CN112822133B - Multi-user orthogonal frequency division multiplexing differential chaos keying communication method - Google Patents

Multi-user orthogonal frequency division multiplexing differential chaos keying communication method Download PDF

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CN112822133B
CN112822133B CN202011565976.5A CN202011565976A CN112822133B CN 112822133 B CN112822133 B CN 112822133B CN 202011565976 A CN202011565976 A CN 202011565976A CN 112822133 B CN112822133 B CN 112822133B
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CN112822133A (en
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任海鹏
赵晓辉
白超
李洁
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Xian University of Technology
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00—Modulated-carrier systems
    • H04L27/001—Modulated-carrier systems using chaotic signals
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04J—MULTIPLEX COMMUNICATION
    • H04J13/00—Code division multiplex systems
    • H04J13/0007—Code type
    • H04J13/0018—Chaotic
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04J—MULTIPLEX COMMUNICATION
    • H04J13/00—Code division multiplex systems
    • H04J13/0007—Code type
    • H04J13/004—Orthogonal
    • H04J13/0048—Walsh

Abstract

The invention discloses a multi-user orthogonal frequency division multiplexing differential chaos keying communication method, which comprises the following steps: 1) setting communication system parameters; 2) allocating index values for P users; 3) each user correspondingly selects a reference symbol sequence by using the index value; 4) generating a chaotic reference signal of each user; 5) distributing sub-carriers for the chaotic reference signals of each user; 6) forming an information bearing signal for the user; 7) constructing an inverse Fourier transform input matrix; 8) obtaining a sending signal; 9) removing a cyclic prefix, performing serial-to-parallel conversion and performing Fourier transform on a received signal in sequence; 10) sampling the point with the maximum signal-to-noise ratio; 11) sample sequence recombination; 12) user index value recovery judgment; 13) selecting an element sequence of a row corresponding to the reference matrix as a new chaotic reference sequence; 14) and decoding user transmission information data. The method of the invention ensures that the chaotic reference sequence is more accurate, and further improves the error rate performance of the communication system.

Description

Multi-user orthogonal frequency division multiplexing differential chaos keying communication method
Technical Field
The invention belongs to the technical field of chaotic communication, and relates to a multi-user orthogonal frequency division multiplexing differential chaotic keying communication method.
Background
The chaotic signal is widely applied to communication due to the characteristics of wide frequency spectrum, noise-like noise, initial value sensitivity and the like, the chaotic communication is initially developed rapidly as a secret communication scheme, and the secret performance of the chaotic secret communication is proved to have no obvious advantages along with the research depth, so the research of the chaotic communication is transferred to the research of improving the communication performance by using chaos under an actual channel. Chaotic communication is not only successfully applied to fiber channels, but also a chaotic differential keying scheme, which is a classic spread spectrum communication scheme, forms a local area network communication standard, such as ieee802.15.6. However, due to the problems of low transmission efficiency, high error rate and the like of the chaotic differential keying scheme, the chaotic differential keying scheme based on the OFDM is provided, the transmission efficiency is improved, the error rate is lower, and a multiple access function is provided. In addition, the latest research results show that the chaos as a baseband signal receiving end can maximize the signal-to-noise ratio through a simple matched filter; meanwhile, the chaotic characteristic can also be used to solve an inter-symbol interference (ISI) problem in wireless communication.
Although the chaos differential keying scheme based on the OFDM has good performance. But the system error rate is higher because the system introduces larger interference among users in the multiple access. Therefore, it is important to further reduce the inter-user interference in multiple access and to obtain a lower error rate.
Disclosure of Invention
The invention aims to provide a multi-user orthogonal frequency division multiplexing differential chaos keying communication method, which solves the problems of large multi-access interference and high error rate in the prior art.
