A dual-mode differential chaotic shift keying method combined with carrier and time slot index modulation

Abstract

This invention claims protection for a dual-mode differential chaotic shift keying method based on joint carrier and time slot index modulation, belonging to the field of communication technology. A chaotic signal c is generated at the transmitting end using a chaotic signal generator. x Copying M is achieved through the Kronecker product operation. S After +1 iterations, a reference signal is generated, and the chaotic signal c is... x Perform Hilbert transform to generate orthogonal signal c y The information index bits are constructed by k-combined mapping of carrier index and time slot index in the frequency and time domains, creating distinguishable DCSK and QCSK signal modes for modulation bit transmission. Finally, multi-carrier technology is used to distribute the signal across different frequency subcarriers for overall signal transmission. At the receiving end, after demodulating the signals of each subcarrier, a noise reduction module reduces noise interference from the reference signal. Then, through carrier and time slot correlation demodulation and corresponding mapping rules, the original input index information is recovered. Finally, dual-mode demodulation is used to recover the modulation bit information.

Description

Technical Field

[0001] This invention belongs to the field of communication technology, specifically a dual-mode differential chaotic shift keying method based on joint carrier and time slot index modulation. Background Technology

[0002] Chaos theory, one of the three major discoveries in 20th-century physics, has been deeply applied in fields such as topography, economics, and communications. Especially in modern society with the rapid development of communication networks, information security has become a crucial issue in social life and national governance. The initial value sensitivity, quasi-randomness, and spectral characteristics of chaotic signals give them significant advantages in modern chaotic communication. Chaotic communication utilizes chaotic signals as carriers in wireless digital communication systems, replacing traditional sine and cosine carriers. The transmitted signal is hidden or superimposed within the chaotic carrier, increasing communication security while directly achieving spectrum spread, showing broad application prospects in secure communication and spread spectrum communication.

[0003] Chaotic communication is typically categorized into coherent and incoherent demodulation schemes based on whether the receiver requires synchronous demodulation of the signal. Since achieving robust chaotic synchronization using coherent schemes is extremely difficult, incoherent chaotic digital modulation techniques, such as Differential Chaos Shift Keying (DCSK) and Correlated Delay Shift Keying (CDSK), are commonly used. DCSK has a simple structure, low cost, and good error rate performance, but it only utilizes half the time for dedicated information transmission, significantly reducing the data transmission rate. CDSK, on ​​the other hand, uses an adder instead of the DCSK switching structure at the transmitter, eliminating the need for a separate reference signal, thus improving transmission rate and security. However, increased interference within the signal leads to poorer noise immunity. In subsequent research, to address the problems of high error rates, low data rates, and poor security in digital communication, the academic community has continuously proposed improved schemes based on DCSK and CDSK. In the Quadrature Chaos Shift Keying (QCSK) system proposed by researchers, two orthogonal chaotic signals are generated through Hilbert transform. The orthogonality is used to eliminate inter-symbol interference, thereby improving the system's error rate performance and doubling the transmission rate compared to DCSK, but also increasing the system's complexity. In 2013, Kaddoum Georges et al. proposed the Multicarrier Differential Chaos Shift Keying (MC-DCSK) system, which transmits a reference signal and multiple information-carrying signals simultaneously on different subcarriers. This not only solves the radio frequency (RF) delay line problem but also improves the information transmission rate.

[0004] To further explore how to effectively improve the data rate and bit error rate performance of chaotic systems, index modulation (IM) technology has become an important means to solve these problems. Index modulation is an emerging communication technology with high energy efficiency and anti-interference capabilities, and it can significantly reduce hardware complexity. In modern communication systems, index modulation has been widely used in IoT, 5G, and future 6G communications, providing new solutions for achieving efficient, secure, and reliable communication, demonstrating enormous potential and application prospects. As representative indexing schemes in the time and frequency domains, Pulse Position Modulation DCSK (PPM-DCSK) and Carrier Index Differential Chaos Shift Keying DCSK (CI-DCSK) systems utilize time slots and subcarrier activation and deactivation states to map index resources. In addition to transmitting traditional modulation bits, index bits are transmitted from another dimension, effectively improving bit error rate performance.

[0005] To improve the transmission rate of a single-index modulation system, this invention combines QCSK and DCSK signal modulation modes and uses carrier and time slot index modulation techniques to allocate the two signals, proposing a dual-mode differential chaotic shift keying method that combines carrier and time slot index modulation.

[0006] A paper on the same type of dual-mode modulation as this invention proposes a dual-mode differential chaotic shift keying (DM-DCSK-IM) system based on index modulation. At the transmitting end, the bitstream is divided into two parts: one part consists of PPM mapping bits used to select active time slots; the other part consists of dual-mode modulation bits, utilizing DCSK and QCSK modes to distinguish between active and inactive time slots, thus improving the system's data rate. At the receiving end, a pair of distinguishable orthogonal reference signals are correlated and demodulated with the information in each time slot to recover the mapping bits and modulation bits. The differences between this paper and this invention are: 1. This paper only uses one type of time slot index based on PPM modulation, while this invention uses both carrier index and time slot index, performing k-combination mapping from two dimensions, effectively increasing the number of transmittable index bits. 2. The paper transmits DCSK signals in active time slots and QCSK signals in inactive time slots. This invention transmits DCSK signals in active time slots on active subcarriers and QCSK signals in inactive time slots (including the 0th time slot), and vice versa on inactive subcarriers (including the 0th subcarrier). This significantly improves transmission rate while enhancing security. 3. The paper did not use noise reduction processing. This invention uses a noise reduction module to reduce reference signal noise interference, improving bit error rate performance. Summary of the Invention

