRa signal physical layer security method based on fractional domain phase pseudo-randomization, the step 1 is specifically, the LoRa signal is based on Chirp spread spectrum technology, which is essentially using the starting frequency point to carry information, and the basic Chirp signal is cyclically shifted to obtain a modulated signal. The commonly used frequency bands of the current Internet of Things include 433MHz, 868MHz and 915MHz, and the bandwidth B and the spreading factor SF are two important parameters of the LoRa symbol, B can adopt three kinds of 125kHz, 250kHz and 500kHz, SF∈{7,8,9,10,11,12}. The binary information bit stream d i to be transmitted is converted into a decimal cyclic shift value K, wherein the value of K is {0,1,···N-1}; each transmission symbol of the LoRa symbol is divided into N=2 SF chips, and the chip period T c =1 / B, then the symbol period T s =N·T c , and the frequency modulation slope μ=B / T s ; for a baseband transmission system, the frequency of the symbol is in [0,T sRises from f0 to B in a time period, and returns to 0 after frequency hopping at T0=(N-K) / B, and then rises from 0 to f0 again;

[0184] The specific mathematical expression can be described as:

[0185]

[0186] Wherein, u(t) is a step function;

[0187] And the corresponding modulated waveform can be expressed as:

[0188]

[0189] 3. The LoRa signal physical layer security method based on fractional domain phase pseudo-randomization according to claim 2, wherein the step 2 is specifically sampling the LoRa signal s(t) to obtain a discrete signal s(n), and if f s represents the sampling frequency, the discrete baseband equivalent equation of s(t) can be expressed as:

[0190]

[0191] The LoRa signal only needs f s =B to realize demodulation,

[0192] Therefore, the single-sampling method can obtain the data sample points equivalent to B as the sampling frequency, the sampling interval is T sample =1 / B, the sequence length after sampling is N, and the discrete signal expression can be simplified as:

[0193]

[0194] A LoRa signal physical layer security method based on fractional domain phase pseudo-randomization, wherein the step 3 is specifically performing N-point Discrete Fractional Fourier Transform (DFRFT) on s(n) to obtain S α (k):

[0195]

[0196] When , the above formula is expressed as:

[0197]

[0198] At this time, the LoRa signal has the most dispersed energy in the fractional domain, and the phase pseudo-randomization operation on the signal can maximize the influence of the pseudo-random phase on the time domain signal amplitude.

[0199] A LoRa signal physical layer security method based on fractional domain phase pseudo-randomization, and the step 4 is specifically as follows: r (r >= SF) bits of data in a pseudo-random sequence are used to map a pseudo-random phase value, and an m sequence b0b1b2b3… is taken as an example for illustration; the process of pseudo-random phase mapping is as shown in the figure Figure 2 . k where a k is the decimal conversion result of the r-bit binary sequence; the generated pseudo-random phase is:

[0200]

[0201] The generated pseudo-random phase is multiplied with the fractional domain signal S α' (k) to obtain a fractional domain FRPLM signal:

[0202] F(k)=S α' (k)·e jθ(k) ,k=0,1,...,N-1 (43)

[0203] Since the inverse discrete fractional Fourier transform (IDFRFT) to the time domain can be expressed as:

[0204]

[0205] Therefore, the FRPLM signal in the time domain with the fractional domain transformation angle of a' is:

[0206]

[0207] From the above formula, the phase pseudo-randomization operation is performed on the fractional domain with the angle of a', so that the amplitude of each point of the time domain FRPLM signal is affected by the pseudo-random phase e jθ , which is irrelevant to the original LoRa signal time domain waveform and has a noise-like characteristic, as shown in the figure Figure 3 , thereby increasing the difficulty of signal existence detection by an illegal interception party and improving the physical layer security of the signal waveform.

[0208] A LoRa signal physical layer security method based on fractional domain phase pseudo-randomization, and the step 5 specifically includes the following steps:

[0209] Step 5.1: Discrete data sample extraction

[0210] Step 5.2: Fractional domain phase adjustment

[0211] Step 5.3: Optimal angle fractional domain transformation

[0212] Step 5.4: Spectrum peak search

[0213] Step 5.5: Conversion from decimal to binary.

