The paper deals with modern technology for transmitting short messages over long distances named LoRa, where the transmitted signal uses linear frequency modulation (chirp). The object of the study to define lack of transmitters that it has a design on LoRa technology for assessment their applicable in condition urban city where there are a lot of radiation sources. The goal of the work is the creation of a method of assessing the act the interference conditions that based on measurement bit error rate and signal-noise ratio and via on which to get individual host vulnerability levels. The processing of these signals is carried out by means of a time-frequency transformation. The chirp signal is characterized by 4 parameters: frequencies, time, modulation rate and amplitude. By analogy with the wavelet transform, the processing of chirp signals involves a chirplet decomposition. Since the chirp signals are strongly influenced by mutual interference due to multipath, the article studies the effectiveness of LoRa technology in conditions of mutual interference of radiation sources. The developed method utilized chirplet decomposition and retrieve symbols of a message in the dictionary. The conducted experiments have confirmed the proposed software operability and allow recommending it for use in practice for solving the problems receiving signal. The prospects for further research may include the creation of parallel methods for calculation of the set of proposed indicators, the improvement of software, as well as an experimental study of proposed indicators in real conditions.
tude, center frequency, deviation range and the center of the pulse. Each symbol is assigned a chirp, characterized by these 4 parameters. A complete set of symbols forms a dictionary of chirplets, named by analogy with wavelets. The analysis of the message consists of selecting symbols from the dictionary and finding the best matching of the chirplets to the symbols of the received message. This analysis, called a chirplet decomposition, is carried out in the time-frequency domain. In spite of the fact that chirp signals use the spreading of the spectrum the jamming in the receiving channel cause some difficulties. Processing of chirp signals is complicated by mutual interference from similar sources, as a result of which the received signal has distortions. The main goal of the paper is to research the effectiveness of the chirplet decomposition under interference conditions. 2
Previous work [
However, the processing of LoRa signals is currently not fully researched. The
quality of signal processing is based on the research of their types and the methods of
protection against interference that are used. It should be noted that the use of
frequency analysis alone, in conjunction with classical digital processing, as it was used
in [
The approach to chirplet-decomposition of the received signal is presented in [
The main result of [
Chirp is a signal that has the form
a(t) cos(2ft ct 2 ) if t 0 / 2; s(t) 0, otherwise,
S ( f ) s(t)e j2ft dt (1) (2) (3) where a (t) is the law of amplitude variation (envelope); f is the central frequency; t is time, and c is the phase modulation coefficient. If c > 0, the frequency increases, if c<0, the frequency decreases, c = 0 corresponds to a harmonic signal that is not modulated in frequency; 0 is the pulse duration.
The received signal can be presented as an additive mixture of a useful signal s(t), a white noise with zero mean n(t) and a signal of re-reflections w(t)
y(t ) s(t) n(t ) w(t)
The main indicators of information network security are topological characteristics, one of which is a host’s vulnerability. Host vulnerability is determined based on known vulnerabilities and the main type of vulnerability for LoRa system is the interference for receiving set. To assess the quality of reception, we use the signal-to-noise ratio and bit error rate and estimate the effectiveness of the LoRa system under consideration by measuring the signal-to-noise ratio in a densely populated urban area. 4
Elements of Protection LoRa technology has a few elements of protection. First of them is a signal spectrum that it is completely determined by the phase modulation component and represents the Fourier transform of the signal s (t), i.e.
For the signal s(t), representing a rectangular pulse of unit amplitude, i.e. a(t) = 1 and duration 0, expression (2) can be written in the form
S ( f ) 0/ 2 e jct2 e j2ft dt
m u tr c e p S e d u ilt p m A
It should be noted that the width of the spectrum is an indirect indicator of security since high-density interference is difficult to create in a wide frequency range.
The next element of protection is encoding a chirp signal. In decoding used to use chirplet decomposition. Chirplet is a Gaussian function of the form where tc, fc are parameters of the time and frequency of the function; is the variance, which determines the duration of the chirp function; and c is the modulation rate. The Gaussian chirplet is a fundamental function. Therefore, it is desirable to represent the receiving signal during its processing as a weighted sum of Gaussian chirplet. The form of the chirplet signal is shown in Fig. 2. For the parameters tc = 0, = 1, c = 0, fc = 0, the function gc(t) takes the form (6) (7)
Expression (6) is called the base function of transformations. Modification (6) can be used for the identification of parameters of the Gaussian function for its representation by a harmonic oscillation with frequency modulation of a given kind.