[0007] This invention aims to solve the problems of the prior art. It proposes a dual-mode differential chaotic shift keying method based on joint carrier and time slot index modulation. The technical solution of this invention is as follows:

[0008] A dual-mode differential chaotic shift keying method based on joint carrier and time slot index modulation includes the following steps:

[0009] Step 1: Use a chaos generator to generate a chaotic signal and copy it to obtain a reference signal;

[0010] Step 2: Perform carrier and time slot index modulation in the frequency and time domains, and combine it with dual-mode modulation to generate the information-carrying signal;

[0011] Step 3: The reference signal and the information-carrying signal are transmitted using a carrier wave;

[0012] Step 4: After the signal passes through the channel, it undergoes carrier demodulation and noise reduction to obtain the reference signal and information signal.

[0013] Step 5: Recover the index information bits and modulation bits by two-dimensional index demodulation and dual-mode demodulation.

[0014] Furthermore, step 1 involves using a chaos generator to generate a chaotic signal and replicating it to obtain a reference signal, specifically including:

[0015] At the transmitting end, the chaotic signal generator employs a second-order Logistic mapping, i.e. c k Let c be the mapping variable. Then, through sign function normalization, a chaotic signal c of length θ is obtained. x =[c x,1 ,c x,2 ,…,c x,θ ], c x,θ c is an intermediate variable in a chaotic signal, which has the characteristics of a mean of 0 and a variance of 1. x With a length of M S Perform the Kronecker product on a single-row matrix I containing all 1s (+1) to make it a copy of M. S +1 times, to obtain the reference signal Length is θ(M) S +1), M S This indicates the number of system time slots (excluding time slot 0).

[0016] Furthermore, step 2, which involves carrier and time slot index modulation in the frequency and time domains, specifically includes:

[0017] First, the binary carrier index bits and time slot index bits are converted into decimal symbols. Then, the carrier and time slot are indexed using a one-to-one k-combination mapping method; that is, for fixed n and m, all symbols... Both can be expressed as strictly decreasing sequences of length m, J = {α} m The expression is: +1,…,α1+1} represents, Representing the operation of combined formulas α m Let α represent a chosen base, where α m >…>α1≥0, take the corresponding element from the set {1,…,n}, expressed by the formula:

[0018]

[0019] in Representing the operation of combined formulas In this invention, the equivalent is n = N S &M S m=N C &M C N S N represents the number of selectable carriers. C To activate the number of carriers, M S M represents the number of selectable time slots. CThe number of active time slots is represented by the elements in set J, which are the selected active resources; therefore, the carrier index bits... Representing the operation of combined formulas in For the floor function, used to extract from N S N are selected from the carriers. C Carrier activation, slot index bits Then used from M S Select M from the time slots C Activation of each time slot, Representing the operation of combined formulas

[0020] Furthermore, step 2, which involves dual-mode modulation to generate the information-carrying signal, specifically includes:

[0021] In a dual-mode modulator, two distinguishable signals, namely d, are transmitted on the active and inactive time slots of the active and inactive carriers. u c y and a u c x +b u c y , where d u The mapping symbol for DCSK, a u b u c represents the mapping symbols for the real and imaginary parts in QCSK, respectively. y The reference signal is an orthogonal signal obtained after undergoing the Hilbert transform. The information symbol carried by the corresponding signal is represented as follows: and The specific signal distribution is represented as follows:

[0022] (1) On the active subcarrier, activate time slot transmission d u c y Inactive time slots include the transmission of time slot 0. u c x +b u c y ;

[0023] (2) On the inactive subcarrier, including the 0th subcarrier, activate the time slot transmission a. u c x +b u c y Inactive time slots include the transmission of time slot 0. u c y ;

[0024] In the information-carrying signal section, the subcarrier index factor is defined. j = 0, 1, ..., N S ,wNS The intermediate variable representing the subcarrier index factor, where w j =1 or w j =0 indicates that the j-th subcarrier is either active or inactive; similarly, the slot index factor is defined. α = 0, 1, ..., M S v MS The intermediate variable representing the slot index factor, where v α =1 or v α =0 indicates that the α-th time slot is in an active or inactive state; therefore, the expression for the j-th subcarrier is e j for:

[0025] (1) When w j When = 1, the subcarrier is activated, e j =R j =[R j (0),R j (1),...,R j (α),...,R j (M S )],in R j Let R be the expression for the activation of the j-th subcarrier. j (M S ) represents the intermediate variable of its time slot;

[0026] (2) When w j When = 0, the subcarrier is not activated, e j =G j =[G j (0),G j (1),...,G j (α),...,G j (M S )],in G j G is represented as the expression for the j-th subcarrier not being activated. j (M S ) represents the intermediate variable of its time slot.

[0027] Furthermore, step 3, which involves transmitting the reference signal and the information-bearing signal using a carrier wave, specifically includes:

[0028] A pulse shaper is used to convert a discrete signal into a continuous signal, i.e. Where h T (t-iT c ) is the impulse response generated by a pulse forming filter with a normalized energy of 1, h T T represents the spectral amplitude obtained through Fourier transform. cThe chip time is used; then, signal transmission occurs on subcarriers of different frequencies; a reference signal is applied to the center frequency f. R Transmitted on a carrier wave, the information signal is loaded onto a center frequency of f. j (j = 0, 1, ..., N) S The signal is transmitted on a carrier wave, therefore the total transmitted signal at the transmitting end can be represented in the following form:

[0029]

[0030] Where e R (t) represents the continuous reference signal, e j (t) represents the continuous information signal of the j-th subcarrier.

