CN115580513A - Modulation and demodulation method of frequency shift chirp spread spectrum index - Google Patents
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Abstract
The invention discloses a modulation and demodulation method of a frequency shift chirp spread spectrum index, which takes a mode of superposing a plurality of chirp signals together as a transmitting signal and simultaneously transmits the plurality of chirp signals; when the number of chirp signals does not exceed half of the total number of modulatable symbols, the more chirp signals are superimposed, the higher the data rate is increased, and the data transmission rate is increased by simultaneously transmitting a plurality of chirp signals. Under the condition of not changing SF, the same resource is used for modulating more information so as to improve the data transmission rate and enhance the communication performance.
Description
Technical Field
The invention relates to the technical field of frequency shift chirp modulation, in particular to a modulation and demodulation method of a frequency shift chirp spread spectrum index.
Background
LoRa is one of the most popular long-distance communication technologies at present, and the communication distance can reach tens of kilometers in the air-to-air condition. The LoRa communication technology has a long communication distance, and benefits from its excellent physical layer design. The physical layer of LoRa is known from Semtech corporation SX1278 official chip manual, loRaWAN protocol specification, and literature [1], and employs scrambling, hamming code, interleaver, gray code, and Frequency Shift Chirp Modulation (FSCM) techniques.
The FSCM technique adopted by LoRa belongs to one of Chirp Spread Spectrum (CSS) modulation techniques. The CSS modulation technique has good anti-interference and anti-fading characteristics, and has good Doppler resistance characteristics due to insensitivity to frequency [2] Has attracted wide attention of domestic and foreign scholars and industry.
The document "t.elshabraway and j.robert," Interleaved Chirp spread LoRa-Based Modulation, "in IEEE Internet of Things Journal, vol.6, no.2, pp.3855-3863, apr.2019" proposes a method of Interleaved Chirp Modulation Based on LoRa, where interleaving of nominal LoRa Chirp signals forms a new multidimensional space, in order to add one bit in each transmitted ICS-LoRa symbol in addition to increase the data rate of a capacity-limited LoRa network. The documents "m.handif and h.h.nguyen," Slope-Shift Keying LoRa-Based Modulation, "in IEEE Internet of Things Journal, vol.8, no.1, pp.211-221, jan.2021" propose a ramp Keying Modulation technique, which utilizes chirp under linear frequency conversion and cyclic Shift thereof to generate a second set of orthonormal basis functions, and increases a set of new orthonormal basis functions on the basis of the existing LoRa system to improve the achievable data rate of the conventional LoRa system.
However, the data transmission rate of the methods is improved by only one bit compared with the standard LoRa, and the improvement is only 14% for the available minimum spreading factor (SF = 7). Due to the variability of application requirements of the internet of things, high-speed data streams such as videos and images need to be transmitted in many scenes, the throughput of the wireless sensor network is susceptible to collision and interference and drops sharply, and a communication method with a higher speed is supported on a physical layer.
Therefore, a modulation and demodulation method for the frequency-shift chirp spread spectrum index is needed.
Disclosure of Invention
The embodiment of the invention provides a modulation and demodulation method of a frequency shift chirp spread spectrum index, which at least solves the technical problem of low data transmission rate in the related technology.
According to an aspect of the embodiments of the present invention, there is provided a method for modulating a frequency-shifted chirped spreading index, including:
a mode of superposing a plurality of chirp signals together is used as a transmission signal, and a plurality of chirp signals are transmitted simultaneously; the more chirp signals are superimposed, the higher the data rate is increased when the number of chirp signals does not exceed half of the total number of modulatable symbols.
Optionally, the expression of the transmission signal is:
in the above formula, s m [n]The obtained transmission signals are formed by m chirp signals, m belongs to [0,2 ] Λ-1 ]，I m Index representing different chirp combinations, n =0,1,.. M-1,m, M is the number of FSCSS modulated orthogonal chirps, x l [n]Is an orthogonal chirp signal.
According to another aspect of the embodiments of the present invention, there is also provided a method for demodulating a frequency-shifted chirped spreading index, including: receiving a signal, demodulating the modulated signal as needed, the demodulating comprising: optimal coherent demodulation, optimal incoherent demodulation, and sub-optimal incoherent demodulation.
