A Multicarrier Chaotic Differential Keying Communication Method Based on Schmitt Orthogonal Signal Reconstruction

Abstract

This invention discloses a multi-carrier chaotic differential keying communication method based on Schmitt orthogonal signal reconstruction. It simultaneously provides two types of information transmission. A chaotic signal generated by a chaotic shaping filter is used as a reference signal. The first type of information, after repetition and initial value calculation, generates a signal for Schmitt orthogonalization through a second-order hybrid chaotic system. Because the transmission of the reference signal not only employs a matched filter to optimize the signal-to-noise ratio but also uses a mean filter to further reduce noise interference, the reference signal carrying the first type of information has extremely high decoding accuracy. Correct decoding of the first type of information ensures that subsequent initial value estimation, the generation of the chaotic signal by the second-order hybrid chaotic system, and the orthogonal signal segment obtained through Schmitt orthogonalization are identical to those at the transmitting end, thereby greatly improving the system's noise and interference immunity and enhancing the error rate performance of the communication system.

Description

Technical Field

[0001] This invention belongs to the technical field of chaotic multicarrier communication methods, and relates to a chaotic differential keying spread spectrum communication method based on accurate reconstruction of Schmitt orthogonalized signals. Background Technology

[0002] Chaotic signals, due to their noise-like characteristics, impulse-like autocorrelation, and near-zero cross-correlation, are widely used in communication system research to improve the multi-carrier and anti-interference performance of communication systems. However, chaotic signals cannot exhibit completely orthogonal properties with short data lengths, thus introducing unavoidable inter-symbol interference (ISI). To improve communication system performance and reduce ISI, researchers have employed Schmitt orthogonalization to orthogonalize chaotic signals, thereby completely eliminating the impact of ISI and enabling multi-carrier transmission, significantly improving the communication system's speed and multi-user transmission capabilities.

[0003] Significant progress has been made in improving the performance of chaotic systems using Schmitt orthogonalization. However, obtaining the same Schmitt orthogonalized signal at the receiver as at the transmitter remains a technical challenge. Currently, chaotic communication schemes based on Schmitt orthogonalization fall into two main categories. The first assumes that the chaotic signals at the transmitter and receiver are synchronized, thus generating the same Schmitt orthogonalized signal. However, robust synchronization of chaotic signals at the transmitter and receiver is difficult to achieve in engineering practice, limiting its research significance. The second category uses the Schmitt orthogonalized signal as a reference signal in chaotic differential keying communication, transmitting it to the receiver via different carriers or time slots. This allows the receiver to directly use the relevant signal, but this method requires transmitting a large amount of information-free reference signal through the channel, wasting channel capacity. Furthermore, the reference signal generated by Schmitt orthogonalization is affected by channel interference during transmission, causing significant distortion in the received reference signal and degrading the communication system performance. Therefore, designing an accurate reconstruction method for the Schmitt orthogonalized signal at the receiver is crucial for improving the performance of multi-carrier chaotic differential keying communication systems. Summary of the Invention

[0004] The purpose of this invention is to provide a multi-carrier chaotic differential keying communication method with accurate reconstruction of Schmitt orthogonalized signals at the receiver. This method eliminates the need to transmit multiple reference signals through a channel, greatly improving the system communication rate. At the same time, the receiver can obtain accurate reference signals, thereby improving the system's bit error rate performance.

[0005] The technical solution adopted in this invention is a multi-carrier chaotic differential keying communication method based on Schmitt orthogonal signal reconstruction, which simultaneously provides two types of information transmission. The first type of bit information is used to generate a chaotic signal through a chaotic shaping filter, and this signal is repeated multiple times as a reference signal. The information carried by the repeated chaotic signal is initially calculated and sent to a second-order chaotic system to generate a new chaotic signal. This signal is then grouped and Schmitt orthogonalized. The orthogonalized signal is multiplied by the second type of bit information to obtain an information signal. The reference signal and multiple information signals are then transmitted. After the receiving end receives the signal and downloads the wave, it first passes the reference signal through a matched filter, downsampling, and mean filtering to recover the first type of bit information. Then, the recovered bit information is initially calculated and sent to a second-order chaotic system to generate a recovered chaotic signal. This signal is then sent to a Schmitt orthogonalized system to generate a reconstructed orthogonalized reference signal. The information signal of the downloaded wave is correlated with the reconstructed orthogonalized reference signal to recover the second type of bit information.