[0031] Furthermore, after the signal in step 4 passes through the channel, it undergoes carrier demodulation and noise reduction to obtain a reference signal and an information signal, specifically including:

[0032] The transmitted signal passes through a multipath Rayleigh fading channel consisting of L independent, identically distributed slow Rayleigh fading paths; the impulse response function of this channel model is defined as... Where L is the number of paths, λ l and τ l These are the channel coefficients and path delay; when l = 1, λ l When = 1, the Rayleigh fading channel behaves as an AWGN channel; therefore, the received signal is expressed as r(t) = s(t) * h(t) + n(t), where * is the convolution operator and n(t) is AWGN noise with zero mean and variance N0 / 2.

[0033] After receiving the signal r(t), the receiver multiplies it by the corresponding frequency carrier of each channel, and then samples it through a matched filter to recover the discrete information signal. The first received signal is then stored in vector A, which can be represented as: This represents an intermediate variable representing the received reference signal. Vector A, after sample averaging and noise reduction, yields a reference signal of length θ. Where n R The mean is 0, and the variance is N0 / [2(M S +1)];Except for the first received signal, all other signal samples are stored in matrix B as the information-carrying signal matrix.

[0034] Furthermore, step 5 recovers the index information bits and modulation bits through two-dimensional index demodulation and dual-mode demodulation, specifically including:

[0035] Step 5.1: Two-dimensional index demodulation: Then the reference signal Orthogonal signals are obtained after Hilbert transform. Since the 0th time slot and 0th subcarrier of information matrix B only carry the index result, the first column of matrix B, excluding r... 0,0 Take out the remaining terms and let them be... Divide r from the first row of matrix B 0,0 Take out the remaining terms and let them be... Reference signal With D ca and D ti Correlated rows are correlated to obtain decision matrices Q1 and Q2. N is then found from the decision variables of Q1 and Q2 respectively. C and M C The maximum value and the corresponding row number are obtained by k-combination inverse mapping to obtain the index symbol, and then the carrier and time slot index bit information are recovered by decimal to binary conversion;

[0036] Step 5.2: Dual-mode demodulation: Based on the recovered active and inactive subcarriers, demodulate the modulation bits using the corresponding two signal modes in their active and inactive time slots respectively; that is, perform DCSK demodulation in the active time slot of the active subcarrier and the inactive time slot (including the 0th time slot) of the inactive subcarrier (including the 0th time slot), and compare their samples with... Correlation is performed; QCSK demodulation is applied to the inactive slots (including slot 0) on the active subcarriers and the active slots (including slot 0) on the inactive subcarriers, and their samples are compared with... and The correlation is performed; the positive and negative results of the two cases are recovered by inverse mapping to obtain the corresponding DCSK and QCSK modulation bits.

[0037] An electronic device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the program, implements a dual-mode differential chaotic shift keying method of joint carrier and slot index modulation as described in any one of the claims.

[0038] A non-transitory computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements a dual-mode differential chaotic shift keying method of joint carrier and slot index modulation as described in any one of the claims.

[0039] A computer program product includes a computer program that, when executed by a processor, implements a dual-mode differential chaotic shift keying method of joint carrier and slot index modulation as described in any one of the present inventions. The advantages and beneficial effects of this invention are as follows:

[0040] To significantly improve transmission rate while maintaining superior bit error rate, this invention proposes a dual-mode differential chaotic shift keying method using joint carrier and time slot index modulation. This method performs index modulation through both carrier and time slot dimensions, and goes beyond single-sample indexing, using a k-combination mapping method to select one or more active samples. Two different signals, DCSK and QCSK, are then used to distinguish between active and inactive samples, increasing system security and making information less susceptible to interception. At the receiver, a noise reduction module processes the signal, effectively improving the system's noise immunity. Index recovery is then performed on the 0th time slot and the carrier separately, ensuring that the two index demodulations do not interfere with each other, thus improving bit error rate performance and reducing complexity to some extent. Finally, DCSK and QCSK demodulation methods are used to recover the modulation bits.

[0041] 1. Two-dimensional index modulation technology is adopted, namely joint carrier and time slot index modulation technology, and implemented through k-combination mapping. It utilizes both frequency and time domain resources to transmit more index information bits, achieving higher bit error rate performance. Information is carried in all active and inactive resources, avoiding the waste of subcarriers and time slots, and also avoiding signal interference problems introduced during demodulation at the receiver.

[0042] 2. A pair of orthogonal signals is generated using Hilbert transform, facilitating the construction of DCSK and QCSK signals. Since each time slot contains one or two modulation bits, the information transmission rate is significantly increased within a given spectrum. Furthermore, by placing DCSK and QCSK signals in the carrier and time slots under two different states according to certain rules, accurate demodulation of information transmission is achieved while enhancing security, thus playing a practical and reliable role in communication.

[0043] 3. Because DCSK modulation maps binary information bits to QCSK modulation maps binary information bits. The bit energy carried in the DCSK modulated resource block is less than 1, which allows the present invention to reduce the transmission energy consumed by the transmitter under the same bandwidth conditions.

[0044] 4. The receiving end employs a noise reduction module. This invention reduces the influence of reference signal noise by averaging the corresponding values ​​of the received signal in segments, thereby reducing the variance of noise in the decision variable and achieving a noise reduction effect. As the number of replications in the system increases with the number of time slots, not only does the system's transmission rate increase, but its error rate performance also improves.