[0214] A LoRa signal physical layer security method based on fractional domain phase pseudo-randomization, the step 5.1 discrete data sample extraction is specifically,

[0215] When the transmitted signal passes through the AWGN channel, the receiving party makes T sample =1 / B single sampling processing on the continuous signal, and the received signal r(n) can be obtained:

[0216] r(n) = f(n) + w(n), n = 0, 1, ···, N-1 (46)

[0217] where w(n) represents a discrete complex AWGN sequence with mean zero and variance σ 2 .

[0218] A LoRa signal physical layer security method based on fractional domain phase pseudo-randomization, the step 5.2 fractional domain phase adjustment is specifically,

[0219] The N-point DFRFT transform of r(n) is performed to obtain the fractional domain signal under the angle α':

[0220]

[0221] where F α' (k) and W α' (k) represent the fractional domain forms of the discrete signals f(n) and w(n), respectively;

[0222] The signal R α' (k) is multiplied by e -jθ(k) to obtain:

[0223]

[0224] where

[0225] A LoRa signal physical layer security method based on fractional domain phase pseudo-randomization, the step 5.3 optimal angle fractional domain transform is specifically,

[0226] According to the rotation additivity of DFRFT The N-point DFRFT transform of R(k) is performed under the angle α-α':

[0227]

[0228] When α = -arccot(2πB 2 / N), the signal fractional spectrum energy is concentrated, and at this time α is the optimal transform angle, then:

[0229]

[0230] wherein

[0231] In the energy-aggregated alpha-optimal angle fraction domain, the envelope of the fractional spectrum is a sinc function, and the fractional domain signal presents the characteristics of an approximate impulse function, and there is a spectrum peak at v=Ksin alpha.

[0232] A LoRa signal physical layer security method based on fractional domain phase pseudo-randomization, and the step 5.4 spectrum peak search is specifically,

[0233] The center of the sinc function is obtained by spectrum peak search Restoration parameters

[0234]

[0235] wherein Indicates rounding down.

[0236] The step 5.5 conversion is specifically,

[0237] The decimal is converted into binary, and the original bit sequence can be recovered

[0238] For the security problem of the LoRa signal physical layer fractional domain characteristics, the present application proposes a physical layer security algorithm for enhancing the transmission security of the LoRa signal, which can make the illegal interception party unable to demodulate useful information and better realize signal hiding without affecting the demodulation performance of the legal receiving party. The algorithm performs phase pseudo-randomization operation on the LoRa signal in the specific fractional domain with the most dispersed energy, so that the time domain amplitude of the transformed signal is pseudo-randomized, thereby presenting a noise-like characteristic; the energy of each transformed angle fractional domain of the LoRa signal is dispersed, thereby increasing the difficulty of the illegal interception party to detect the signal; the original energy distribution law of the LoRa signal is changed, the calculation result of the fourth-order cumulative quantity of the signal is completely changed, so that the illegal interception party cannot correctly estimate the communication parameters; the illegal interception party cannot recover the time domain waveform of the signal, thereby achieving the purpose of deteriorating the BER of the illegal interception party and enhancing the physical layer security of the LoRa signal.

[0239] Embodiment 1: schematic diagram of each fractional domain signal

[0240] Figure 4The figure shows the schematic diagram of each fractional domain LoRa signal and FRPLM signal. Both the legitimate receiver and the illegal interceptor use spectral peak search to obtain effective information, and thus dispersing the signal energy can increase the difficulty of search for the illegal interceptor. As known from the principle, the LoRa signal has energy aggregation characteristics in the optimal transform angle fractional domain, but the energy of the FRPLM signal in the angle fractional domain becomes dispersed due to the influence of fractional domain phase pseudo-randomization, and has no aggregation characteristics. In the non-optimal transform angle fractional domain, the FRPLM signal is more widely distributed than the LoRa signal, which further illustrates the dispersing ability of the fractional domain phase pseudo-randomization on the signal energy.