[0006] The invention is further characterized by:

[0007] The multi-carrier chaotic differential keying communication method based on Schmitt orthogonal signal reconstruction is implemented according to the following steps:

[0008] Step 1: System Parameter Configuration

[0009] Set the system sampling frequency f s The number N of the first type of bit information A in a frame of signal s The number of times the first type of bit information is repeated, N r The oversampling rate n of the chaotic signal symbols output by the chaotic shaping filter s The number of signal groups N used for Schmitt orthogonalization, and the number of carriers N. c ;

[0010] Step 2: Transfer the first type of information to be transmitted, A = [a1, a2, ..., a...] Ns Repeat N r This yields a repeating information sequence. will sequence The signal is fed into a chaotic shaping filter to obtain an output signal u, which is then used as a reference signal.

[0011] Step 3: Repeat the information sequence Initial value calculations are performed, and the calculated initial value c0 is fed into a second-order chaotic system, generating a time period of t = N. l / f s The chaotic signal c;

[0012] Step 4: The chaotic signal c is processed according to the sampling frequency f. s Sampling, obtaining N lThe chaotic sequence of sampling points is segmented and subjected to Schmitt orthogonalization to obtain the orthogonalized signal segment [x1, x2, ..., x]. i ,…,x N ];

[0013] Step 5: Prepare the second type of information B to be transmitted, multiply it with the orthogonalized signal segment obtained in step 4 and then sum them to obtain a transmission signal, which is used as the information signal.

[0014] Step 6: Superimpose the reference signal and the multiple information signals to obtain the transmission signal, which is then transmitted to the wireless channel via different carriers.

[0015] Step 7: The receiving end receives the signal, downloads the signal, and obtains the download signal. Then, the reference signal is passed through a matched filter to obtain the matched filtered signal ξ(t).

[0016] Step 8: Downsample the matched filter output signal ξ(t) to obtain a downsampled sequence. After mean filtering and symbol decision, recover the first type of bit information from the downsampled sequence.

[0017] Step 9: Recover the first type of information Repeat the same steps as in step 2 to obtain the repeating information sequence. Then, follow the steps in step 3 to obtain the estimated initial value. Will The system is fed into the same second-order chaotic system as in step 3, resulting in a system of length N. l chaotic signals Then, following the same procedure as in step 4, the chaotic signal... Grouping and Schmidt orthogonalization yield the estimated orthogonalized signal segments.

[0018] Step 10: Pass the information path signal of the downloaded wave through a low-pass filter to remove the influence of high-frequency signals, and then filter the output signal v(t) according to the sampling frequency f. s The sampled sequence obtained from sampling;

[0019] Step 11: Compare the low-pass filtered output signal v(t) with the orthogonalized signal segments estimated in Step 9. Perform the relevant operations and sample and determine the recovery of the second type of bit information.

[0020] The chaotic shaping filter in step 2 is specifically as follows:

[0021]

[0022] in, It is a sequence The m-th element in the equation, where t is the system time, f = f s / n s The fundamental frequency of the chaotic system. Defined as the largest positive integer less than t, δ(t) is the system basis function, as follows:

[0023]

[0024] Among them, ω=2πf and β=fln2.

[0025] In step 3, the initial value is calculated according to equation (3):

[0026]

[0027] in It is a sequence The m-th element in;

[0028] The second-order hybrid chaotic system in step 3 is specifically as follows:

[0029]

[0030] Where c(t) is a chaotic signal. and Let be the first and second derivatives of signal c, respectively. The parameters ω, β, and f are the same as in formula (2). The discrete symbol s is defined as when c = 0.

[0031]

[0032] Step 4 is as follows:

[0033] The chaotic signal c is sampled at frequency f. s Sampling, to obtain N l A chaotic sequence of sampling points is divided into N segments [c1, c2, ..., c]. i ,…,c N ], where the length of each segment is the system spreading gain L, as follows:

[0034]

[0035] And N chaotic signal segments [c1,c2,…,c i ,…,c N The signal is fed into equation (6) for Schmitt orthogonalization to obtain the orthogonalized signal segment [x1, x2, ..., x]. i ,…,x N ], where the i-th segment can be represented as x i =[x i (1),x i (2),…,xi (n),…,x i (L)],

[0036]

[0037] Step 5 specifically involves:

[0038] Preparing the second type of information to be transmitted According to formula (7), each line of information [b j,1 ,b j,2 ,…,b j,N (1≤j≤2N) c -1) respectively with orthogonalized signal segments [x1,x2,…,x] i ,…,x N Multiplying (1≤i≤N) and summing the results yields one transmitted signal:

[0039]

[0040] This transmitted signal is used as an information signal.