The technical scheme adopted by the invention is that a multi-user orthogonal frequency division multiplexing differential chaos keying communication method is implemented according to the following steps:
step 1, setting relevant parameters of a communication system;
step 2, distributing index value I for P users of information to be sent p Preparing binary bit information b to be transmitted for each user i,p The subscript i ═ 1,2, …, M, P ═ 1,2, …, P denotes the ith bit of the transmission data of the pth user in a frame;
step 3, each user correspondingly selects element sequences of different rows of the Hadamard matrix by using the index values as reference symbol sequences
Figure BDA0002860934410000021
Step 4, the reference symbol sequence corresponding to each user is used as the input of the chaotic shaping filter to generate chaotic reference signals corresponding to each user;
step 5, copying the chaotic reference signals of all users, distributing subcarriers for the chaotic reference signals of all users, and distributing the chaotic reference signal X obtained in the step 4 p (t) repeating C times to obtain
Figure BDA0002860934410000022
C1, 2, 4, each user is allocated with C private sub-carrier frequencies which are uniformly distributed in the use frequency band to transmitA corresponding chaotic reference signal;
step 6, multiplying the bit data of the information to be transmitted of each user by the user chaotic reference signal to form an information bearing signal of the user, adding the information bearing signals corresponding to the users to obtain a transmitting signal in a shared subcarrier, sampling each subcarrier signal according to a sampling frequency to obtain corresponding sampling points to form partial rows of an input matrix of inverse Fourier transform, and preparing for the inverse Fourier transform;
step 7, adding comb-shaped pilot frequency, filling zero, and constructing an inverse Fourier transform input matrix;
step 8, performing inverse Fourier transform on the inverse Fourier transform input matrix column by column, performing parallel-serial conversion on the output of the inverse Fourier transform input matrix, and adding a cyclic prefix to obtain a sending signal;
step 9, after receiving the sending signal, the receiving end sequentially removes the cyclic prefix, performs serial-to-parallel conversion and performs Fourier transform on the received signal, extracts the received user chaotic reference signal and the information bearing signal according to the preset subcarrier, averages the C times chaotic reference signal transmitted by the user, and performs matched filtering with the information bearing signal respectively;
step 10, sampling the maximum signal-to-noise ratio points of the filtered chaotic reference signal and the filtered information-bearing signal to obtain maximum signal-to-noise ratio point sequences X 'and Y' respectively sampled by the chaotic reference signal and the information-bearing signal;
step 11, sample sequence recombination, namely recombining a chaos reference signal sample sequence and an information bearing sample sequence of a user respectively;
step 12, user index value recovery judgment, wherein each row of the Hadamard matrix which is the same as the transmitting end is firstly subjected to maximum signal-to-noise ratio point sampling on the output signal of the matched filter through a forming filter and the matched filter respectively to obtain a new reference matrix; calculating the Euclidean distance between the reference sequence recombined by the user and each row of the reference matrix, and selecting the row with the minimum distance as the recovered user index value;
step 13, selecting the element sequence of the corresponding row of the reference matrix as a new element sequence by using the recovered index valueChaotic reference sequences, i.e. estimates of the index values obtained according to step 12
Figure BDA0002860934410000031
Selecting the row corresponding to the mapping reference matrix as a new chaotic reference sequence
Figure BDA0002860934410000032
Substitution of the recombined chaotic reference sequence
Figure BDA0002860934410000041
Step 14, decoding the user transmission information data, and carrying out the information bearing sequence Y in step 11 inf And the chaos reference sequence obtained in step 13
Figure BDA0002860934410000042
The transpose of the data is multiplied, the symbol judgment is taken from the product result, and the transmission data is recovered to finish the decoding.
The invention has the beneficial effects that the invention comprises the following aspects:
1) the technology of the invention can reduce the multiple access interference. And each user at the transmitting end generates a chaotic reference signal by using row elements of the Hadamard matrix as a reference symbol sequence according to the index value, and the interference of other users to the current user is smaller when the users are distinguished due to the complete orthogonality among the rows of the Hadamard matrix. Since the order of the Hadamard matrix is an integral power of 2, the error rate will not be deteriorated with the increase of the number of users as long as the number of actual users is less than the maximum limited number of users in a certain spread spectrum range. Therefore, compared with the traditional OFDM differential keying scheme, the invention has smaller multiple access interference, thereby improving the system error rate performance.
2) The invention can obtain lower transmission error rate by utilizing the chaotic forming filter and the corresponding matched filter. The effect of maximizing the signal-to-noise ratio is achieved by using the corresponding matched filter at the receiving end, and the bit error rate performance is better due to the application of the point of maximizing the signal-to-noise ratio. The receiving end recovers the index value by using a maximum likelihood method, and then obtains an accurate reference sequence by using the index value, thereby further improving the system error rate performance.
Drawings
FIG. 1 is a block diagram of a transmitting end employed in the method of the present invention;
FIG. 2 is a block diagram of a receiving end employed by the method of the present invention;
FIG. 3 is a graph of the basis function of a chaotic shaping filter used in the method of the present invention;
FIG. 4 is a chaotic reference signal generated by a chaotic shaping filter according to a method symbol sequence of the present invention;
FIG. 5 is an information bearing signal to be transmitted in accordance with an embodiment of the method of the present invention;
FIG. 6 is a real part of a transmission signal according to an embodiment of the method of the present invention;
FIG. 7 illustrates an embodiment of the method of the present invention receiving an output signal of a chaotic reference signal through a matched filter;
FIG. 8 is a block diagram of a method embodiment of the present invention for receiving an information-bearing signal and outputting the signal through a matched filter;
fig. 9 is the bit error rate simulation results of different methods for single user and 3 users under different spread spectrum gains under the gaussian channel;
fig. 10 shows bit error rate simulation results of different methods for different spreading gains of single users and 3 users under a wireless channel;
Detailed Description
The invention is described in detail below with reference to the drawings and the detailed description.