[0241] Example 2: Comparison of LoRa signal and FRPLM signal constellation

[0242] In order to more intuitively reflect the dispersing effect of the fractional domain phase pseudo-randomization operation on the LoRa signal energy, the signal constellation is used for further illustration. In order to more clearly compare, SF=5 is taken as an example, Figure 5 The comparison figure of LoRa signal and FRPLM signal constellation is given. The blue points represent the LoRa signal, and the green points represent the FRPLM signal after phase pseudo-randomization. The specific mapping rule of the constellation points is:

[0243]

[0244] where C k represents the constellation point, the amplitude is |C k | = |F α (k) / N, and the phase is α is the optimal transform angle.

[0245] The LoRa signal has energy aggregation characteristics in the optimal transform angle fractional domain, so for each cyclic shift value K, the LoRa signal has only one constellation point k=K. The FRPLM signal has dispersed energy in the fractional domain, so one FRPLM signal corresponds to N constellation points. That is, the pseudo-randomization phase of the fractional domain causes the dispersion of signal energy, and the signal constellation point is split from one point into N points. For the illegal interceptor, even if the signal constellation point is detected, due to the unknown pseudo-random phase, the corresponding inverse operation cannot be performed, and the N dispersed points cannot be re-aggregated into one point, and thus the useful information cannot be obtained.

[0246] Example 3: Comparison of demodulation of legitimate receiver and illegal interceptor

[0247] The legitimate receiver, knowing the pseudo-random phase, performs fractional-domain phase adjustment, thus correctly demodulating the transmitted information; see step 5 for details. The illegitimate interceptor, unaware of the phase pseudo-randomization operation, directly demodulates the intercepted signal: assuming the illegitimate interceptor knows the spreading factor SF, i.e., at the optimal transformation angle α = -arccot(2πB)... 2 Performing a DFRFT operation under / N) yields:

[0248]

[0249] Among them W α (k) denotes the fractional field form of w(n), and:

[0250]

[0251] Due to the unknown pseudo-random phase e on the transformation angle α' of the illegal interceptor jθ(k) The phase of the fractional-domain signal cannot be adjusted, and there is no energy-converging spectral peak at the optimal transformation angle α. Therefore, the illegal interceptor can intercept the signal by adjusting R″. α (k) Cyclic shift estimate obtained by peak search and bit sequence estimates Unable to recover the cyclic shift value K and the original bit sequence d corresponding to the original information. i .

[0252] contrast Figure 6 It is evident that a legitimate receiver can still demodulate the correct information using spectral peak search even in noisy conditions. However, due to the influence of fractional-domain phase pseudo-randomization, an illegitimate interceptor cannot detect the energy-accumulated spectral peaks even when performing DFRFT at the optimal transformation angle α, and the fractional spectrum of the signal is hidden in noise, making it even more difficult to obtain effective information.

[0253] Example 4: Comparison of Signal Presence Detection in Different Domains

[0254] Figure 7 This chart compares the detection probabilities of signals in different domains. LoRa signals, due to their excellent spread spectrum properties, can transmit under negative signal-to-noise ratio (SNR) conditions. However, even under negative SNR conditions, the fractional-domain LoRa signal at the optimal transformation angle exhibits an extremely high detection probability due to its energy concentration characteristics; that is, an unauthorized interceptor can detect the presence of the communication signal in the fractional-domain at this angle. For FRPLM signals, the fractional-domain phase pseudo-randomization operation causes the signal amplitude in each domain to be affected by the pseudo-random phase, thus dispersing the signal energy in each domain. Therefore, in amplitude-based signal presence detection, the detection probability values ​​of FRPLM signals in each domain are extremely small, further demonstrating the ability of this invention to improve signal physical layer security.