[0041] In step 6, the reference signal and the information signal are superimposed according to equation (8):

[0042]

[0043] In step 7, the reference signal is passed through the following matched filter to obtain the matched filtered signal ξ(t):

[0044]

[0045] Where ξ(t) is the output signal of the matched filter, g(t)=δ(-t) is the time inverse function of the basis function δ(t), and τ is the integration variable.

[0046] Step 8 specifically includes:

[0047] The matched filter output signal ξ(t) is downsampled according to a sampling interval of t = 1 / f, and the downsampled sequence is obtained according to equation (11).

[0048]

[0049] The downsampled sequence Y = [y(1), y(2), ..., y(N)] is used. s N r Regrouped

[0050]

[0051] Next, the average of matrix X by each column is calculated to obtain N. s A sequence of means, where the l-th mean is represented as:

[0052]

[0053] The mean-filtered output J l Send the following symbolic judgment to restore the first type of information.

[0054]

[0055] Step 11 is as follows:

[0056] The low-pass filtered output signal v(t) is compared with the orthogonalized signal segment estimated in step 9. Perform the relevant operations as follows:

[0057]

[0058] Z j,i v is the correlation value of the i-th information to be recovered on the j-th carrier. j =[v j (1),v j (2),...,v j (L)],(1≤j≤2N c -1) is the sampling sequence of the low-pass filtered signal in step 10. The estimated orthogonalized signal obtained in step 9 is given by r, which is defined as the transpose operation.

[0059] The second type of information matrix to be recovered Information in row j and column i Can be decoded as

[0060]

[0061] The beneficial effects of this invention are:

[0062] (1) In the method of the present invention, there is no need to assume that the chaotic systems of the transmitter and receiver are synchronized, so the Schmitt orthogonalized signal can be directly used. There is also no need to transmit the orthogonal signal group as a reference signal to the wireless channel. The method of the present invention only needs to use the signal containing the first type of bit information as the reference signal, which effectively improves the communication system rate.

[0063] (2) In the method of the present invention, the chaotic signal used as the reference signal is subjected to matched filtering and mean filtering at the receiving end, which not only maximizes the signal-to-noise ratio of the received signal but also greatly enhances the noise immunity and interference immunity of the transmitted signal. This makes the bit error rate of the recovered first type of information from the reference signal extremely low, and the chaotic signal regenerated for Schmitt orthogonalization has extremely high accuracy, greatly enhancing the bit error rate performance of the communication system.

[0064] (3) Due to the orthogonal characteristics of the modulation signal, the communication system of the present invention has multiple access communication capability and can transmit multiple information simultaneously. Attached Figure Description

[0065] Figure 1 This is a block diagram of the sending end of the method of the present invention;

[0066] Figure 2 This is a block diagram of the receiving end of the method of the present invention;

[0067] Figure 3 It is the chaotic signal generated by the first type of information in Embodiment 1 of the present invention after passing through the chaotic shaping filter;

[0068] Figure 4 It is the chaotic signal generated by the second-order hybrid chaotic system in Embodiment 1 of the present invention;

[0069] Figure 5 It is the grouped signal generated by the grouping module in Embodiment 1 of the present invention;

[0070] Figure 6 It is the signal that has undergone Schmitt orthogonalization in Embodiment 1 of the present invention;

[0071] Figure 7 These are the three information signals corresponding to the second type of transmitted information in Embodiment 1 of the present invention;

[0072] Figure 8 It is the upcarrier signal of the reference signal and the three information signals in Embodiment 1 of the present invention;

[0073] Figure 9 This is the transmitted signal in Embodiment 1 of the present invention;

[0074] Figure 10 These are the download waveform signal of the reference signal and the corresponding matched filter output signal in Embodiment 1 of the present invention;

[0075] Figure 11 It is the output signal of the three information signals of the download wave in Embodiment 1 of the present invention after passing through a low-pass filter;

[0076] Figure 12 These are the bit error rate results under Gaussian channel and multipath attenuation channel in Embodiment 2 of the present invention;

[0077] Figure 13 The bit error rate results of the method and comparison method of the present invention in embodiment 3 of the present invention under a Gaussian channel. Detailed Implementation

