Design of a Differential Chaotic Shift Keying Communication System Based on Noise Reduction with Orthogonal Double Bit Rate

Abstract

In this paper, a differential chaotic shift keying communication system based on noise reduction with orthogonal double bit rate (NR-ODBR-DCSK) is proposed. The system incorporates Walsh orthogonalization at the transmitter side to orthogonalize the information signals so that two mutually orthogonal signals can be superimposed. At the receiving end, because the principle of orthogonal signals is used, it achieves the characteristic of double information transmission rate for information signal transmission while avoiding the problem of chaotic synchronization. In addition, the system employs a noise reduction transmission mechanism, which reduces the noise variance in the received signal, further reducing the BER of the system and thus improving the performance of the communication system. By analyzing the signal format of the system, the transmitter and receiver structures of the communication system are designed. Subsequently, theoretical analyses and simulations in an additive white Gaussian noise (AWGN) channel demonstrate the good performance of the system, including a low bit error rate (BER) and a good data-energy to bit-energy ratio (DBR). Finally, a simulation test of the NR-ODBR-DCSK system for a semi-physical communication system was carried out using two USRP devices to verify the experimental feasibility of the system. The simulation analysis results show that comparative analyses with conventional DCSK and SR-DCSK systems highlight the superior performance of the NR-ODBR-DCSK system.

1. Introduction

In the era of increasing threats to information security, developing robust and cost-effective solutions for secure communication has become a critical challenge, particularly in scenarios requiring resistance to eavesdropping and interference. Chaos signals, characterized by their wide continuous spectra, randomness, and ease of generation, offer a promising low-cost carrier solution for spread spectrum communication. These signals have unique properties that make them highly suitable for secure communication systems. By embedding information into chaotic signals, chaos-based communication systems inherit the well-established advantages of traditional spread spectrum systems—such as low detection probability, high interference resistance, and the ability to mitigate multipath effects. Additionally, chaotic signals further enhance data security due to their inherent unpredictability and complexity [1,2].

Chaotic digital modulation techniques, known for their simple circuitry and resistance to interception, are highly resilient to adverse channel conditions, making them particularly useful for secure communication in dynamic environments [3,4]. However, in practical applications, systems that rely on chaotic synchronization may face challenges due to the complexity of achieving and maintaining synchronization in real time. To address this, non-coherent chaos-based communication systems, which eliminate the need for synchronization, have emerged as a more feasible and attractive solution for real-world secure communication scenarios.

Differential chaos shift keying (DCSK) is a non-coherent digital modulation scheme that leverages chaotic signals. In DCSK, half of the bit duration is allocated to transmitting a reference chaotic signal, which reduces both energy efficiency and data rate [5]. Despite this, DCSK-based communication systems are well-suited for wireless sensor networks due to their low power consumption, simplicity, and robustness against channel distortion. Over time, various enhancements have been introduced to improve the energy efficiency, data rate, and error performance of DCSK systems. Reference [6] proposed the short reference differential chaos shift keying (SR-DCSK) technique to shorten the reference time slot length and improve the energy efficiency. Reference [7] improved SR-DCSK to realize wireless transmission of information and power, simplify system design and save energy. Reference [8] proposed high efficiency DCSK (HE-DCSK), which improved the data transmission efficiency by two times. Reference [9] points out that a chaotic reference sequence as a carrier reduces security. To improve the BER, reference [10] introduces the LSTM-OFDM-DCSK technique, while reference [11] proposes two-dimensional frequency and time diversity-assisted OFDM-DCSK for enhanced security. Reference [12] proposed a multicarrier DCSK (MC-DCSK) system to improve the data rate and security through a simple design, and references [13,14] further optimized its bit rate and peak-to-average power ratio. The multiuser MC-DCSK (ANC-MU-MC-DCSK) system proposed in reference [15] improves spectral efficiency and energy consumption, and reference [16] improves the reliability of multiuser transmissions through sparse code expansion. Multi-carrier chaotic modulation proposed in reference [17] is robust in time-varying hydroacoustic channels. In order to reduce the performance degradation caused by noise affecting the reference and data signals in traditional DCSK systems, reference [18] proposes a noise reduction DCSK (NR-DCSK) system, which reduces noise variance and improves system performance by averaging multiple chaotic samples. Furthermore, coding technology has been utilized to further enhance DCSK in references [19,20,21]. To enhance the data rate and energy efficiency of DCSK systems, several improvement schemes were proposed in reference [22,23,24,25].