[0045] 5. The index demodulation method adopted in this invention makes correlation decisions only through the 0th time slot and the carrier. This is because it carries index information, which ensures that the demodulation results between the two indices do not affect each other, reducing the demodulation difficulty. This makes the system's bit error rate performance better while also reducing its complexity. Attached Figure Description

[0046] Figure 1 This is a preferred embodiment of the transmitter structure diagram provided by the present invention;

[0047] Figure 2 This is a schematic diagram of the information-bearing signal frame structure of the present invention.

[0048] Figure 3 This is a block diagram of the receiver of the present invention;

[0049] Figure 4 Comparison of system simulation values ​​and theoretical values ​​when θ = 100, 200, 300 in this invention;

[0050] Figure 5 This invention differs from N C M C Comparison of BER curves for the system at different values;

[0051] Figure 6 This invention differs from E b At a value of / N0, the system N S M S The impact of changes on BER;

[0052] Figure 7 Comparison of BER curves of the present invention with those of the DM-DCSK-IM and PPM-DCSK systems when m=4,8;

[0053] Figure 8 Comparison of BER curves of this invention with CI-DCSK and MC-DCSK systems when n=5, 10;

[0054] Figure 9 This is a schematic diagram of a dual-mode differential chaotic shift keying method with joint carrier and time slot index modulation provided by the present invention in a preferred embodiment. Detailed Implementation

[0055] The technical solutions of the embodiments of the present invention will be clearly and thoroughly described below with reference to the accompanying drawings. The described embodiments are merely some embodiments of the present invention.

[0056] The technical solution of the present invention to solve the above-mentioned technical problems is:

[0057] The implementation of the present invention will now be described in detail with reference to the accompanying drawings. A system launch block diagram is shown below. Figure 1As shown. The chaotic signal generator uses a second-order Logistic mapping, i.e. Then, a chaotic signal c of length θ is obtained by normalization using a sign function. x =[c x,1 ,c x,2 ,...,c x,θ This chaotic signal has the digital characteristics of a mean of 0 and a variance of 1. x The signal is transformed by Hilbert to obtain c, which is orthogonal to it. y The signal is used for dual-mode modulation in the bit information transmission section.

[0058] In the information-carrying signal, the total transmitted bits are divided into three parts: carrier index bits k1, time slot index bits k2, and modulation bits k3. k1 is used to transmit data from N... S N are selected from the carriers. C One carrier is activated, and k2 is used to activate from M. S Select M from the time slots C Each time slot is activated. Specifically, the binary carrier index bits and time slot index bits are first converted into decimal symbols, and the carrier and time slot are indexed using the one-to-one k-combination mapping method proposed in reference

[18] . For fixed n and m, all symbols... Both can be expressed as strictly decreasing sequences of length m, J = {α} m The expression {α+1,…,α1+1} represents the sequence of numbers, where α... m >…>α1≥0, elements are extracted from {1,…,n}, which can be achieved using the following formula:

[0059]

[0060] For example, when n=5 and m=2, The mapping formula can then be expressed as:

[0061]

[0062] Using the above method, the decimal symbols obtained from the information bit mapping can correspond to the index carrier, such as... Figure 2 As shown, when N S =4,N C When M = 2, the carrier index bit 10 maps to symbol 2, selecting the two carriers with sequence numbers 3 and 2 to activate. Similarly, when M... S =5,M C When = 2, the sign mapped to time slot index bit 111 is 7, and the two time slots with sequence numbers 5 and 2 are selected for activation. Specifically, in Figure 2In the frame structure of the information-carrying signal, the 0th time slot and the 0th carrier are used to present the index result, which is not included in the carrier and time slot index selection range, and also facilitates the index demodulation at the receiving end.

[0063] In a dual-mode modulator, two distinguishable signals, d, are transmitted on selected and unselected carriers in selected and unselected time slots. u c y and a u c x +b u c y The information symbols carried by the corresponding signals are represented as follows: and The specific signal distribution is as follows: Figure 2 As shown, on the active subcarrier, the active time slot transmission d u c y Transmission of a inactive time slot (including time slot 0) u c x +b u c y On inactive subcarriers (including the 0th subcarrier), the active time slot transmission a u c x +b u c y Transmission of inactive time slots (including the 0th time slot) d u c y By carrying different signals in the frequency and time domains, the transmission rate can be effectively increased, and the system's security can be enhanced.

[0064] In this invention, the transmission bits of the three parts are combined with each other through corresponding indexes and modulation to obtain the total transmission bits k. T = k1 + k2 + k3. In the index bit part, since from N... S N subcarriers were selected C One subcarrier is active, therefore the number of carrier indices is [number]. in For the floor function. Similarly, from M S M was selected from the time slots. C One time slot is active, so the number of time slot indices is [number]. In the modulation bit portion, the number of modulation bits in the inactive time slots and the number of modulation bits in the active time slots on the active subcarrier are 2N respectively. C (M S -M C +1) and N C M C The number of modulation bits in the active and inactive time slots on the inactive subcarriers are 2M each. C (N S -N C+1) and (N S -N C +1)(M S -M C +1), therefore the total number of modulation bits k3 is expressed as:

[0065]

[0066] In this invention, the transmitted signal is divided into two parts: a reference signal and an information-bearing signal. In the reference signal part, c... x With a length of M S Perform a Kronecker product on the all-1 sequence I with +1 to make it copy M. S +1 times, to obtain the reference signal Length is θ(M) S +1). In the information-carrying signal section, for ease of analysis, the subcarrier exponential factor W = [w0, w1, ..., w j ,…,w NS ], j = 0, 1, ..., N S , where w j =1 or w j =0 indicates that the j-th subcarrier is either active or inactive. Similarly, the slot exponent factor is defined. α = 0, 1, ..., M S , where v α =1 or v α =0 indicates that the α-th time slot is either active or inactive. Therefore, the expression for the j-th subcarrier is:

[0067]

[0068] On the active subcarrier, the expression for each time slot can be written as:

[0069]

[0070] On inactive subcarriers, the expression for each time slot can be written as:

[0071]

[0072] A pulse shaper is used to convert a discrete signal into a continuous signal, i.e. Where h T (t-iT c ) is the impulse response generated by a pulse forming filter with a normalized energy of 1, T c This refers to the chip time. Furthermore, the paper defines the spreading factor β = θ(M). S +1). Then, signal transmission is performed on subcarriers of different frequencies. The reference signal is loaded onto the center frequency f. RTransmitted on a carrier wave, the information signal is loaded onto a center frequency of f. j Transmission on a carrier wave, assuming the center frequency is 1 / T c Multiples of and f >> 1 / T c Therefore, the total transmitted signal at the transmitting end can be represented in the following form:

[0073]

[0074] The transmitted signal passes through a multipath Rayleigh fading channel consisting of L independent, identically distributed slow Rayleigh fading paths. The impulse response function of this channel model is defined as... Where L is the number of paths, λ l and τ l These are the channel coefficients and path delay. When l = 1, λ l When τ = 1, the Rayleigh fading channel behaves as an AWGN channel. To approximate zero inter-symbol interference, the channel delay must be much smaller than the spreading factor, i.e., τ l << β. Therefore, the received signal is represented as:

[0075] r(t)=s(t)*h(t)+n(t) (7)

[0076] Where * is the convolution operator, and n(t) is AWGN noise with zero mean and variance N0 / 2.

[0077] The receiving block diagram of the present invention is as follows: Figure 3 As shown. After receiving the signal r(t), the receiver multiplies it with the corresponding carrier wave of each channel, and then samples it through a matched filter to recover the discrete information signal. The first received signal is then stored in vector A, which can be represented as: The reference signal is obtained after vector A is denoised by sample averaging. Where n R The mean is 0, and the variance is N0 / [2(M S +1). Its working principle is to divide the signal into segments, sum the values ​​at the same positions in each segment, and then calculate the average value to achieve noise reduction. The resulting new signal has a length equal to the previous one. Then the reference signal Orthogonal signals are obtained after Hilbert transform. Except for the first received signal, all other signal samples are stored in matrix B as the information-carrying signal matrix, represented as:

[0078]

[0079] Since the 0th time slot and 0th subcarrier of information matrix B are non-indexed objects, only carrying the index results, the index information can be directly demodulated on the 0th time slot and 0th subcarrier. Dividing r from the first column of matrix B...0,0 Take out the remaining terms and let them be... Similarly, divide r from the first row of matrix B. 0,0 Take out the remaining terms and let them be... Compare the reference signal with D ca and D ti Correlate each row to obtain decision matrices Q1 and Q2:

[0080]

[0081] Find N from the decision variables of Q1 and Q2 respectively. C and M C The maximum value and its corresponding row number are used to obtain the index symbol through k-combination inverse mapping, thereby recovering the carrier and time slot index bit information. Based on the recovered active and inactive subcarriers, the modulation bits are demodulated using the corresponding two signal modes in their active and inactive time slots, respectively. Specifically, DCSK demodulation is performed on the active time slot of the active subcarrier and the inactive time slot (including the 0th time slot) of the inactive subcarrier (including the 0th time slot), and its samples are compared with... Correlation is performed to recover the DCSK modulation bits; QCSK demodulation is applied to the inactive time slots (including the 0th time slot) on the active subcarrier and the active time slots (including the 0th subcarrier) on the inactive subcarrier, and their samples are compared with... and The correlation is performed to recover the QCSK modulation bits.

[0082] The Gaussian approximation method is used to analyze the noise immunity performance of this invention in Gaussian channels and multipath Rayleigh fading channels. Since the carrier and time slot index demodulation methods are consistent, the decision variables for both index demodulations are equal; therefore, only one type of index decision variable needs to be derived. When the carrier index demodulation is correct, With c x,i The QCSK received signal samples are correlated, and their decision variables are determined. Represented as:

[0083]

[0084] When carrier index demodulation is incorrect With only c y,i The DCSK received signal samples are correlated, and their decision variables are determined. Represented as:

[0085]

[0086] When θ is large in the above formula, the random variable and Since they follow a Gaussian distribution, the mean and variance of these two random variables can be calculated as follows:

[0087]

[0088] Where E[·] and Var[·] are the mean and variance operations, respectively, representing the average bit energy. In the formula E s For symbolic energy, Δ can be specifically represented as:

[0089]

[0090] Similarly, the decision variables and their mean and variance for slot index demodulation can be derived through the above calculation steps, i.e., when slot index demodulation is correct: When the time slot index demodulation is incorrect:

[0091] In the demodulation of this invention, the decision variable and All satisfy independent and identically distributed, defined

[0092] If the decision variable The minimum value is less than If the maximum value of I1 < I2 is reached, a carrier demodulation error occurs; simultaneously, a carrier demodulation error is defined. and Where n3∈{1,2,…,M} C},n4∈{1,2,…,M S -M C If the decision variable The minimum value is less than If the maximum value of I3 < I4 is reached, then a time slot demodulation error occurs. Therefore, the carrier demodulation error probability can be obtained. and time slot demodulation error probability The expression is as follows:

[0093]

[0094] in and It is a distribution function. and It is a probability density function. Due to the decision variable... and It is an independent and identically distributed Gaussian random variable, therefore the random variable and If a random variable satisfies a folded Gaussian distribution, its distribution function and probability density function can be obtained as follows:

[0095]

[0096] Where exp(·) is the exponential function and erf(·) is the error function, expressed as: Then, the bit error rate P of carrier demodulation ca Bit error rate P of time slot demodulation ti It can be represented as:

[0097]

[0098] Assuming the carrier index and time slot index are correctly demodulated, the modulation mode of each signal sample can be obtained. First, the DCSK signal sample is compared with... The relevant data represents the decision variables:

[0099]

[0100] Then the in-phase branch of the QCSK signal sample and Perform related, reverse branch and Since the two correlations are identical, it is sufficient to express only one of them. The correlation decision variable for the in-phase branch is:

[0101]

[0102] The mean and variance of formulas (27) and (28) are derived respectively, i.e.: E[Z au ] = E[Z bu ] = μ1, Therefore, the modulation bit error probabilities corresponding to the two signal modes, DCSK and QCSK, are derived as follows:

[0103]

[0104] in erfc(·) is the complementary error function, expressed as:

[0105] Since the carrier index demodulation and slot index demodulation of the system are independent of each other, and the modulation bit demodulation is related to the index result, the modulation bit error probability of this invention is divided into four cases, namely P mod =P mod1 +P mod2 +P mod3 +P mod4 Each case is represented as follows:

[0106] 1. When both the carrier index and the time slot index are demodulated correctly, the modulation bit error probability P is... mod1 for:

[0107]

[0108] in The calculation is as follows:

[0109]

[0110] 2. When the carrier index demodulation is correct but the slot index demodulation is incorrect, the modulation bit error probability P is... mod2 for:

[0111]

[0112] in The calculation is as follows:

[0113]

[0114] 3. When the carrier index demodulation is incorrect but the slot index demodulation is correct, what is the modulation bit error probability P? mod3 for:

[0115]

[0116] in The calculation is as follows:

[0117]

[0118] 4. When both the carrier index and the time slot index are demodulated incorrectly, what is the modulation bit error probability P? mod4 for:

[0119]

[0120] in The calculation is as follows:

[0121]

[0122] In summary, the bit error rate P of this invention can be derived. sys for:

[0123]

[0124] In a multipath Rayleigh fading channel, different paths are independent of each other and have the same channel gain. Let the signal-to-noise ratio gain of the l-th path in the multipath Rayleigh fading channel be... Therefore, the average signal-to-noise ratio gain is Then γ b The instantaneous probability density function can be expressed by the following formula:

[0125]

[0126] Finally, the average bit error rate formula of this invention under multipath Rayleigh fading channels can be expressed as:

[0127]

[0128] Figure 4 The influence of different chaotic sequence lengths θ on the BER performance of a dual-mode differential chaotic shift keying system with joint carrier and slot index modulation in AWGN and multipath Rayleigh fading channels was analyzed. θ was set to 100, 200, and 300, and other parameters were set to N. S =5,N C =2,M S =5,M C =2. As can be seen from the figure, the simulated value agrees well with the theoretical value, verifying the correctness of the theoretical formula derivation. Furthermore, as θ increases, the system's BER performance gradually deteriorates. This is because the noise component increases with θ, causing noise interference to severely affect the bit error rate performance. Figure 5 Analysis of the effect of the number of active subcarriers N C and the number of activation slots M C The BER performance of a dual-mode differential chaotic shift keying system with varying joint carrier and slot index modulation in AWGN and multipath Rayleigh fading channels is shown, with parameters set to θ = 100 and N. S =6,M S =8. As shown in the graph, the simulation results and the theoretical results are in good agreement. When N... C M remains constant C When M changes from 2 to 4, the bit error rate increases; when M... C N remains constant C When the value changes from 1 to 3, the bit error rate also increases. This is because the error probability of carrier and slot index detection increases with N. C and M C The increase in BER leads to a deterioration in overall BER performance. Figure 6 The bit error rate of a dual-mode differential chaotic shift keying system with joint carrier and time slot index modulation under an AWGN channel increases with the total number of index time slots M. S The changing curve. The signal-to-noise ratio E is taken separately. b / N0 is 10dB and 12dB, respectively, with relevant parameters θ = 100 and N. C =1,M C =1. Observing the curve in the graph, we can see that when M... S As the number of index slots increases, the bit error rate decreases and gradually levels off. This is because as the total number of index slots increases, the total number of transmittable bits increases, leading to a decrease in the system's bit error rate. However, M... SIncreasing the number of bits also means introducing more noise, so the trend of decreasing bit error rate diminishes, and the impact of noise gradually outweighs the impact of the total number of transmitted bits. Meanwhile, when N... S As the value increases, the system bit error rate also decreases, and E... b / N0=12dB compared to E b The BER reduction is greater when / N0 = 10dB, and overall, the bit error rate performance is better with a higher signal-to-noise ratio. Therefore, it can be concluded that the system bit error rate is significantly affected by the signal-to-noise ratio. Let the total number of carriers in the information transmission part be n, and the total number of time slots be m, i.e., n = N. S +1, m=M S +1. Figure 7 The bit error rate (BER) curves of dual-mode differential chaotic shift keying (DDS), DM-DCSK-IM, and PPM-DCSK with joint carrier and slot index modulation under different slot numbers m are presented in AWGN and multipath Rayleigh fading channels. The parameters are set to θ = 100, N. S =4, N C =1,M C =1. As can be seen from the figure, this invention exhibits better bit error rate performance than the other two systems in both channels. Furthermore, as m increases, the bit error rate performance of the dual-mode differential chaotic shift keying system with joint carrier and time slot index modulation and the PPM-DCSK system improves, while the bit error rate performance of the DM-DCSK-IM system slightly deteriorates. In the AWGN channel, when BER = 10... -4 When m=4, the performance gain of the present invention compared to the DM-DCSK-IM system and the PPM-DCSK system is approximately 1.2dB and 2.4dB, respectively. Figure 8 The bit error rate (BER) curves of dual-mode differential chaotic shift keying (DCS), CI-DCSK, and MC-DCSK systems with joint carrier and time slot index modulation under different carrier numbers n are presented in AWGN and multipath Rayleigh fading channels. Other parameters are θ = 100, M... S =4, M C =1,N C =1. As shown in the figure, this invention significantly outperforms other systems in both AWGN and multipath Rayleigh fading channels, and the bit error rate (BER) of all systems decreases as n increases. In AWGN channels, when BER = 10... -4 When n=10, the present invention requires E compared to CI-DCSK and MC-DCSK. b / N0 is reduced by approximately 1dB and 2.2dB, thus the present invention has better noise immunity.