[0255] Example 5: Instantaneous frequency change estimation accuracy comparison

[0256] Take SF = 7, B = 125 kHz, K = 50 as an example, Figure 8 and Figure 9 respectively give the fourth-order cumulant diagram of LoRa signal and FRPLM signal, where (a) (b) two subgraphs respectively represent the actual transmitted signal and the result calculated by the fourth-order cumulant of the illegal interception party, (c) subgraph is the estimated instantaneous frequency change rate. Comparing Figure 8 (c) and Figure 9 (c), the effect of fractional domain phase pseudo-randomization on signal fourth-order cumulant is very obvious, the fourth-order cumulant of LoRa signal has a clear spectrum peak, and the pseudo-randomization phase changes the calculation result of signal fourth-order cumulant, which causes the recovery error of time domain waveform, and further affects the parameter estimation of the original signal instantaneous frequency change rate.

[0257] To more intuitively illustrate the influence of the present application on the accuracy of communication parameter estimation, Figure 10 Under the conditions of sampling multiple m = 8 and discrimination accuracy of 0.1, the instantaneous frequency change rate estimation accuracy comparison diagram of LoRa signal and FRPLM signal under different SNR is simulated. When the absolute error between the estimated value and the true value is less than or equal to the discrimination accuracy, it is considered that the estimation is correct, otherwise it is considered that the estimation is incorrect. The parameter estimation accuracy of LoRa signal increases with the increase of SNR, while the estimation accuracy of FRPLM signal is always lower than 3%. This is due to the influence of pseudo-random phase, which completely disrupts the calculation result of signal fourth-order cumulant, so that the illegal interception party cannot obtain the correct instantaneous frequency change rate, and further cannot correctly recover the transmitted signal waveform.

[0258] Example 6: BER performance comparison between legal receiver and illegal interception party

[0259] Even if the illegal interception party detects the frequency band of the signal through longer time, higher level detection means and larger calculation amount, accurately learns the modulation mode and communication parameters, and cannot accurately demodulate the real information bits, it still cannot complete the real interception. In order to more intuitively reflect the security of the algorithm, the BER performance of the legal receiver and the illegal interception party is compared, as shown in Figure 11 For the legal receiver, the effective information can be correctly demodulated after phase adjustment, and the BER performance is similar to that of the original LoRa signal. For the illegal interception party, due to the inability to obtain the pseudo-random phase value, it cannot perform the key step of phase adjustment, the energy of the fractional domain signal is in a scattered state, there is no energy gathering spectrum peak, so it cannot demodulate the correct information through spectrum peak search, and the BER is around 0.5. That is, the algorithm can worsen the BER performance of the illegal interception party without affecting the demodulation of the legal receiver.

[0260] The above description is only the preferred embodiment of the present application, and is not intended to limit the present application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A LoRa signal physical layer security method based on fractional field phase pseudo-randomization, characterized in that, The LoRa signal physical layer security method comprises the following steps: Step 1: generating a LoRa signal, based on the LoRa signal comprising a bandwidth B with a spreading factor SF resulting in a modulated waveform ; Step 2: Modulating the waveform of Step 1 Sampling results in a discrete signal ; Step 3: Discrete signal based on step 2 Generating An angle under a fractional domain signal, wherein, is a fractional domain transform angle with the most dispersed fractional domain energy distribution for a LoRa signal Step 4: phase pseudo-randomization is performed on the fractional domain signal of step 3, and the resulting fractional domain signal is transformed into time domain, so that the amplitude of each point of the new time domain waveform of the fractional domain pseudo-random phase LoRa modulated FRPLM signal with noise-like characteristics is affected by the pseudo-random phase Step 4: phase pseudo-randomization is performed on the fractional domain signal of step 3, and the resulting fractional domain signal is transformed into time domain, so that the amplitude of each point of the new time domain waveform of the fractional domain pseudo-random phase LoRa modulated FRPLM signal with noise-like characteristics is affected by the pseudo-random phase Step 5: demodulating the step 4 time domain new time domain waveform with the noise-like characteristic of the fractional domain pseudo-random phase LoRa modulation FRPLM signal to obtain the original physical layer bit sequence of the LoRa signal.