[0078] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0079] This invention relates to a multi-carrier chaotic differential keying communication method based on Schmitt orthogonal signal reconstruction. It simultaneously provides two types of information transmission. The first type of bit information is used to generate a chaotic signal through a chaotic shaping filter. This chaotic signal is repeated multiple times as a reference signal to improve its noise immunity. The information carried by the repeated chaotic signal is sent to an initial value calculation module, and the calculated initial value is sent to a second-order chaotic system to generate a new chaotic signal. The generated new chaotic signal is grouped and Schmitt orthogonalized. The Schmitt orthogonalized signal is multiplied by the second type of bit information to obtain the information signal. Then, the reference signal and multiple information signals are transmitted through different carriers to a wireless channel. After receiving the signal and downloading the waveform, the receiving end first processes the reference signal through a matched filter, downsampling, mean filtering, and symbol decision to recover the first type of bit information. Then, the recovered bit information is used for initial value calculation and sent to a second-order chaotic system to generate a recovered chaotic signal. This signal is then sent to a Schmitt orthogonalized system to generate a reconstructed orthogonalized reference signal. The information path signal of the downloaded wave is passed through a low-pass filter to remove the influence of high-frequency signals. The low-pass filter output signal is correlated with the reconstructed orthogonalized reference signal, and then sampled and decided to recover the second type of bit information.

[0080] Figure 1 and Figure 2 The following are system block diagrams of the transmitter and receiver of this invention, respectively. Figure 1 and Figure 2 As shown, the method of the present invention is implemented according to the following steps:

[0081] Step 1: Configure system parameters and set the system sampling frequency f. s The number N of the first type of bit information A in a frame of signal s The number of times the first type of bit information is repeated, N r The oversampling rate n of the chaotic signal symbols output by the chaotic shaping filter s The number of signal groups N used for Schmitt orthogonalization, and the number of carriers N. c The length N of the resulting chaotic signal l =N s ×n s ×N r ×N, system spreading gain L=N s ×n s ×N r Communication rate v b =f s / L×((2×N c -1)×N+N s );

[0082] Step 2: Transfer the first type of information to be transmitted, A = [a1, a2, ..., a...] Ns Repeat N rThis yields a repeating information sequence.

[0083]

[0084] and sequence The signal is fed into a chaotic shape-forming filter (CSF) as follows to obtain the output signal u.

[0085]

[0086] in, It is a sequence The m-th element in the equation, where t is the system time, f = f s / n s The fundamental frequency of the chaotic system. Defined as the largest positive integer less than t, δ(t) is the system basis function, as follows:

[0087]

[0088] Where ω = 2πf, β = f ln2. The resulting output signal u is used as the reference signal.

[0089] Step 3: Repeat the information sequence Input the values ​​into the following formula to calculate the initial values.

[0090]

[0091] in It is a sequence The m-th element in the system. The calculated initial value c0 is fed into the following second-order chaotic system, generating a time-duration system t = N. l / f s The chaotic signal c,

[0092]

[0093] Where c(t) is a chaotic signal. and Let be the first and second derivatives of the signal c, respectively. The parameters ω, β, and f are the same as in formula (2). The discrete symbol s is defined as when . hour,

[0094]

[0095] Step 4: Grouping and Schmitt Orthogonalizing the Chaotic Signal. The chaotic signal c(t) is grouped according to the sampling frequency f. s Sampling is performed to obtain N l The chaotic sequence of sampling points is divided into N segments [c1, c2, ..., c].i ,…,c N ], where the length of each segment is the system spreading gain L, as follows:

[0096]

[0097] And N chaotic signal segments [c1,c2,…,c i ,…,c N The signal is fed into equation (6) for Schmitt orthogonalization to obtain the orthogonalized signal segment [x1, x2, ..., x]. i ,…,x N ], where the i-th segment can be represented as x i =[x i (1),x i (2),…,x i (n),…,x i (L)],

[0098]

[0099] Step 5: Prepare the second type of information to be transmitted According to formula (7), each line of information [b j,1 ,b j,2 ,…,b j,N (1≤j≤2N) c -1) respectively with orthogonalized signal segments [x1,x2,…,x] i ,…,x N Multiplying (1≤i≤N) and summing the results yields one transmitted signal.