Referring to fig. 1 and fig. 2, which are block diagrams of a transmitting end and a receiving end of a communication system adopted by the method of the present invention, the method of the present invention is based on a chaos shaping filter and a Hadamard index modulation multi-user OFDM differential keying communication, and is specifically implemented according to the following steps:
step 1, setting relevant parameters of a communication system,
setting fundamental frequency f of chaotic shaping filter s Spread spectrum gain coefficient beta, sampling frequency f c A gain coefficient n of chaotic sign s ＝f c /f s Defining the number P of users and the transmission capability per user in a frame of transmission signalThe binary information digit is M;
setting subcarrier parameters including total carrier number N and number N of shared information transmission subcarriers m The number of the extended subcarriers C of each user reference signal, the number of the comb pilot subcarriers Nct and the number of the guard interval subcarriers No, and N is equal to N m +P*C+N ct +N o (ii) a Defining the length L of cyclic prefix, and setting the dimension N of Hadamard matrix s ＝β/n s Generating a Hadamard matrix;
in the embodiment, the fundamental frequency f of the chaotic shaping filter is set s 2.5MHz, sampling frequency f c 40MHz, a chaotic sign gain coefficient n s Let Hadamard matrix dimension N16 s When the spreading gain coefficient is 8, the spreading gain coefficient is n s *N s 128, the number P of users is 5, and each user sends information M of one frame of transmission signal with 48 bits (binary number); subcarrier setting N128, Nm 48, C4, Nct 4, cyclic prefix length L4, the Hadamard matrix generated is as follows:
Figure BDA0002860934410000061
step 2, distributing index value I for P users of information to be sent p Preparing binary bit information b to be transmitted for each user i,p The subscript i ═ 1,2, …, M, P ═ 1,2, …, P denotes the ith bit of the transmission data of the pth user in a frame;
in the embodiment, it is assumed that 5 users of information to be transmitted are assigned index values, i.e. I 1 ＝1，I 2 ＝2，I 3 ＝3，I 4 ＝4，I 5 Each user transmits 48 binary bits of information b ═ 5 i,p Wherein i is 1,2, 48, and p is 1,2, 5.
Step 3, each user correspondingly selects element sequences of different rows of the Hadamard matrix by using the index values as reference symbol sequences
Figure BDA0002860934410000062
In the examples, the selectionSelecting 5 user scenes, where the selection order selects the first 5 rows as indexes, the 1 st user is based on the index value I 1 The first row of the Hadamard matrix is selected as the reference symbol sequence 1, i.e.
Figure BDA0002860934410000071
w＝1,2,...,N s Represents a vector subscript; and so on to obtain the reference symbol sequences of other 4 users
Figure BDA0002860934410000072
Step 4, the reference symbol sequence corresponding to each user is used as the input of the chaotic shaping filter to generate the chaotic reference signal corresponding to each user,
will be provided with
Figure BDA0002860934410000073
The output Chaotic reference signals are respectively obtained as the inputs of a Chaos Shaping Filter (CSF) as follows, and are shown in formula (1):
Figure BDA0002860934410000074
wherein t is the time for generating a user chaotic reference signal, X p (T) is the output of the chaotic shaping filter as the chaotic reference signal for the pth user, T s ＝1/f s For the duration of one symbol in the reference symbol sequence, the basis function ψ (t) is as shown in equation (2):
Figure BDA0002860934410000075
wherein, f s For the base frequency of the chaotic shaping filter set in the step 1, the parameter omega is 2 pi f s ，η＝f s ln2；
In the embodiment, the sampling frequency f is set in step 1 c 40MHz, chaotic signal fundamental frequency f s 2.5MHz, one chaotic symbol gainCoefficient n s 16, the corresponding sampling time t is 0,1/f c ,2/f c …, fig. 3 is a plot of the basis functions of the corresponding chaotic shaping filter. The chaos shaping filter realizes the convolution operation of the digital signal and the primary function psi (t), and the reference symbol sequence of each user in step 3
Figure BDA0002860934410000081
As the input of the chaotic shaping filter, the chaotic reference signal of the 3 rd user in the embodiment is shown in FIG. 4, where the solid line is the generated chaotic reference signal X 3 (t) dashed lines are corresponding reference symbol sequences
Figure BDA0002860934410000082
In addition, due to the fundamental frequency f s 2.5MHz, available X 3 (t) duration t ∈ [0,3.2 × 10 ] -6 )s。
Step 5, copying the chaotic reference signals of all users, distributing subcarriers for the chaotic reference signals of all users, and enabling the chaotic reference signal X obtained in the step 4 p (t) repeating C times to obtain
Figure BDA0002860934410000083
C, 1,2, 4, allocating C private subcarrier frequencies uniformly distributed in the used frequency band for each user to transmit corresponding chaotic reference signals;
in an embodiment, C is 4, that is, the chaotic reference signal of each user obtained in step 4 is repeated C is 4 times, for example, the chaotic reference signal X of the 3 rd user 3 (t) repeating the reaction 4 times to obtain
Figure BDA0002860934410000084
The user's 4 private subcarriers are evenly distributed across the entire available spectrum to cope with frequency selective fading in the channel. In 5 user scenarios, 20 private subcarriers are used together to transmit the chaotic reference signal. The total carrier number is 128, and the 5-user private carrier range is set to ([31: 35)],[49:53],[67:71],[85:89])。