In this paper, a novel non-coherent communication scheme called differential chaotic shift keying based on orthogonal double-rate noise reduction (NR-ODBR-DCSK) is presented. The aim is to enhance the information transmission rate of the NR-DCSK system. The design of the transmitter and receiver mechanisms is accomplished by analyzing the signal structure, and the system performance is evaluated by simulation. The results show that the proposed method not only retains a lower BER, but also enhances the information transmission rate of the system without using chaotic synchronization by incorporating the Walsh quadrature into the NR-DCSK system.

The main contributions of this paper are as follows:

Firstly, a novel non-coherent communication scheme, i.e., the reference orthogonal double-rate noise reduction based on the differential chaotic shift keying (NR-ODBR-DCSK) communication system and method, was proposed to address the low information transmission rate of the NR-DCSK system. The article described the signal frame structure, modulator, and receiver design of the system.

Secondly, the article derived the data energy ratio (DBR) and theoretical bit error rate of the NR-ODBR-DCSK system in Gaussian channels and analyzed its energy efficiency. Compared with the DCSK and NR-DCSK systems, the NR-ODBR-DCSK system saved transmission bit energy and reduced the system BER.

Finally, the article explored the optimal number of replications and the semi-diffusion factor of the NR-ODBR-DCSK system through simulation analysis and verified the physical feasibility of the NR-ODBR-DCSK system through USRP. It was found that the NR-ODBR-DCSK system outperformed the NR-DCSK and DCSK systems in terms of transmitted data rate and BER under specific SNR conditions.

2. System Model of NR-ODBR-DCSK

The main limitation of the DCSK system is the use of half of the bit duration for transmitting reference samples that do not carry information, resulting in lower data rates and reduced energy efficiency. Therefore, the development of new and improved DCSK communication systems is essential to provide higher data rates and lower BER. To address this challenge, this paper improves upon the NR-DCSK system and focuses on an NR-ODBR-DCSK system that aims to improve the energy efficiency and transmission rate of NR-DCSK. This section details the chaotic signal generator and several important elements of this system, including the signal frame structure, as well as the modulation and demodulation processes of the NR-ODBR-DCSK system.

2.1. Chaotic Signal Generator

Since chaotic signals have noise-like properties and excellent secrecy when used as carrier signals, they have received much attention and in-depth study in the field of communication research. Typical chaotic dynamical systems are categorized into discrete chaotic mapping systems, continuous chaotic systems and hyper chaotic systems, and a common method to generate chaotic signals in chaotic digital modulation systems is to utilize chaotic system mapping. In this paper, we will take logistic mapping as an example and focus on the statistical characteristics of chaotic signals. The expression of logistic mapping is as follows:

$$x_{n+1}=\mu x_n(1-x_n) n=1,2,\cdots$$

(1)

where the control parameter $\mu \in (0,1]$, and the system is in a chaotic state when $3.5699\cdots <\mu \le 4$.