Optionally, the received signal y [ n ] is:
y[n]＝hx m [n]+w[n]，
where m is a random symbol value, h represents the channel gain, w n]Is of variance N 0 Zero mean circularly symmetric white gaussian noise, x m [n]Modulating other orthogonal chirp signals than the orthogonal chirp for the M traditional FSCSSs;
chirp signal x l [n]Orthogonal to each other, then:
alternatively, x m [n]The expression for modulating other orthogonal chirp signals than the orthogonal chirp for M conventional FSCSS is:
wherein n and m are more than or equal to 0<M，x 0 [n]A discrete chirp complex signal.
Optionally, the optimal coherent demodulation comprises: the optimal coherent maximum likelihood receiver first correlates the received signal with a down-chirped base signal, then performs a DFT operation on the correlation output, and estimates the transmitted message by maximizing a weighted sum of DFT values.
Optionally, the optimal coherent demodulation comprises:
the maximum likelihood estimation of the transmitted information aims at maximizing the log-likelihood function, the observed signal samples y = { y [0], y [1], …, y [ M-1] } and the channel information h, the likelihood function of the information M is given by a multivariate complex gaussian density function:
wherein, the first and the second end of the pipe are connected with each other,
the constant C is the real part of a complex number:
taking logarithm of two sides of formula (10), and combining with transmitted signal expression and information symbol
The maximum likelihood estimate of (c) is:
finally, other orthogonal chirp signals x except the orthogonal chirp are modulated according to M conventional FSCSS m [n]Obtaining:
wherein, l =0,1]Is at the index of
Discrete fourier transform of (d).
Optionally, the sub-optimal non-coherent demodulation comprises:
estimating m by maximizing the likelihood function f (m | y) = E [ f (m | y, h) ], first to know for calculating f (m | y):
wherein equation (14) is derived from the area under the probability density function;
therefore, the temperature of the molten metal is controlled,
wherein, the constant C' is:
using the transmitted signal expression in conjunction with equation (15), the maximum likelihood estimate of m is obtained:
finally, the combined formula x l [n]＝x 0 [l]x 0 [n]exp (j 2 π ln/M), yielding:
optionally, the sub-optimal non-coherent demodulation comprises: multiplying the received signal by the chirp-based signal, then respectively carrying out DFT, and then carrying out algorithm detection to obtain
Finally, de-mapping to obtain demodulated symbols
Compared with the prior art, the invention has the following beneficial effects:
the Modulation method for the frequency-shift chirp spread spectrum Index introduces Index Modulation (IM) into CSS communication, and the method takes a mode of superposing a plurality of chirp signals together as a transmission signal and simultaneously transmits the plurality of chirp signals; the more chirp signals are superimposed, the higher the data rate is increased when the number of chirp signals does not exceed half of the total number of modulatable symbols, and the data transmission rate is increased by transmitting a plurality of chirp signals simultaneously. Under the condition of not changing SF, the same resource is used for modulating more information so as to improve the data transmission rate and enhance the communication performance.
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In order to more clearly illustrate the technical solution of the present invention, the drawings needed to be used in the description of the embodiments are briefly introduced below, and it is obvious that the drawings in the following description are only one embodiment of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on the drawings without creative efforts.
Fig. 1 is a flowchart of a modulation method of frequency-shifted chirped spreading factor according to an embodiment of the present invention;
fig. 2 is a flowchart of a demodulation method for shifting a frequency-chirped spreading index according to an embodiment of the present invention.
Detailed Description
It should be noted that the embodiments and features of the embodiments in the present application may be combined with each other without conflict. The present application will be described in detail below with reference to the embodiments with reference to the attached drawings.
In order to make the technical solutions better understood by those skilled in the art, 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, and it is obvious that the described embodiments are only partial embodiments of the present application, but not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present application.