[0100]

[0101] This transmitted signal is used as an information signal;

[0102] Step 6: Prepare the transmission signal. Superimpose the reference signal and the information signal according to the following formula (8) to obtain the transmission signal, as follows:

[0103]

[0104] Then, after being transmitted via different carrier waves, it is sent to the wireless channel;

[0105] Step 7: The receiving end receives the signal, and the received signal rt is downloaded according to equation (9) to obtain the downloaded signal:

[0106]

[0107] Where N c r represents the number of carrier frequencies. k(t) represents the k-th download waveform signal. When k = 1, r1(t) is the reference signal, and the other download waveform signals are r1(t). k (t),(2≤k≤2N c () is an information signal.

[0108] The reference signal r1(t) is passed through a matched filter (MF) as follows to obtain the matched filtered signal ξ(t).

[0109]

[0110] Where ξ(t) is the output signal of the matched filter, g(t) = δ(-t) is the time inverse function of the basis function δ(t), and τ is the integration variable;

[0111] Step 8: Downsample the matched filter output signal ξ(t) according to a sampling interval of t = 1 / f, and obtain the downsampled sequence according to equation (11).

[0112]

[0113] The downsampled sequence Y = [y(1), y(2), ..., y(N)] is used. s N r Regrouped

[0114]

[0115] Next, the average of matrix X by each column is calculated to obtain N. s A sequence of means, where the l-th mean is represented as:

[0116]

[0117] The mean-filtered output J l Send the following symbolic judgment to restore the first type of information.

[0118]

[0119] Step 9: Recover the first type of information By repeating the same steps as in step 2, a repeating information sequence is obtained.

[0120]

[0121] Then, according to equation (3) in step 3, the estimated initial value is obtained. And By feeding the second-order hybrid chaotic system into equations (4) and (5), we obtain a system of length N. l chaotic signals Following the same procedure as in step 4, the chaotic signal Grouping and Schmidt orthogonalization yield the estimated orthogonalized signal segments.

[0122] Step 10: Pass the information path signal of the downloaded waveform through a low-pass filter to remove the influence of high-frequency signals, as shown below.

[0123] v j (t)=L P (r j+2 (t),f p ), 1≤j≤2N c -1,

[0124] Where v(t) is the filtered output signal, L P Defined as a low-pass filter function, r(t) is the information path signal in equation (9) of step 7, and the cutoff frequency f is set. p The filtered output signal v(t) is processed according to the sampling frequency f. s The sampled sequence obtained by sampling is defined as v j =[v j (1),v j (2),...,v j [(L)], 1≤j≤2N c -1, where L is the system spreading gain;

[0125] Step 11: Compare the low-pass filtered output signal v(t) with the orthogonalized signal segments estimated in Step 9. Perform the relevant operations as follows:

[0126]

[0127] Z j,i v is the correlation value of the i-th information to be recovered on the j-th carrier. j =[v j (1),v j (2),...,v j (L)],(1≤j≤2N c -1) is the sampling sequence of the low-pass filtered signal in step 10. The estimated orthogonalized signal obtained in step 9 is r, which is defined as the transpose operation.

[0128] The second type of information matrix to be recovered Information in row j and column i Can be decoded as

[0129]

[0130] Example 1

[0131] Step 1: In this embodiment, f is sets =40MHz, the number N of first-type bit information A transmitted in one frame of signal. s =3, the number of times the first type of bit information is repeated N r =3, the oversampling rate n of the chaotic signal symbols output by the chaotic shaping filter. s =16, the number of signal packets used for Schmitt orthogonalization N=3, the number of carrier frequencies N c If the value is 2, then the length N of the generated chaotic signal can be calculated. l =432, system spreading gain L=144, communication rate v b =3.333Mbps;

[0132] Step 2: Assume the first type of information to be transmitted is A = [a1, a2, a3] = [1, -1, -1]. Repeat this information N times. r =3 times, to obtain a repeating information sequence Will The chaotic reference signal u(t) is obtained by feeding it into the CSF of equation (1), where the fundamental frequency of the chaotic system is f = 2.5 Mbps, as shown below. Figure 3 As shown;

[0133] Step 3, Sequence Substituting into equation (3), we obtain the initial value c0 = 0.1426. Then, substituting the initial value c0 into equation (4), we set the system c(t=0) = 0.1426 and s(t=0) = +1 when t = 0. As time t evolves, we obtain a time length of t = N. l / f s A chaotic signal with a duration of 10.8 μs, such as Figure 4 As shown. It can be seen that in the first N... s ×N r = Within 9 chaotic symbols (i.e., 0 ≤ t ≤ 3.6 μs), the chaotic system, due to its use of... Figure 3 Same information sequence Therefore, a result was generated. Figure 3 The same chaotic signal. Afterwards (t>3.6μs), the chaotic signal evolves according to the system's own characteristics, with the evolution terminating at t=10.8μs;