Step 6, multiplying the bit data of the information to be transmitted of each user by the user chaotic reference signal to form an information bearing signal of the user, adding the information bearing signals corresponding to the users to obtain a sending signal in a shared subcarrier, sampling each subcarrier signal according to a sampling frequency to obtain corresponding sampling points to form a part of rows of an inverse Fourier transform input matrix to prepare for inverse Fourier transform,
the information carrying signal transmitted by the ith shared subcarrier carries the ith bit superposition information of all P users, and the information carrying signal is shown in the following formula (3):
Figure BDA0002860934410000091
wherein b is i,p I-th binary data, i-1, 2, M, X, representing the p-th user transmission p (t) is the chaotic reference signal of the p-th user,
transmitting signal Y for each subcarrier i (t) according to the sampling frequency f c Sampling to obtain a sampling matrix of the information bearing signal:
Figure BDA0002860934410000092
wherein Y is i (k)＝Y i (kΔt)，Δt＝1/f c Is the sampling time;
in an embodiment, the 3 rd information bearing signal
Figure BDA0002860934410000093
Is shown in fig. 5, in which the sampling points are marked with crosses, during which time the time is equal to 1/f in terms of Δ t c ＝4*10 -7 Second sampling may result in 128 sample points. And drawing graphs and obtaining sampling points for other carrier transmission signals. In addition, 48 shared subcarriers are set to be allocated to the 128 subcarriers (36: 47)],[54:65],[72:83],[90:101])。
Step 7, adding comb-shaped pilot frequency, filling zero, constructing an inverse Fourier transform input matrix,
set N ct Each subcarrier transmits a comb-shaped pilot signal consisting of bipolar symbols of (N) ct X beta) matrix, and pilot frequency sub-carriers are uniformly inserted into sub-carriers of the chaotic reference signal and the information carrying signal; the chaotic reference signal obtained in the step 5 is processed
Figure BDA0002860934410000094
According to the sampling period delta t as 1/f c Sampling to obtain a sampling matrix of the chaotic reference signal, the sampling matrix Y of the information bearing signal obtained in the step 6 and a comb-shaped pilot signal matrix in the front of the step, and arranging the sampling matrix Y of the information bearing signal and the comb-shaped pilot signal matrix in parallel according to a preset sequence, wherein the rest N are 0 Row complementary zero matrix U o Obtaining a matrix with the size of (Nxbeta) as an inverse Fourier transform input matrix;
in the examples, N ct 4, comb pilot is composed of [1,1, -1,1] T Spreading 128 times results in a (4 × 128) comb pilot signal matrix. And arranging the obtained reference signal sampling (20 multiplied by 128) matrix, the information bearing signal sampling (48 multiplied by 128) matrix and the comb-shaped pilot signal (4 multiplied by 128) matrix in parallel according to a preset sequence, and complementing (56 multiplied by 128) zero matrixes to obtain (128 multiplied by 128) inverse Fourier transform input matrixes. In the embodiments of step 5 and step 6, the chaotic reference signal and the information carrying signal subcarrier range are given, and the comb pilot subcarrier range is ([30,48,66, 84)]) The remaining two sides of the subcarrier range ([1:31 ]],[102:128]) Is a guard interval.
Step 8, inverse Fourier transform is carried out on the inverse Fourier transform input matrix column by column, the output is added with cyclic prefix after parallel-serial conversion to obtain a sending signal,
step 7, obtaining an inverse fourier transform input matrix of (N × β) as an input of inverse fourier transform, performing IFFT operation on N points in each column to complete an OFDM symbol transform, performing IFFT operation on a frame for β times (columns), and performing parallel-to-serial conversion on IFFT output to obtain a time domain signal s (t), which is represented by formula (4):
Figure BDA0002860934410000101
where k is a sampling point of a signal on one subcarrier, and f is a sampling point of a signal on one subcarrier c,p The sub-carrier frequency of the c reference expansion of the p user, f i For the ith information carrying signal subcarrier frequency, f d And f o The carrier frequencies of the comb pilot and the zero padding matrix are respectively, d is 1,2, …, N ct ，o＝1,2,…,N o (ii) a Then, copying L sampling points at the tail of the beta sampling points corresponding to each OFDM symbol, and adding the copied sampling points to the front end of the symbol to be used as cyclic prefixes, so as to obtain a sending signal;
in an embodiment, the inverse fourier transform is input as a (128 × 128) matrix, and the output matrix is parallel-to-serial converted to a duration of (128 × 128) T c S (T), T c ＝1/f c For the duration of one sample, then L-4 samples (corresponding to 4T) at the end of each OFDM symbol c Duration) is added at the front of the symbol, resulting in a duration of (128 x (128+4)) T c The transmission signal of (2). The center frequency is set to be 1MHz in the formula (4), f c,p 、f i 、f d 、f o Corresponding to the subcarrier ranges in the embodiments of step 5, step 6 and step 7, respectively. The real part of the corresponding time domain signal s (t) is shown in fig. 6.