It should be noted that the terms "first," "second," and the like in the description and claims of this application and in the drawings described above are used for distinguishing between similar elements and not necessarily for describing a particular sequential or chronological order. It should be understood that the data so used may be interchanged under appropriate circumstances such that embodiments of the application described herein may be used. Furthermore, the terms "comprises," "comprising," and "having," and any variations thereof, are intended to cover a non-exclusive inclusion, such that a process, method, system, article, or apparatus that comprises a list of steps or elements is not necessarily limited to those steps or elements expressly listed, but may include other steps or elements not expressly listed or inherent to such process, method, article, or apparatus.
Example 1
In accordance with an embodiment of the present invention, there is provided an embodiment of a modulation method for frequency-shifted chirped spreading factor, it should be noted that the steps illustrated in the flowchart of the accompanying drawings may be executed in a computer system, such as a set of computer-executable instructions, and that although a logical order is illustrated in the flowchart, in some cases, the steps illustrated or described may be executed in an order different from that shown.
Two parameters mainly determine the data rate of LoRa modulation, one is the spreading factor SF, and the other is the bandwidth BW, and the original data rate R can be calculated according to the SF and BW b Comprises the following steps:
the LoRa modulation adds forward error correction code (FEC) to each data transmission, and improves the robustness of the system by encoding 4-bit data with redundancy into 5 bits, 6 bits, 7 bits, and 8 bits, and the final Data Rate (DR) of LoRa is:
in LoRa modulation, SF can be 6-12, BW can be 125, 250 and 500kHz, CR can be 4/5, 4/6, 4/7 and 4/8. The larger the SF, the lower the communication rate, but the longer the transmission distance. Then the maximum transmission data rate is only 37.5kbps even at the maximum bandwidth. Therefore, a modulation method for shifting the frequency of the chirped spreading factor is needed.
In the conventional FSCSS modulation mode, other chirp signals are generated by using chirp base signals, and a discrete chirp complex signal x 0 [n]Can be expressed as:
where j is the imaginary unit, M is the number of samples in one symbol, n =0,1, and M-1,M is the number of conventional FSCSS modulated orthogonal chirps, and other orthogonal chirp signals can be expressed as:
x m [n]＝x 0 [n+m]， (4)
wherein n is more than or equal to 0, M is less than M, and the formula (4) is substituted into the formula (3) to obtain:
therefore, the M-th chirp signal is different from the instantaneous digital frequency of the base chirp signal by (M/M).
In conventional FSCSS modulation, there is Λ bits of information per chirp symbol, set to (b) 0 ,b 1 ,…,b Λ-1 ) M is the decimal form corresponding thereto,
let the transmitted signal be s m [n]，s m [n]＝x m [n]. It can be noted that Λ = log 2 M，M＝2 Λ 。
Fig. 1 is a flowchart of a modulation method for shifting the frequency chirp spreading factor according to an embodiment of the present invention, and as shown in fig. 1, the modulation method includes the following steps:
a mode of superposing a plurality of chirp signals together is used as a transmission signal, and a plurality of chirp signals are transmitted simultaneously; the more chirp signals are superimposed, the higher the data rate is increased when the number of chirp signals does not exceed half of the total number of modulatable symbols.
Wherein, the expression of the transmitting signal is:
in the above formula, s m [n]For m chirp signals forming the resulting transmitted signal, m is for [0,2 ∈ [ ] Λ-1 ]，I m Index representing different chirp combinations, n =0,1,.. M-1,m, M is the number of FSCSS modulated orthogonal chirps, x l [n]The modulated orthogonal chirp signal corresponding to symbol l.
Taking M =8, K =2 as an example, and K is the number of superimposed chirp signals, the calculation is performed by permutation and combination
There are 28 different symbol combinations in total, and the symbol set can be represented as I m : {0,1}, {0,2}, {0,7}, {1,2}, {1,3}, { 32. Cndot., {1,7}, {2,3}, {2,4}, {2,7}, {3,4}, {3,5}, { 5325 zxft 3825 }, { 23 zxft 5623 }, { 62 zxft 6262 }, {4,7}, {5,6}, {5,7, {6,7. First symbol, i.e. when m =0, I 0 = {0,1}, and the transmitted symbol information is
Likewise, when m =12,i 12 = {1,7}, and the 13 th symbol information transmitted is
Table 1 shows the set I m According to the variation value of m.