[0134] Step 4: The generated chaotic signal with a time length of t = 10.8 μs is processed according to the sampling frequency f. s = 40MHz sampling, resulting in a length of N l A chaotic sequence with 432 sampling points is divided into N=3 segments, denoted as [c1, c2, c3]. Each segment has a length of L=144 and a corresponding t=3.6μs. The grouped signal segments are as follows: Figure 5As shown. Then, the three chaotic signals [c1,c2,c3] are fed into equation (6) to obtain the Schmitt orthogonalized signal [x1,x2,x3], and the corresponding sampling sequence can be expressed as...

[0135]

[0136] like Figure 6 As shown;

[0137] Step 5: In this embodiment, it is assumed that the second type of information to be transmitted... Multiplying each row in B by the orthogonal signal [x1,x2,x3] and summing the results, we can obtain the three transmitted signals as follows:

[0138]

[0139] like Figure 7 As shown;

[0140] Step 6, due to the number of carrier frequencies N c =2, and choosing carrier frequencies f1 = 8MHz and f2 = 18MHz respectively, the transmitted signal can be written as

[0141] st=u sin(2πf1t)+s1 sin(2πf2t)+s2 cos(2πf1t)+s3 cos(2πf2t),

[0142] The corresponding transmission waveform for each channel is as follows: Figure 8 As shown, the transmitted signal waveform is as follows: Figure 9 As shown;

[0143] Step 7: In this embodiment, to facilitate observation of the related processing at the receiving end, channel noise and other interference effects are ignored, i.e., let rt = st. According to equation (9), four download wave signals can be obtained, namely:

[0144]

[0145] The reference signal r1(t) is as follows: Figure 10 As shown by the dashed line, when r1(t) is fed into the matched filter of equation (10), the resulting matched filter output signal is as follows: Figure 10 As shown by the solid line;

[0146] Step 8: In this embodiment, the downsampled signal of the matched filter output signal ξ(t) is shown in Table 1 and... Figure 10 As shown in the Chinese box:

[0147] Table 1. Sampling time and sampled value of the reference signal matched filter signal in Example 1.

[0148]

[0149]

[0150] Reorganize Table 1 according to Equation (12)

[0151]

[0152] Then, by performing mean filtering on X according to equation (13), the mean-filtered output sequence can be obtained.

[0153] J1=12.3174,J2=-10.5700J3=-10.3843

[0154] Substituting the mean-filtered output sequence into equation (14), the first type of information can be recovered.

[0155] Step 9: Recover the first type of information After repeating the same steps as in step 2, a repeating information sequence is obtained. Due to the recovery of the first type of information The resulting sequence of duplicate information is consistent with the information A to be sent by the sender. With the transmitter They are completely consistent. Substituting them into equation (3) gives the estimated initial value. Similar to the transmitter, substituting equations (4) and (5) into the second-order chaotic system will also produce... Figure 4 Identical chaotic signals Next, follow step 4 to obtain the result. Figure 5 The same three estimated chaotic signals and with Figure 6 The same Schmitt orthogonalized signal segment Due to the generated estimated graph and Figure 4 , Figure 5 , Figure 6 They are exactly the same, and will not be given again here;

[0156] Step 10: In this embodiment, since the low-pass filter is a widely used filtering operation in the field of signal processing, it will not be described in detail here. Set the cutoff frequency f. p =3MHz, the filtered output signals v1(t), v2(t), and v3(t) corresponding to the information signals r2(t), r3(t), and r4(t) in step 7 are as follows: Figure 11 As shown. Since the system spreading gain L = 144, the corresponding sampling sequence can be obtained.

[0157]

[0158] Step 11: According to formula (15), all the second type of information to be recovered can be obtained. The corresponding results are as follows:

[0159]

[0160] Substituting the relevant results into equation (16), we can decode the result.

[0161]

[0162] The decoding process has ended.