2. The LoRa signal physical layer security method based on fractional domain phase pseudo-randomization according to claim 1, characterized in that, The step 1 is specifically ; the binary information bit stream to be transmitted is converted into a cyclic shift value in decimal system , wherein is the value of ; each transmission symbol of the LoRa symbol is divided into chips, and the chip period is ; therefore, the symbol period is , and the frequency modulation slope is ; For a baseband transmission system, the frequency of the symbol is in the time period from rises to B , at occurs a frequency jump and returns to 0, and again rises from 0 frequency to ; The specific mathematical expression can be described as: （1） wherein is a step function; And the corresponding modulated waveform can be expressed as: （2）。 3. The LoRa signal physical layer security method based on fractional domain phase pseudo-randomization according to claim 2, wherein, The step 2 is specifically, to LoRa signal Sampling obtains discrete signal If the sampling frequency is represented as f s The discrete baseband equivalent equation of f s Can be expressed as: (3) LoRa signals only need to be demodulated, Therefore, by means of single sampling, the equivalent data samples are obtained B The sampling interval is The length of the sampled sequence is N and the discrete signal expression can be simplified as （4）。 4. The LoRa signal physical layer security method based on fractional domain phase pseudo-randomization of claim 3, wherein, The step 3 is specifically, to make N point discrete fractional Fourier transform to obtain : （5） wherein is the rotation angle of the fractional Fourier transform, Then The above equation is expressed as: （6） At this time, the energy of the LoRa signal is most dispersed in the fractional domain, and the phase pseudo-random operation on the signal can maximize the influence of the pseudo-random phase on the time domain signal amplitude.

5. The LoRa signal physical layer security method based on fractional domain phase pseudo-randomization according to claim 4, wherein, The step 4 is specifically mapping the pseudo-random phase value with the bit data in the pseudo-random sequence, wherein , is the decimal conversion result of the bit binary sequence; the generated pseudo-random phase is: （7） The generated pseudo-random phase is multiplied with the fractional domain signal to obtain a fractional domain FRPLM signal: （8） Since the inverse discrete fractional order Fourier transform to the time domain can be expressed as: （9） Therefore, the fractional field transformation angle is The time domain of the FRPLM signal is: （10）。 6. The LoRa signal physical layer security method based on fractional domain phase pseudo-randomization according to claim 5, wherein, The step 5 specifically comprises the following steps: Step 5.1: discrete data sample extraction; Step 5.2: fractional domain phase adjustment; Step 5.3: optimal angle fractional domain transformation; Step 5.4: spectrum peak search; Step 5.5: radix conversion.

7. The LoRa signal physical layer security method based on fractional domain phase pseudo-randomization according to claim 6, wherein, The step 5.1 discrete data sample extraction is specifically, When the transmitted signal passes through an AWGN channel, the receiving party obtains the received signal by processing the continuous signal : （11） wherein represents a complex AWGN sequence with zero mean and variance of 1.

8. The LoRa signal physical layer security method based on fractional domain phase pseudo-randomization of claim 6, wherein, The step 5.2 fractional domain phase adjustment is specifically, The Do N point DFRFT transform, get angle under the fractional domain signal: （12） wherein and denote the fractional domain form of the discrete signals and respectively; The signal is multiplied by to obtain: （13） wherein .

9. The LoRa signal physical layer security method based on fractional domain phase pseudo-randomization of claim 6, wherein, The step 5.3 optimal angle fractional domain transformation is specifically, According to the rotation additivity of DFRFT , the DFRFT of a complex-valued function f(x) is defined as N point DFRFT transform:​​ （14） When the signal fractional spectrum energy is concentrated, at this time is the optimal transform angle, then: （15） wherein ; In the energy-aggregated The envelope of the fractional spectrum is a sinc function over the optimal angle-frequency domain, and the fractional domain signal exhibits the characteristics of an approximate impulse function, with a spectral peak at .

10. The LoRa signal physical layer security method based on fractional domain phase pseudo-randomization of claim 6, wherein, The step 5.4 spectrum peak search is specifically, Finding the center of the sinc function using spectral peak search reduction parameters : （16） wherein represents the floor function; The step 5.5 radix conversion is specifically, Converting the decimal number into binary, the original bit sequence can be recovered .​

Images