The statistical properties of the logistic mapping are discussed below, and the probability density function of the logistic mapping is

$$\rho (x)=\left\{\begin{array}{c}{\displaystyle \frac{1}{\pi \sqrt{x(1-x)}}}, 0<x<1\\ 0, else\hfill \end{array}\right.$$

(2)

The average value is

$$\overline{x}=\underset{N\to +\infty }{\lim }{\displaystyle \sum _{i=1}^N{x}_i}={\displaystyle \frac{1}{2}}$$

(3)

Autocorrelation, and cross-correlation functions, respectively:

$$\begin{array}{l}{R}_{xx}(\tau )=\underset{N\to +\infty }{\lim }{\displaystyle \frac{1}{N}}{\displaystyle \sum _{n=0}^N{x}_n{x}_{n+\tau }=\left\{\begin{array}{c}0.125,\tau =0\\ 0, \tau \ne 0\hfill \end{array}\right.}\\ R_{xy}(\tau )=\underset{N\to +\infty }{\lim }{\displaystyle \frac{1}{N}}{\displaystyle \sum _{n=0}^N{x}_n{y}_{n+\tau }=0}\end{array}$$

(4)

The improved logistic mapping expression is

$$x_{n+1}=1-2x_n^2{x}_n\in (-1,1)$$

(5)

The probability density function of the improved logistic mapping is

$$\rho (x)=\left\{\begin{array}{c}{\displaystyle \frac{1}{\pi \sqrt{1-x^2}}}, -1<x<1\\ 0, else\hfill \end{array}\right.$$

(6)

The average value is

$$\overline{x}=\underset{N\to +\infty }{\lim }{\displaystyle \sum _{i=1}^N{x}_i}=0$$

(7)

The improved logistic mapping autocorrelation and mutual correlation functions are respectively:

$$\begin{array}{l}{R}_{xx}(\tau )=\underset{N\to +\infty }{\lim }{\displaystyle \frac{1}{N}}{\displaystyle \sum _{n=0}^N{x}_n{x}_{n+\tau }=\left\{\begin{array}{c}0.5,\tau =0\\ 0, \tau \ne 0\hfill \end{array}\right.}\\ R_{xy}(\tau )=\underset{N\to +\infty }{\lim }{\displaystyle \frac{1}{N}}{\displaystyle \sum _{n=0}^N{x}_n{y}_{n+\tau }=0}\end{array}$$

(8)

The autocorrelation function of the logistic mapping is plotted in Figure 1a below, and the inter-correlation function of the logistic mapping for initial values of 0.4 and 0.4001 is plotted in Figure 1b below. The reason for the absence of correlation peaks is due to the initial-value sensitivity of the chaotic system, and it is clear that even a small change in the initial chaotic values can lead to significant modifications in the entire chaotic sequence.

2.2. Signal Slot Structure of NR-ODBR-DCSK

In order to increase the information transmission rate of the NR-DCSK system, the NR-ODBR-DCSK utilizes a two-dimensional information transmission scheme. In this scheme, the one-dimensional information bits are composed of $a_k$ k-bit information bits. The information signal part of the transmitter is equipped with a Walsh quadrature converter, which aims to perform quadrature conversion processing of the delayed chaotic signal, and then multiply it with another dimension consisting of k-bit information bits $b_k$ and finally add the two mutually orthogonal chaotic signals, so as to achieve the purpose of transmitting two information bits in the information time slot.

The NR-ODBR-DCSK frame structure is shown in Figure 2.

The reference signal of the NR-ODBR-DCSK system uses only $N(N=\beta /P)$ different chaotic samples, and the chaotic samples are repeated P times consecutively to obtain a total of $\beta$ samples of the reference signal, and the reference signal is processed by the Walsh function to modulate the two bits of data information, $a_k$ and $b_k$, respectively, in the information time slot. The purpose of the orthogonal transformation is to generate two chaotic signals that are orthogonal to each other so they can be easily separated at the demodulation side.

At the receiving end, the received signal is averaged through a sliding average filter with a window length of P, and the length of the averaged signal becomes N. The principle of the sliding average filter in Figure 3 is as follows: starting from the 1st code slice of the incoming signal, the sliding average filter will sum and average P code slices at a time according to the size of the window, until it has finished averaging $\beta$ code slices, where $g_{i,k}$ is the $g(t)$ obtained by sampling the discrete signal. Finally, the resulting averaged signal is correlated with the original reference signal one way to recover the information $a_k$. The other way is correlated with the reference signal processed by the Walsh function to recover the information $b_k$.