[0163] Example 2

[0164] The simulation performance results of this invention are as follows: Figure 12 As shown, the simulation employed both a Gaussian channel and a multipath attenuation channel. The average power gains of the multipath attenuation channel were E1 = 0.8 and E2 = 0.2, with corresponding delays τ1 = 0 μs and τ2 = 0.8 μs, respectively. The system parameters were configured as f. s =40MHz, the number of Type I information N in one frame of signal s =4, Number of times information is repeated N r =2, chaotic signal symbol oversampling rate n s =16, number of carrier frequencies N c =2, and the number of signal packets used for Schmitt orthogonalization is N = 1, 2, 3, 4 respectively, and the corresponding communication rates can be calculated to be 2.1875Mbps, 3.125Mbps, 4.0625Mbps, and 5Mbps respectively. The simulation results show that, with a fixed E... b When / N0, the larger the number of packets N used for Schmitt orthogonalization, the better the bit error rate performance. At the same number of packets N, the performance under a Gaussian channel is significantly better than that under a multipath fading channel.

[0165] Example 3

[0166] To further verify the superiority of the present invention, this embodiment conducts comparative simulations of the present invention's scheme and a multi-user differential chaotic shift keying (OMU-DCSK) scheme based on orthogonal chaotic carriers under a Gaussian channel. The communication system configuration parameters are the same as in Embodiment 2, and the spreading gain L = 128 is set in the corresponding OMU-DCSK scheme. The simulation comparison results when the number of orthogonal signals is N = 1, 2, and 4 are as follows. Figure 13As shown, the OMU-DCSK scheme exhibits a relatively small trend in bit error rate performance as the number of orthogonal signals N changes, while the proposed scheme shows continuous performance improvement with increasing N. Furthermore, the proposed scheme significantly outperforms the OMU-DCSK scheme; even when N=1, the bit error rate performance is approximately 2-6 dB better than the comparative scheme. This is because the reference signal reconstruction method using a chaotic shaping filter design in the proposed scheme allows the receiver to accurately recover the reference signal waveform, enhancing the communication system's noise and interference immunity and achieving a lower bit error rate compared to traditional chaotic incoherent communication schemes.

[0167] In summary, the method of this invention uses a chaotic signal generated by a chaotic shaping filter as a reference signal. After repeated initial value calculations, the first type of information is used to generate a signal for Schmitt orthogonalization through a second-order hybrid chaotic system. Since the transmission of the reference signal not only employs a matched filter to optimize the signal-to-noise ratio but also uses a mean filter to further reduce noise interference, the reference signal carrying the first type of information has extremely high decoding accuracy. Correct decoding of the first type of information ensures that subsequent initial value estimation, the chaotic signal generated by the second-order hybrid chaotic system, and the orthogonal signal segment obtained through Schmitt orthogonalization are identical to those at the transmitting end, thereby greatly improving the system's noise and interference immunity and enhancing the error rate performance of the communication system.

Claims

1. A method of multi-carrier chaotic differential keying communication based on reconstruction of Schmidt-orthogonal signals, characterized in that, The method is implemented according to the following steps: Step 1, system parameter configuration Setting system sampling frequency f s Number of first type bit information A in a frame of signal N s Repetition number of first type bit information N r Symbol oversampling rate of chaotic signal output by chaotic shaping filter n s Number of signal groups for Schmidt orthogonalization N Number of carriers N c ; Step 2, the first type of information to be transmitted repeat N r second, the sequence of repeated information , the sequence is sent into a chaotic shaping filter to obtain an output signal u, and the output signal u obtained is used as a reference signal; Step 3, repeating the information sequence performing initial value calculation and inputting the calculated initial value c 0 into the second-order hybrid chaotic system to generate a chaotic signal with a time length of t = N l / f s c ;​ Step 4, the chaotic signal c According to the sampling frequency f s Sampling, obtaining a chaotic sequence with N l sampling points, segmenting and Schmidt orthogonalizing the chaotic sequence to obtain an orthogonal signal segment [x1, x2, …, x i , …, x N ]; Step 5, preparing the second type of information to be transmitted B, multiplying it with the orthogonalized signal segment obtained in step 4 and summing up to obtain a transmission signal, taking the transmission signal as the information signal; Step 6, superimposing the reference signal and the multiple information signals to obtain a sending signal, and then transmitting the sending signal to the wireless channel through different carriers; Step 7, the receiving end receives the signal, receives the download wave, obtains the download wave signal, and then passes the reference signal through a matched filter to obtain a matched filter signal ; Step 8, outputting the matched filter output signal down-sampling to obtain a down-sampled sequence, and recovering the first analog bit information after the down-sampled sequence is subjected to mean filtering and symbol decision ; Step 9: Recover the first type of information Repeat the same steps as in step 2 to obtain the repeating information sequence. Then, follow the steps in step 3 to obtain the estimated initial value. ,Will The system is fed into the same second-order chaotic system as in step 3, resulting in a system of length . N l chaotic signals Then, following the same procedure as in step 4, the chaotic signal... Grouping and Schmidt orthogonalization yield the estimated orthogonalized signal segments. ; Step 10, the information signal of the download wave is filtered by a low-pass filter to remove the high-frequency signal effect, and the filtered output signal v t ) according to the sampling frequency f s The sampling sequence obtained by sampling​ Step 11, correlate the low-pass filtered output signal v ( t ) with the estimated whitened signal segment from Step 9, respectively, and sample decision recover the second type of bit information.