Table 1 m =8, K =2 time I m As a function of m
Table 1 also lists the index p and set I m The corresponding relationship of (1). For a given
Wherein
p can be calculated as:
example 2
According to another aspect of the embodiments of the present invention, there is also provided a modulation and demodulation method of a frequency-shift chirp spread spectrum index, including: receiving a signal, demodulating the modulated signal as needed, the demodulating comprising: optimal coherent demodulation, optimal non-coherent demodulation, and sub-optimal non-coherent demodulation.
Specifically, the received signal y [ n ] is:
y[n]＝hx m [n]+w[n]， (8)
where m is a random symbol value, h represents the channel gain, w n]Is of variance N 0 Zero mean circularly symmetric white gaussian noise, x m [n]Modulating other orthogonal chirp signals than the orthogonal chirp for the M traditional FSCSSs;
chirp signal x l [n]Orthogonal to each other, then:
as an alternative embodiment, the optimal coherent demodulation comprises: the optimal coherent maximum likelihood receiver first correlates the received signal with a down-chirped base signal, then performs a DFT operation on the correlation output, and estimates the transmitted message by maximizing a weighted sum of DFT values.
The optimal coherent demodulation specifically includes:
the maximum likelihood estimation of the transmitted information aims at maximizing the log-likelihood function, the observed signal samples y = { y [0], y [1], …, y [ M-1] } and the channel information h, the likelihood function of the information M is given by a multivariate complex gaussian density function:
wherein the content of the first and second substances,
is the real part of a complex number, N 0 For noise power spectral density, the constant C is:
taking logarithm of both sides of the equation (10), and combining the transmitted signal expression (6) and the information symbol
The maximum likelihood estimate of (c) is:
finally, other orthogonal chirp signals x except the orthogonal chirp are modulated according to M conventional FSCSS m [n]The formula (5) gives:
wherein, l =0,1]Is at the index of
Discrete fourier transform of (d).
As an alternative embodiment, the sub-optimal non-coherent demodulation comprises:
non-coherent solutionTuning by maximizing the likelihood function f (m | y) = E [ f (m | y, h)]M is estimated, where the distribution according to h is expected to vary. For Rayleigh fading environment, h is a circularly symmetric Gaussian random variable, and h = h R +jh I ，h R And h I Are independent, identically distributed, and have zero mean gaussian random variables of variance. To calculate f (m | y), first of all:
wherein σ is the noise variance, β is a complex number independent of h, and equation (14) is derived from the area under the probability density function;
therefore, the temperature of the molten metal is controlled,
wherein the content of the first and second substances,
for the average channel signal-to-noise ratio, the constant C' is:
combining equation (15) with the transmitted signal expression equation (6), we obtain the maximum likelihood estimate of m:
finally, the combined formula x l [n]＝x 0 [l]x 0 [n]exp (j 2 π ln/M), yielding:
in general, when more than one chirp signal is transmittedConventional demodulation schemes search for the maximum of all models to find the demodulation information
This can require a significant amount of computational work and memory. Therefore, the patent provides a sub-optimal incoherent detection scheme, which can reduce the computational complexity and the memory overhead.
As an alternative embodiment, as shown in fig. 2, the optimal non-coherent demodulation includes: multiplying the received signal by the chirp-based signal, then respectively carrying out DFT, and then carrying out algorithm detection to obtain
Finally, de-mapping to obtain demodulated symbols
Specifically, the low complexity demodulation scheme estimates l in a recursive manner m . Once set I is found m The value of the symbol m can be determined by first considering the case where the information is combined by two chirp signals, i.e. | I m |＝2，I m ＝{l 1 ,l 2 }. First estimate l 1 ：
Estimate of the above equation 1 The method of (3) is the same as that of conventional FSCSS demodulation. In the formation of l 1 Then according to l 1 Combined (18) estimation of l 2 ：
For | I m |>2 case, demodulation scheme and | I m The demodulation scheme when | =2 is similar. Estimating a set by means of recursion
The formula is as follows:
and
wherein k =1,2, · I | I m |-1。
Preferably, the present invention employs sub-optimal non-coherent demodulation for signal demodulation.