[0129] The dual-mode differential chaotic shift keying method proposed in this invention, based on joint carrier and time slot index modulation, implements carrier and time slot indexing through a k-combination mapping method, and carries the information bits of the index result on the 0th time slot and carrier, reducing the complexity of demodulating the index bits. Then, Hilbert transform is used to generate two orthogonal sequences to construct the QCSK signal carrying the modulation bits, while another portion of the modulation bits is carried by the DCSK signal. These two signals distinguish between active and inactive time slots on each carrier, effectively improving system security. Simultaneously, noise reduction operations are employed at the receiver to reduce noise interference, achieving better bit error rate performance. The BER formula for this invention is derived in AWGN and multipath Rayleigh channels, and the accuracy and performance trend of the theoretical derivation are verified through Monte Carlo simulations. Compared with DM-DCSK-IM, PPM-DCSK, CI-DCSK, and MC-DCSK systems, this invention exhibits a lower bit error rate and better noise immunity, demonstrating its operability in practical applications and promoting the rapid development of DCSK in practical communication applications.

[0130] The systems, devices, modules, or units described in the above embodiments can be implemented by computer chips or entities, or by products with certain functions. A typical implementation device is a computer. Specifically, a computer can be, for example, a personal computer, laptop computer, cellular phone, camera phone, smartphone, personal digital assistant, media player, navigation device, email device, game console, tablet computer, wearable device, or any combination of these devices.

[0131] Computer-readable media includes both permanent and non-permanent, removable and non-removable media that can store information using any method or technology. Information can be computer-readable instructions, data structures, modules of programs, or other data. Examples of computer storage media include, but are not limited to, phase-change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technologies, CD-ROM, digital versatile optical disc (DVD) or other optical storage, magnetic tape, magnetic magnetic disk storage or other magnetic storage devices, or any other non-transferable medium that can be used to store information accessible by a computing device. As defined herein, computer-readable media does not include transient computer-readable media, such as modulated data signals and carrier waves.

[0132] It should also be noted that the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0133] The above embodiments should be understood as illustrative only and not as limiting the scope of protection of the present invention. After reading the description of the present invention, those skilled in the art can make various alterations or modifications to the present invention, and these equivalent changes and modifications also fall within the scope defined by the claims of the present invention.

Claims

1. A dual-mode differential chaotic shift keying method based on joint carrier and time slot index modulation, characterized in that, Includes the following steps: Step 1: Use a chaos generator to generate a chaotic signal and copy it to obtain a reference signal; Step 2: Perform carrier and time slot index modulation in the frequency and time domains, and combine it with dual-mode modulation to generate the information-carrying signal; Step 3: The reference signal and the information-carrying signal are transmitted using a carrier wave; Step 4: After the signal passes through the channel, it undergoes carrier demodulation and noise reduction to obtain the reference signal and information signal; Step 5: Recover the index information bits and modulation bits by two-dimensional index demodulation and dual-mode demodulation; Step 2, which involves dual-mode modulation to generate the information-carrying signal, specifically includes: In a dual-mode modulator, two distinguishable signals are transmitted on the active and inactive time slots of both the active and inactive carriers. and ,in The mapping symbol representing DCSK, , These represent the mapping symbols for the real and imaginary parts in QCSK, respectively. The orthogonal signals obtained by the Hilbert transform of the reference signal are represented by the information symbols carried by the corresponding signals. and The specific signal distribution is represented as follows: (1) Activate time slot transmission on the activated subcarrier. Inactive time slots include the transmission of time slot 0. ; (2) Activate time slot transmission on inactive subcarriers, including the 0th subcarrier. Inactive time slots include the transmission of time slot 0. ; In the information-carrying signal section, the subcarrier index factor is defined. , , The intermediate variable representing the subcarrier index factor, where or Indicates the first The subcarrier is either active or inactive; similarly, the slot index factor is defined. , , The intermediate variable representing the slot index factor, where or Indicates the first The first time slot is either active or inactive; therefore, the second time slot... Expression for striped subcarriers for: (1) When When the subcarrier is activated, ,in , Represented as the first The expression for striped subcarrier activation, Intermediate variables representing its time slots; (2) When At that time, the subcarrier was not activated. ,in , Represented as the first The expression for inactive subcarriers. The intermediate variable representing its time slot.