2. The multi-carrier chaotic differential keying communication method based on reconstruction of Schmidt-orthogonal signals according to claim 1, characterized in that, The chaotic shaping filter in step 2 is specifically: ,（1） wherein is the sequence of the m th element, t is the system time, f = f s / n s is the fundamental frequency of the chaotic system, defined as the largest positive integer smaller than t , is the system basis function, as follows （2） wherein , .

3. The multi-carrier chaotic differential keying communication method based on reconstruction of Schmidt-orthogonal signals according to claim 1, characterized in that, The initial value calculation in step 3 is performed according to formula (3): （3） wherein , is the element of the sequence of length m ; The second-order hybrid chaotic system in step 3 is specifically: （4） where c ( t ) is a chaotic signal, and are the first and second derivatives of the signal c , respectively, and the parameters , , f are the same as in equation (2), and the discrete symbol s is defined as when （5）。 4. The multi-carrier chaotic differential keying communication method based on reconstruction of Schmidt-orthogonal signals according to claim 1, characterized in that, Step 4 is specifically: Chaotic signals are mixed c According to the sampling frequency f s Sampling, get N l Chaotic sequence of sampling points, the sequence is divided into N [c1, c2, …, c i , …, c N ], wherein each length is system spread gain L As follows , And will N Segment chaos signal segment [c1, c2, …, c i , …, c N ] into formula (6) Schmidt orthogonalization, get orthogonal signal segment [x1, x2, …, x i , …, x N ], wherein the i Segment can be expressed as x i = [ x i (1), x i (2),…, x i ( n ),…, x i ( L )] （6）。 5. The multi-carrier chaotic differential keying communication method based on reconstruction of Schmidt-orthogonal signals according to claim 1, characterized in that, Step 5 is specifically: Preparing the second type of information to be transmitted According to formula (7), each line of information (1≤ j ≤2 N c -1) respectively with orthogonalized signal segments [x1, x2, …, x i , …, x N ] (1≤ i ≤ N Multiply and then sum to obtain one transmitted signal: （7） The transmission signal is taken as the information signal.

6. The multi-carrier chaotic differential keying communication method based on reconstruction of Schmidt-orthogonal signals according to claim 1, characterized in that, In step 6, the reference signal and the information signal are superimposed according to formula (8): （8）。 7. The multi-carrier chaotic differential keying communication method based on reconstruction of Schmidt-orthogonal signals according to claim 1, characterized in that, The matched filter signal is obtained by matching filtering the reference signal in step 7 : ,（10） wherein is the matched filter output signal, is a basis function is the time inverse function of Step 8 is specifically: is the integration variable.

8. The multi-carrier chaotic differential keying communication method based on reconstruction of Schmidt-orthogonal signals according to claim 1, characterized in that, Step 11 is specifically: According to t =1 f The matched filter output signal is down-sampled with a sampling interval of =1 to obtain a down-sampled sequence according to equation (11) （11） downsampled sequence Y=[ y (1), y (2),…, y ( N s N r )] is re-grouped into （12） Afterwards, the matrix X is averaged by columns to obtain N s a sequence of means, where the l th mean is given by ,（13） The mean filter output J l The first type of information is recovered by feeding the following symbol decision （14）。 9. The multi-carrier chaotic differential keying communication method based on reconstruction of Schmidt-orthogonal signals according to claim 1, characterized in that, ​ The low-pass filtered output signal v ( t ) is correlated with the estimated orthogonalized signal segment from step 9, respectively, as follows ,（15） wherein Z j,i for the first j carrier the correlation value of the first i information to be recovered, , is the sequence of samples of the low-pass filtered signal in step 10, , is the estimated whitened signal obtained in step 9, r is defined as the transposition operation; The second type of information matrix to be recovered The middle column j The middle row i The column of information Can be decoded into 。

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