In the above embodiments of the present invention, the descriptions of the respective embodiments have respective emphasis, and for parts that are not described in detail in a certain embodiment, reference may be made to related descriptions of other embodiments.
The foregoing is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, various modifications and decorations can be made without departing from the principle of the present invention, and these modifications and decorations should also be regarded as the protection scope of the present invention.
Claims (9)
1. A method for modulating a frequency-shifted chirped spreading index, comprising:
a mode of superposing a plurality of chirp signals together is used as a transmission signal, and a plurality of chirp signals are transmitted simultaneously; the more chirp signals are superimposed, the higher the data rate is increased when the number of chirp signals does not exceed half of the total number of modulatable symbols.
2. The method for modulating the frequency-shifted chirped spreading index according to claim 1, wherein the expression of the transmitted signal is:
in the above formula, s m [n]For m chirp signals forming the resulting transmitted signal, m is for [0,2 ∈ [ ] Λ-1 ]，I m Denotes the index of the different chirp combinations, n =0,1, so, M-1,m, M is the number of FSCSS modulated orthogonal chirps, x l [n]Is an orthogonal chirp signal.
3. A method for demodulating a frequency-shifted chirped spreading index, comprising: receiving a signal, demodulating the modulated signal as needed, the demodulating comprising: optimal coherent demodulation, optimal non-coherent demodulation, and sub-optimal non-coherent demodulation.
4. The method of demodulating frequency-shifted chirped spreading index according to claim 3, wherein the received signal y [ n ] is:
y[n]＝hx m [n]+w[n]，
where m is a random symbol value, h represents the channel gain, w n]Is of variance N 0 Zero mean circularly symmetric white gaussian noise, x m [n]Modulating other orthogonal chirp signals than the orthogonal chirp for the M traditional FSCSSs;
chirp signal x l [n]Orthogonal to each other, then:
5. the method of demodulating frequency-shifted chirped spreading index according to claim 4, characterized in that x is m [n]The expression for modulating other orthogonal chirp signals than the orthogonal chirp for M conventional FSCSS is:
wherein n and m are more than or equal to 0<M，x 0 [n]A discrete chirp complex signal.
6. The method for demodulating frequency-shifted chirped spreading index according to claim 3, wherein the optimal coherent demodulation comprises: the optimal coherent maximum likelihood receiver first correlates the received signal with a down-chirped base signal, then performs a DFT operation on the correlation output, and estimates the transmitted message by maximizing a weighted sum of DFT values.
7. The method of demodulating frequency-shifted chirped spreading index according to claim 6, wherein the optimal coherent demodulation comprises:
the maximum likelihood estimation of the transmitted information aims at maximizing the log-likelihood function, the observed signal samples y = { y [0], y [1], …, y [ M-1] } and the channel information h, the likelihood function of the information M is given by a multivariate complex gaussian density function:
wherein the content of the first and second substances,
the constant C is the real part of a complex number:
taking logarithm of two sides of formula (10), and combining with transmitted signal expression and information symbol
The maximum likelihood estimate of (c) is:
modulating other orthogonal chirp signals x than the orthogonal chirp according to M conventional FSCSS m [n]Obtaining:
wherein, l =0,1]Is at the index of
Discrete fourier transform of (d).
8. The method for demodulating frequency-shifted chirped spreading index according to claim 3, wherein the sub-optimal noncoherent demodulation comprises:
estimating m by maximizing the likelihood function f (m | y) = E [ f (m | y, h) ], first to know for calculating f (m | y):
wherein equation (14) is derived from the area under the probability density function;
therefore, the number of the first and second electrodes is increased,
wherein, the constant C' is:
using the transmit signal expression in conjunction with equation (15), the maximum likelihood estimate of m is obtained:
combined x l [n]＝x 0 [l]x 0 [n]exp (j 2 π ln/M), yielding:
9. the method of demodulating a frequency-shifted chirped spreading index according to claim 3, wherein the sub-optimal non-coherent demodulation comprises: multiplying the received signal by the chirp-based signal, then respectively carrying out DFT, and then carrying out algorithm detection to obtain
Finally, de-mapping to obtain demodulated symbols
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