2.3. Transmitter Structure of NR-ODBR-DCSK

Figure 4 shows the transmitter of the NR-ODBR-DCSK system. A chaotic sequence of length R is first generated by the chaotic sequence generator and sent to the buffer for cache processing. The chaotic sequence is split into two signals with equal time intervals for transmission under the control of the clocker. The first chaotic sequence is transmitted to the switch selector as a reference signal of length R. The other chaotic sequence is transmitted to the delay unit of the modulator, which is divided into two signals after delay processing and transmitted to the modulated multiplier and modulated Walsh quadrature, respectively. Subsequently, one chaotic sequence is multiplied with the initial k-bit information bit $a_k$ through the modulation multiplier to generate the modulating signal $a_k$ and transmitted to the adder, at the same time, the other chaotic sequence is orthogonally transformed through the modulating Walsh orthogonalization, and the obtained chaotic signal is then multiplied with the initial k-bit information bit $b_k$ to generate the modulating signal $b_k$ and transmitted to the adder. Finally, the modulating signal $a_k$ and the modulating signal $b_k$ are added to generate an information signal of length R for transmission to the switch selector. Each of the initial k information bits $a_k$ and $b_k$ takes the value of +1 or −1. The reference signal is summed with the information signal to generate a transmission signal, which is sent to the demodulator through the modulator via a transmission channel.

The role of the Walsh orthogonalization function in the modulator is to obtain a chaotic signal after orthogonal transformation of a chaotic sequence, and the chaotic signal is multiplied with the initial k-bit information bits b through the modulation multiplier to obtain the modulation signal b transmitted to the adder, so that the demodulator can be restored to the two sets of bits different and orthogonal to each other in binary sequences and thus obtain the chaotic signal. The clock in this modulator is used to generate a fixed-frequency clock signal, which is used to synchronize and coordinate the operation of the various parts, where the clock signal is transmitted to the chaotic sequence generator, the sampler, and the buffer, respectively, and the clock signal is multiplied by the replication parameter P for transmission to the chaotic sequence generator, and the clock signal is multiplied by the time-delay parameter for transmission to the sampler. The closure of the switch selector in the modulator is subject to the delay time generated from the clock transmitted to the sampler and controlled by the sampler, and the initial position of the switch selector is in the upper branch, which receives the chaotic sequences transmitted by the chaotic sequence generator to form a reference signal; the chaotic signals are obtained after delay and quadrature processing by Walsh’s orthogonalization function, and the switch selector is adjusted to the lower branch, and the chaotic signals are obtained by the delay time of the chaotic sequence generated by the chaotic sequence generator to form the reference signal. The switch selector is adjusted to the lower branch and by delaying the chaotic sequence transmitted by the chaotic sequence generator to form the information signal; each closure of the switch forms the first and last of the reference signal and the information signal.

The following

Table 1. Mathematical symbols applied in this chapter and their meanings.

Mathematical Symbol	Connotation
$s_{i,k}$	Modulated signal
$\beta$	Half-spreading factor
$a_k$$,b_k$	Transmitting bits of information
$x_{i,⌈\frac{k}{p}⌉}$$,x_{i,⌈\frac{k}{p}⌉-\beta }^{\prime }$	Chaotic signals and time-delayed versions
$r_i$$,r_{i-\beta }$	Received signals and time-delayed versions
$n_i$	Noise
${\displaystyle \sum }$	Summing the entire chaotic signal

is a compilation of several important mathematical symbols and the meanings they denote that are applied in this chapter.