Step 9, after receiving the sending signal, the receiving end sequentially removes the cyclic prefix, performs serial-to-parallel conversion and performs fourier transform on the received signal, extracts the received user chaotic reference signal and the information bearing signal according to the preset subcarrier, averages the C-time chaotic reference signal transmitted by the user, and performs matched filtering with the information bearing signal respectively;
i.e. the received signal r of the p-th user p (t) obtaining an (Nxbeta) Fourier transform output matrix by removing the cyclic prefix, performing serial-to-parallel conversion and Fourier transform, and then extracting the chaotic reference signal X 'and the information bearing signal Y' of the user according to preset subcarrier allocation, as shown in formula (5):
Figure BDA0002860934410000111
wherein the content of the first and second substances,
Figure BDA0002860934410000112
kth sample point, Y 'representing the c-th replica of the received p-th user chaotic reference signal' i,k A kth sampling point representing a received ith information-bearing signal; n is 1 (k) And n 2 (k) Respectively representing the noise of a channel during the transmission of the chaotic reference signal and the noise of the channel during the transmission of the information bearing signal; h k,p,fc Represents the equivalent multi-path fading channel impulse response transmitted by the c-th chaotic reference signal copy of the p-th user in the channel,
Figure BDA0002860934410000127
representing the equivalent multipath fading channel impulse response transmitted by the information-bearing signal received by the p-th user in the ith subcarrier channel, the expression of the impulse responses of the two multipath fading channels is shown as the formula (6):
Figure BDA0002860934410000121
wherein the content of the first and second substances,
Figure BDA0002860934410000122
and τ l,p,c Respectively representing the attenuation coefficient and delay time of the ith path of the channel in which the chaotic reference signal is transmitted, L p,c The number of multi-paths of the c sub-carrier channel of the p user; in the same way as above, the first and second,
Figure BDA0002860934410000123
and τ l′,i Respectively representing the attenuation coefficient and delay time of the L' th path of the channel in which the information-bearing signal is transmitted, L i As to the number of multi-paths,
since the chaotic reference signal of each user is copied for C times, the received C chaotic reference signals are averaged to obtain an averaged chaotic reference signal of the user
Figure BDA0002860934410000124
As shown in the following formula (7):
Figure BDA0002860934410000125
then, the chaos reference signal and the information bearing signal after averaging are subjected to matched filtering to obtain a chaos reference signal X 'and an information bearing signal Y' after matched filtering, and the matched filtering output is as shown in formula (8):
Figure BDA0002860934410000126
wherein g (t) ═ ψ (-t) is the time inverse function of the basic function of the chaotic shaping filter, X ″) p,k The k sampling point, Y ', of the signal output by the filter after the average of the p user's chaotic reference signal i,k A kth sampling point representing an output signal of the ith information-bearing signal after passing through the filter;
in the embodiment, in order to clearly show the signal variation law, an ideal channel model is considered, namely n 1 (t)＝n 2 (t) is 0 and H k,p,fc ＝H k,p,fi 1. The matched filter realizes the convolution operation of the received signal and the time inverse of the basis function, and the 3 rd user filtered chaotic reference signal and the ith (3) bit information bearing signal X ″ 3 (t) and Y ″) 3 (t) is shown in FIGS. 7 and 8, respectively.
Step 10, maximum signal-to-noise ratio point sampling is carried out on the filtered chaotic reference signal and the information-bearing signal, so as to obtain maximum signal-to-noise ratio point sequences X '"and Y'" respectively sampled by the chaotic reference signal and the information-bearing signal, and an expression is shown in formula (9):
Figure BDA0002860934410000131
wherein w' is 1,2 s Sampling points for the maximum signal-to-noise ratio;
in the examples, β 128, N s The filtered signal obtained in step 9 is sampled according to the above formula (9), and the corresponding sampling sequence and sampling value are shown in table 1 below, and the star marks in fig. 7 and fig. 8.
Table 1, sample sequences and sample values of the 3 rd user chaotic reference signal and the ith ═ 3 information carrying signal after filtering in the embodiment
Figure BDA0002860934410000132
Step 11, sample sequence recombination, namely, respectively recombining a chaos reference signal sample sequence and an information bearing sample sequence of a user, wherein an expression is shown as a formula (10):
Figure BDA0002860934410000141
in the embodiment, the sampling sequences obtained in step 10 are respectively recombined according to the above formula (10) to obtain the chaos reference sequence and the information bearing sequence of the 3 rd user, and the expression is as follows:
Figure BDA0002860934410000142
step 12, judging the recovery of the user index value, namely, firstly, respectively passing each row of the Hadamard matrix which is the same as the transmitting end through a forming filter and a matched filter, and sampling the maximum signal-to-noise ratio point of an output signal of the matched filter to obtain a new reference matrix; then calculating the Euclidean distance between the reference sequence recombined by the user and each row of the reference matrix, selecting the row number with the minimum distance as the recovered user index value,
the reference matrix obtained by sampling each row of the Hadamard matrix with the maximum signal-to-noise ratio point after CSF and MF is set as
Figure BDA0002860934410000145
g q Is the q-th row in the reference matrix; then calculating Euclidean distance between the recombined reference sequence and each row in the reference matrix G, and selecting the row with the minimum distance as the estimated value of the user index value
Figure BDA0002860934410000143
The expression is shown in formula (11):
Figure BDA0002860934410000144
wherein sum (& gt) is summation operation, and min { & gt is minimum value operation;
in an embodiment, the expression of the reference matrix is:
Figure BDA0002860934410000151
subjecting to step 11
Figure BDA0002860934410000152
And the reference matrix is substituted in the formula (11) to obtain
Figure BDA0002860934410000153
Step 13, selecting the element sequence of the row corresponding to the reference matrix as a new chaotic reference sequence by using the recovered index value, namely, according to the estimated value of the index value obtained in step 12
Figure BDA0002860934410000154
Selecting the row corresponding to the mapping reference matrix as a new chaotic reference sequence
Figure BDA0002860934410000155
Substitution of the recombined chaotic reference sequence
Figure BDA0002860934410000156
In the embodiment, the 3 rd user meter is arranged at the receiving endThe index value is estimated as
Figure BDA0002860934410000157
Thus, the 3 rd row of the mapping reference matrix G is selected as a new chaotic reference sequence, i.e.