A set of chirplets can be used for the representation of chirp particles. For this
purpose, in [
Recently, a direction has been developed, related to the development of the Fourier transform, in particular, a fractional Fourier transform, which measures the angular distribution of the signal energy in the time-frequency plane. This operator, given by the Wigner distribution for the signal s(t)
W (t, ) 1 st s * t e j d 2 2 2 rotates the signal in the time-frequency plane. In formula (7) asterisk for signal s*(t) means the complex conjugate signal s(t), is the angular frequency equal to 2f. Rotation represents a special combination of chirp convolution and of multiplication chirp as a result of an orthogonal transformation of time-frequency coordinates. This property is achieved by multiplying on the scale factor, using rotation, and by the time and frequency shifts that form the four time-frequency atom parameters. However, it is possible to use the chirplet decomposition to represent the complex signal in a compact form. The appropriate time-frequency transform is presented in Fig. 3. where pe is the bit error probability of the information bit or bit error rate (BER), N is the number of bits in the packet. Assuming pe small, we get
p p pe N.
To reduce the errors in the transmission of the information packets if they have equal length of the packet N, we need to decrease the value of the bit error pe as follows from expression (7).
There are known [
In the chirplet expansion, the signal parameters g()= g [(l, , t, )] are determined. The received signal is digitized, resulting in a set of g(n)= g[(ln, n, tn, n)], n N. And n is the set of possible sampled parameter values form a dictionary D, i.e. n D. Any function s(t) can be represented by a set of atoms g(). An algorithm that allows searching a suitable combination of data from a dictionary should provide a maximum of the search function (9) (20) (31) (42) (53) and carry out the next steps
R0 s(t)
R1 R0 sg0 g0
The parameters s(t) specifying a maximum (10), will determine the maximum approximation to the original signal. In this case, the parameter ln determines the time domain dilatation, and its reciprocal value is the signal compression in the frequency domain, the ellipse rotation angle n corresponds to the linear modulation of the signal center frequency, and the variables tn, n are the time and frequency of the central part of the signal. It becomes necessary to develop an algorithm for searching s(n).
The peculiarity of the algorithm is that a set of parameters is selected from the parameter block dictionary. The algorithm is iterative to provide the best internal signal structure by computing the scalar product of the functions s( n ), gcn . The received value must satisfy the condition sg0 sup sg
Further, we compute the remainder term, which at the beginning of the algorithm is equal to the signal itself The stopping criterion is the ratio (75) (16) (87) (98)
The higher this ratio value, the worse the chosen decomposition parameters. 5
Consider a typical signal LoRa system that is a linear frequency modulated pulse signal. This signal can be obtained, for example, with a voltage-controlled oscillator in the form (1). A useful signal is a packet of pulses with binary modulation. In this case, the logical signal “1” corresponds to the condition с > 0 and the opposite signal, a logical “0”, is obtained if c < 0.
In the experiment, a LoRa system transceiver is based on the SX1276 chip to transmit a short message at a frequency of 868 MHz. The receiver is installed on the top floor of the building. The transmitter gradually moves through the building from the top floor to the basement room, which creates interference. In addition, interference is created by mobile communication transmitters, whose antennas are located on the roof of the building. In addition to the signal-to-noise ratio, the reception quality was also determined by determining the number of erroneous bits in a message and measuring the bit error rate (BER). The measurement scheme is shown in Fig. 5.
The transmitting antennas of mobile operators and Wi-Fi routers that located near the building create jamming with reception. The signals of these devices create an interfering background, which is taken for "white" noise n(t). Crosstalk w(t) is created by multiple re-reflection raying from the interior of the building from the reinforced concrete structures. On each floor of the building, the level of signal and noise is fixed and the quality of the message is controlled. The panoramic receiver selected as the benchmark additionally documents the measurement results. A preliminary analysis of the interference situation presented in Fig. 6.
The results of the measured BER and signal error ratio are presented in Fig. 7.
The obtained results allow us to represent the vulnerability of the host numerical scale, when the high level of vulnerability corresponds to BER = 10%, SNR = -10 dB, the average level of vulnerability BER = 5%, SNR = -5 dB, weak level BER = 2%, SNR = 2 дБ. 6
Although LoRa technology is relatively new for telecommunication systems, linear frequency modulation signals are used for data transmission, which are considered standard in wireless communication systems over short distances (IEEE 802.15.4a). The complexity of processing this type of signals is associated with the need for simultaneous time-frequency analysis of the received signal.
Moreover, an improvement in the accuracy of time measurement leads to deterioration in the accuracy of frequency measurement and vice versa, which is explained by the time-frequency uncertainty principle known in radar. The output in this situation is the time-frequency decomposition of the received signal using the matching pursuit algorithm to the message dictionary. The peculiarity of the study is the most suitable use environment-a densely populated district in the city. The result of the study shows that the placement of devices on the surface gives quite good results. Acceptable results are achieved on the 1st and 2nd floor, where BER is about 1% and the signal-tonoise ratio is not worse than 1-2 dB. Future research is planned to focus on the creation of parallel methods for calculation of the set of proposed indicators, the improvement of software, as well as an experimental study of proposed indicators in real conditions.