2. The dual-mode differential chaotic shift keying method based on joint carrier and time slot index modulation according to claim 1, characterized in that, Step 1 involves using a chaos generator to generate a chaotic signal and then replicating it to obtain a reference signal. Specifically, this includes: At the transmitting end, the chaotic signal generator employs a second-order Logistic mapping, i.e. , Let them be mapping variables; then, through sign function normalization, we obtain a length of... chaotic signals , As an intermediate variable in a chaotic signal, this chaotic signal has the digital characteristics of a mean of 0 and a variance of 1; With a length of A row matrix consisting entirely of 1s Perform the Kronecker product to make it replicate Next, a reference signal is obtained. , length is , This indicates the number of system time slots excluding time slot 0.

3. The dual-mode differential chaotic shift keying method based on joint carrier and time slot index modulation according to claim 1, characterized in that, Step 2, which involves carrier and time slot index modulation in the frequency and time domains, specifically includes: First, the binary carrier index bits and time slot index bits are converted into decimal symbols. Then, the carrier and time slot are indexed using a one-to-one k-combination mapping method; that is, for a fixed... and All symbols All use length of Strictly decreasing sequence express, Representing the operation of combined formulas , Represents a selected radix, where From the set To extract the corresponding element, the formula is as follows: in Representing the operation of combined formulas ,make =n, , For the number of optional carriers, To activate the number of carriers, The number of time slots is optional. To activate the number of time slots, the set The middle element is the selected active resource; therefore, the carrier index bit. , Representing the operation of combined formulas ,in For floor functions, used to extract from Select from carriers Carrier activation, slot index bits Then used from Select from time slots Activation of each time slot, Representing the operation of combined formulas .

4. The dual-mode differential chaotic shift keying method based on joint carrier and time slot index modulation according to claim 1, characterized in that, Step 3 involves transmitting the reference signal and the information-carrying signal using a carrier wave, specifically including: A pulse shaper is used to convert a discrete signal into a continuous signal, i.e. ,in It is the impulse response generated by a pulse forming filter with a normalized energy of 1. This represents the spectral amplitude obtained through the Fourier transform. The chip time is used; then, signal transmission occurs on subcarriers of different frequencies; the reference signal is loaded at the center frequency. Transmitted on a carrier wave, the information signal is loaded onto the center frequency. ( The signal is transmitted on a carrier wave, therefore the total transmitted signal at the transmitting end is represented in the following form: ； in Indicates a continuous reference signal. Indicates the first A continuous information signal of a subcarrier.

5. The dual-mode differential chaotic shift keying method based on joint carrier and time slot index modulation according to claim 1, characterized in that, After the signal in step 4 passes through the channel, it undergoes carrier demodulation and noise reduction to obtain the reference signal and the information signal, specifically including: Sending signals through a channel A multipath Rayleigh fading channel consists of several independent, identically distributed slow Rayleigh fading paths; the impulse response function of this channel model is defined as... ,in It is the number of paths. and These are the channel coefficients and path delay; when , At this time, a Rayleigh fading channel behaves as an AWGN channel; therefore, the received signal is represented as ,in, For convolution operators, The mean is zero and the variance is... AWGN noise; The receiver receives the signal The signal is then multiplied by the corresponding frequency carrier of each path, and after passing through a matched filter, it is sampled to recover the discrete information signal; subsequently, the first received signal is stored in a vector. In, it is represented as: , Intermediate variables representing the received reference signal; vector The length is obtained after sample averaging and noise reduction. Reference signal ,in The mean is 0 and the variance is Except for the first received signal, all other signal samples are stored in the matrix. The signal matrix serves as the information carrier.

6. The dual-mode differential chaotic shift keying method based on joint carrier and time slot index modulation according to claim 1, characterized in that, Step 5 recovers the index information bits and modulation bits through two-dimensional index demodulation and dual-mode demodulation, specifically including: Step 5.1: Two-dimensional index demodulation: Then the reference signal Orthogonal signals are obtained after Hilbert transform. Due to the information matrix The 0th time slot and the 0th subcarrier only carry the index result, so the matrix... In the first column, except Take out the remaining terms and let them be... ; to matrix In the first row, except Take out the remaining terms and let them be... ; reference signal and and Correlate each row to obtain the decision matrix. and ; respectively from and Find the decision variable and The maximum value and the corresponding row number are obtained by k-combination inverse mapping to obtain the index symbol, and then the carrier and time slot index bit information are recovered by decimal to binary conversion; Step 5.2: Dual-mode demodulation: Based on the recovered active and inactive subcarriers, demodulate the modulation bits using the corresponding two signal modes in their active and inactive time slots respectively; that is, perform DCSK demodulation in the active time slot of the active subcarrier and the inactive time slot of the inactive subcarrier, and compare their samples with... Correlation is performed; QCSK demodulation is applied to the inactive slots of the active subcarrier and the active slots on the inactive subcarrier, and their samples are compared with... and The correlation is performed; the positive and negative results of the two cases are used to recover the corresponding DCSK and QCSK modulation bits through inverse mapping.

7. An electronic device, characterized in that, The method includes a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, when the processor executes the program, it implements the dual-mode differential chaotic shift keying method of joint carrier and time slot index modulation as described in any one of claims 1 to 6.

8. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the dual-mode differential chaotic shift keying method of joint carrier and slot index modulation as described in any one of claims 1 to 6.

9. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by the processor, it implements the dual-mode differential chaotic shift keying method of joint carrier and slot index modulation as described in any one of claims 1 to 6.

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