Figure BDA0002860934410000158
And so on to analogize the chaotic reference sequences of the other four users.
Step 14, decoding the user transmission information data, and carrying the information bearing sequence Y in step 11 inf And the chaotic reference sequence obtained in step 13
Figure BDA0002860934410000159
The transpose of the data is multiplied, the symbol decision is taken from the product result, the transmission data is recovered to finish decoding,
m binary data estimates recovered by the p-th user
Figure BDA00028609344100001510
As shown in equation (12):
Figure BDA00028609344100001511
wherein (.) T Represents matrix transposition, sgn represents symbol taking operation, and finally obtains
Figure BDA00028609344100001512
The matrix is used for completing the decoding process for M binary data transmitted by a frame of the pth user;
in the embodiment, the example of decoding the transmission bit data of the 3 rd user and the information carrying sequence Y obtained in step 11 inf And the chaotic reference sequence obtained in step 13
Figure BDA0002860934410000161
And (5) carrying in (12), wherein the calculation result is as follows:
Figure BDA0002860934410000162
the remaining users transmitting binary data estimates
Figure BDA0002860934410000163
And by parity of reasoning, finishing the whole decoding process to obtain the final product.
Simulation verification:
1) error rate in single path channel.
The gaussian channel model is adopted for simulation, the bit error rate performance of different schemes under the same spreading gain and the same user access quantity is tested, and the simulation result is shown in fig. 9. The simulation is compared with a chaos keying modulation scheme based on multi-user OFDM. The spread spectrum gain of all schemes is set to be beta 64 and 256, the number of users is single user and 3 users, and the sampling frequency f c 40MHz, wherein the scheme has a chaotic signal fundamental frequency f s 2.5MHz, then corresponds to n s 16. Set M to 48, which means that 48 binary bits of information are transmitted per user per frame. In fig. 9, the abscissa represents the signal-to-noise ratio and the ordinate represents the bit error rate. Dash-dot lines and circular dash-dot lines in the figure are respectively error rate curves of the comparison scheme in a single-user scene and a 3-user scene beta of 64, a left triangular dash-dot line and a right triangular dash-dot line are respectively error rate curves of the comparison scheme in a single-user scene and a 3-user scene beta of 256, a dotted line and a circular dotted line are respectively error rate curves of the proposed scheme in a single-user scene and a 3-user scene beta of 64, and a solid line and a circular straight line are respectively error rate curves of the proposed scheme in a single-user scene and a 3-user scene beta of 256. As can be seen from the simulation result of fig. 9, compared with the comparison scheme (the chaos keying modulation scheme based on multi-user OFDM), the method of the present invention has a lower error rate at the same spreading gain and the same number of users accessed. Meanwhile, different from the comparison scheme, the method provided by the invention has the advantage that the information error rate is basically kept constant along with the increase of the user number M on the premise of a single-path channel and fixed spread spectrum gain.
2) Bit error rate under a wireless channel.
Bit error rate performance under the condition of same spread spectrum gain and same user access number under wireless channelAs shown in fig. 10, all communication parameter settings are consistent with the simulation under the gaussian channel, and the curves in fig. 10 are represented as consistent with fig. 9. The average power gain of three paths in the simulation is E 1 ＝0.6、E 2 ＝0.3、E 3 0.1, each corresponding delay time τ 1 0 second,. tau 2 0.0000009 seconds,. tau 2 0.000001 sec. It can be seen that the method of the present invention always has better error code performance under the same spread spectrum gain and user number.
In summary, the method of the present invention uses the chaos shaping filter to generate the chaos reference signal, and uses the matched filter to reduce the interference effect, and the chaos signal realizes the modulation of the user index Hadamard matrix symbol, so that the communication system has multi-user capability, and the multiple access interference is greatly reduced. The receiving end uses the corresponding matched filter to reduce the influence of environmental noise, and simultaneously uses a method for calculating Euclidean distance and mapping to ensure that the chaotic reference sequence is more accurate, thereby further improving the error rate performance of the communication system.

Claims (1)

1. A multi-user orthogonal frequency division multiplexing differential chaos keying communication method is characterized by being implemented according to the following steps:
step 1, setting relevant parameters of a communication system, specifically comprising the following steps,
setting the fundamental frequency f of the chaotic shaping filter s Spread spectrum gain coefficient beta, sampling frequency f c A chaotic sign gain coefficient n s ＝f c /f s Defining the number P of users and the number M of binary information bits which can be sent by each user in a frame of transmission signal;
setting subcarrier parameters including total carrier number N and shared information transmission subcarrier number N m The number of spreading sub-carriers C, the number of comb pilot sub-carriers Nct and the number of guard interval sub-carriers No of each user reference signal satisfy N ═ N m +P*C+N ct +N o (ii) a Defining the length L of a cyclic prefix, and setting the dimension N of a Hadamard matrix s ＝β/n s Generating a Hadamard matrix;
step 2,Allocating index value I to P users of information to be transmitted p Preparing binary bit information b to be transmitted for each user i,p The subscript i ═ 1,2, …, M, P ═ 1,2, …, P denotes the ith bit of the transmission data of the pth user in a frame;
step 3, each user correspondingly selects element sequences of different rows of the Hadamard matrix by using the index values as reference symbol sequences
Figure FDA0003586191630000011
Step 4, the reference symbol sequence corresponding to each user is used as the input of the chaotic shaping filter to generate the chaotic reference signal corresponding to each user, the specific process is,
will be provided with
Figure FDA0003586191630000012
The chaos reference signals are respectively used as the input of the following chaos shaping filter to obtain the output chaos reference signals, as shown in formula (1):
Figure FDA0003586191630000013
wherein t is the time for generating a user chaotic reference signal, X p (T) is the output of the chaotic shaping filter as the chaotic reference signal of the pth user, T s ＝1/f s For the duration of one symbol in the reference symbol sequence, the basis function ψ (t) is as shown in equation (2):
Figure FDA0003586191630000021
wherein f is s For the fundamental frequency of the chaotic shaping filter set in step 1, the parameter ω is 2 π f s ，η＝f s ln2；
Step 5, copying the chaotic reference signals of all users, distributing subcarriers for the chaotic reference signals of all users, and carrying out the chaotic reference processing on the chaotic reference signals obtained in the step 4Signal X p (t) repeating C times to obtain X p C (t), wherein C1, 2, 4, C is allocated to each user to uniformly allocate C private subcarrier frequencies within the used frequency band to transmit corresponding chaotic reference signals;
step 6, multiplying the bit data of the information to be transmitted of each user by the user chaotic reference signal to form an information bearing signal of the user, adding the information bearing signals corresponding to the users to obtain a sending signal in a shared subcarrier, sampling each subcarrier signal according to a sampling frequency to obtain corresponding sampling points to form a part of rows of an inverse Fourier transform input matrix to prepare for inverse Fourier transform, wherein the specific process is that,
the information-bearing signal transmitted by the ith shared subcarrier carries the ith bit superposition information of all P users, and the information-bearing signal is shown in the following formula (3):
Figure FDA0003586191630000022
wherein b is i,p I-th binary data, i-1, 2, M, X, representing the p-th user transmission p (t) is the chaotic reference signal of the p-th user,
transmitting signal Y for each subcarrier i (t) according to the sampling frequency f c Sampling to obtain a sampling matrix of the information bearing signal:
Figure FDA0003586191630000031
wherein Y is i (k)＝Y i (kΔt)，Δt＝1/f c Is the sampling time;
step 7, adding comb-shaped pilot frequency, filling zero, and constructing an inverse Fourier transform input matrix,
setting N ct Each subcarrier transmits a comb-shaped pilot signal consisting of bipolar symbols of (N) ct X beta) matrix with pilot subcarriers uniformly inserted in the chaosReference signals and information-bearing signals; the chaotic reference signal obtained in the step 5 is used for
Figure FDA0003586191630000032
According to the sampling period delta t being 1/f c Sampling to obtain a chaotic reference signal sampling matrix, an information bearing signal sampling matrix Y obtained in the step 6 and a comb-shaped pilot signal matrix in the front of the step, and arranging the chaotic reference signal sampling matrix, the information bearing signal sampling matrix Y and the comb-shaped pilot signal matrix in parallel according to a preset sequence, wherein the rest N are 0 Row complementary zero matrix U o Obtaining a matrix with the size of (Nxbeta) as an inverse Fourier transform input matrix;
step 8, inverse Fourier transform is carried out on the inverse Fourier transform input matrix column by column, the output of the inverse Fourier transform input matrix is added with cyclic prefix after parallel-serial conversion, and a sending signal is obtained,
taking the inverse Fourier transform input matrix (Nxbeta) obtained in the step 7 as the input of inverse Fourier transform, performing IFFT operation of N points on each column to complete OFDM symbol transformation, performing IFFT operation on the columns for beta times in a frame, performing parallel-serial conversion on IFFT output to obtain a time domain signal s (t), wherein the time domain signal s (t) is represented by a formula (4):
Figure FDA0003586191630000041
where k is a sampling point of a signal on one subcarrier, and f is a sampling point of a signal on one subcarrier c,p Sub-carrier frequency of c-th reference extension for p-th user, f i For the ith information carrying signal subcarrier frequency, f d And fo are the subcarrier frequencies of the comb pilot and zero-padding matrix, respectively, d is 1,2, …, N ct ，o＝1,2,…,N o (ii) a Then, copying L sampling points at the tail of the beta sampling points corresponding to each OFDM symbol, and adding the copied sampling points to the front end of the symbol to be used as cyclic prefixes, so as to obtain a sending signal;
step 9, after receiving the sending signal, the receiving end sequentially removes the cyclic prefix, performs serial-to-parallel conversion and fourier transform on the received signal, extracts the received user chaotic reference signal and information carrying signal according to the preset subcarrier, averages the C-time chaotic reference signal transmitted by the user, and performs matched filtering with the information carrying signal respectively, the specific process is,
i.e. the received signal r of the p-th user p (t) obtaining an (Nxbeta) Fourier transform output matrix by removing the cyclic prefix, performing serial-to-parallel conversion and Fourier transform, and then extracting the chaotic reference signal X 'and the information bearing signal Y' of the user according to preset subcarrier allocation, as shown in formula (5):
Figure FDA0003586191630000042
Figure FDA0003586191630000043
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0003586191630000044
a kth sample point, Y, representing the c-th replica of the received p-th user chaotic reference signal i, ′ k A kth sample point representing an ith received information-bearing signal; n is a radical of an alkyl radical 1 (k) And n 2 (k) Respectively representing the noise of a channel during the transmission of the chaotic reference signal and the noise of the channel during the transmission of the information bearing signal; h k,p,fc The equivalent multipath fading channel impulse response, H, of the transmitted c chaos reference signal copy of the p-th user in the channel k,p,fi Representing the equivalent multipath fading channel impulse response transmitted by the information-bearing signal received by the p-th user in the ith subcarrier channel, the expression of the impulse responses of the two multipath fading channels is shown as the formula (6):
Figure FDA0003586191630000051
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0003586191630000052
and τ l,p,c Respectively represents the first path attenuation coefficient and delay time of the channel in which the chaotic reference signal is transmitted, L p,c The number of multipath of the c sub-carrier channel of the p user; in the same way as above, the first and second,
Figure FDA0003586191630000053
and τ l′,i Respectively representing the attenuation coefficient and delay time of the L' th path of the channel in which the information-bearing signal is transmitted, L i In order to be the number of multi-paths,
since the chaotic reference signal of each user is copied for C times, the received C chaotic reference signals are averaged to obtain the averaged chaotic reference signal of the user
Figure FDA0003586191630000054
As shown in the following formula (7):
Figure FDA0003586191630000055
then, the chaos reference signal and the information bearing signal after averaging are subjected to matched filtering to obtain a chaos reference signal X 'and an information bearing signal Y' after matched filtering, and the matched filtering output is as shown in formula (8):
Figure FDA0003586191630000056
wherein g (t) ═ ψ (-t) is the time inverse function of the basic function of the chaotic shaping filter, X ″) p,k The k sampling point, Y ', of the signal output by the filter after the average of the p user's chaotic reference signal i,k A kth sampling point representing an output signal of the ith information-bearing signal after passing through the filter;
step 10, maximum signal-to-noise ratio point sampling is carried out on the chaos reference signal and the information-carrying signal after filtering, and maximum signal-to-noise ratio point sequences X '"and Y'" respectively sampled by the chaos reference signal and the information-carrying signal are obtained,
maximum signal-to-noise ratio point sequences X 'and Y' after the chaos reference signal and the information carrying signal are respectively sampled, and an expression formula is shown as a formula (9):
Figure FDA0003586191630000061
wherein w' is 1,2 s Sampling points for the maximum signal-to-noise ratio;
step 11, sample sequence recombination, which is to recombine the chaos reference signal sample sequence and the information bearing sample sequence of the user respectively,
the chaos reference signal sampling sequence and the information bearing sampling sequence of the user are recombined respectively, and the expression is shown as the formula (10):
Figure FDA0003586191630000062
Figure FDA0003586191630000063
step 12, judging the recovery of the user index value, namely, firstly, respectively passing each row of the Hadamard matrix which is the same as the transmitting end through a forming filter and a matched filter, and sampling the maximum signal-to-noise ratio point of an output signal of the matched filter to obtain a new reference matrix; then calculating Euclidean distance between the reference sequence recombined by the user and each row of the reference matrix, selecting the row with the minimum distance as the recovered user index value, and the specific process is,
the reference matrix obtained by sampling each row of the Hadamard matrix with the maximum signal-to-noise ratio point after CSF and MF is set as
Figure FDA0003586191630000071
g q Is the q-th row in the reference matrix; then calculating the recombinant ginsengThe Euclidean distance is calculated for each row in the reference sequence and reference matrix G, and the row with the minimum distance is selected as the estimated value of the user index value
Figure FDA0003586191630000072
The expression is shown in formula (11):
Figure FDA0003586191630000073
wherein sum (·) is summation operation, and min {. } is minimum value calculation;
step 13, selecting the element sequence of the corresponding row of the reference matrix as a new chaotic reference sequence by using the recovered index value, namely, according to the estimated value of the index value obtained in step 12
Figure FDA0003586191630000074
Selecting the row corresponding to the mapping reference matrix as a new chaotic reference sequence
Figure FDA0003586191630000075
Substitution of a recombined chaotic reference sequence
Figure FDA0003586191630000076
Step 14, decoding the user transmission information data, and carrying out the information bearing sequence Y in step 11 inf And the chaotic reference sequence obtained in step 13
Figure FDA0003586191630000077
The transpose of the data is multiplied, the symbol decision is taken as the product result, and the transmission data is recovered to finish decoding.
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