The specific formula for said transmission signal is

$$s_{i,k}=\left\{\begin{array}{c}{x}_{i,⌈\frac{k}{p}⌉}, 0<k\le \beta \hfill \\ a_k{x}_{i,⌈\frac{k}{p}⌉-\beta }^{\prime }+b_k{x}_{i,⌈\frac{k}{p}⌉-\beta }^{\prime },\beta <k\le 2\beta \end{array}\right.$$

(9)

where $s_{i,k}$ is the ith frame of the transmitted signal, $2\beta$ is the sum of the lengths of the reference and information signals within a frame, $a_k$ is the k-bit information bit a corresponding to the ith frame signal, $b_k$ is the k-bit information bit b corresponding to the ith frame signal, $x_{i,⌈\frac{k}{p}⌉}$ is the ith frame of the chaotic sequence, $x_{i,⌈\frac{k}{p}⌉-\beta }^{\prime }$ is the chaotic signal obtained by delaying the ith frame of the chaotic signal by $\beta$, k denotes the kth frame of the transmitted signal, and $\beta$ is the length of the reference signal within a frame.

2.4. Receiver Structure of NR-ODBR-DCSK

Shown in Figure 5 is the receiver structure of NR-ODBR-DCSK.

The receiving end receives the signal from the transmitting end and generates the initial received signal. Next, the initial received signal is fed into a sliding average filter, and the signal is smoothed using a sliding average filter with a window size of P to generate a three-way transmission-averaged received signal. Subsequently, two signals are transmitted to two multipliers, and the other signal is transmitted to a delayer with a delay length of β/P. The delayed signal is divided into two transmissions, one of which is transmitted to a Walsh orthogonalization function, which performs orthogonality processing, and is subsequently multiplied with a multiplier to generate a delayed received signal, and the other transmission is transmitted to the other multiplier, which generates another delayed received signal. Next, the separately generated delayed signals are correlated with the initial received signal of one way, and the correlation value is obtained and summed to generate an output signal. At the same time, the delayed received signal is correlated with the initial received signal of the other way, the correlation value is obtained and summed, and another output signal is generated.

In order to recover the information bits $a_k$ and $b_k$, the correlator at the receiving end correlates the received signal $r_i$ with the delayed received signal $r_{i-\beta }$. The correlator is a bit time correlator. At the end of the ith bit time, the output of the correlator is

$$r_i=s_i+n_i$$

(10)

Substituting Equation (9) into (10), we get

$$\left\{\begin{array}{l}{Z}_{i,1}={\displaystyle \sum _{k=1}^{\beta /P}(x_{i,⌈\frac{k}{P}⌉}+\frac{1}{P}{\displaystyle \sum _{p=1}^P{n}_{i,P+k}})(a_k{x}_{i,⌈\frac{k}{P}⌉}+b_k{x}_{i,⌈\frac{k}{P}⌉-\beta }^{\prime }+\frac{1}{P}{\displaystyle \sum _{p=1}^P{n}_{i,P+k+\frac{\beta }{P}}})}\\ Z_{i,2}={\displaystyle \sum _{k=1}^{\beta /P}(x_{i,⌈\frac{k}{P}⌉}+\frac{1}{P}{\displaystyle \sum _{p=1}^P{n}_{i,P+k}})(b_k{x}_{i,⌈\frac{k}{P}⌉}+a_k{x}_{i,⌈\frac{k}{P}⌉-\beta }^{\prime }+\frac{1}{P}{\displaystyle \sum _{p=1}^P{n}_{i,P+k+\frac{\beta }{P}}})}\end{array}\right.$$

(11)

Notice that the input to the detector consists of three components, namely, the required signal, inter-user interference and noise.

The kth decoded symbol for the lth user, denoted by ${\widehat{a}}_k$ and ${\widehat{b}}_k$, is determined according to the following rule:

$$\begin{array}{l}{\widehat{a}}_k=\left\{\begin{array}{l}+1, Z_{i,1}>0\\ -1, Z_{i,1}\le 0\end{array}\right.\\ {\widehat{b}}_k=\left\{\begin{array}{l}+1, Z_{i,2}>0\\ -1, Z_{i,2}\le 0\end{array}\right.\end{array}$$

(12)

3. Bit Error Rate Analysis of NR-ODBR-DCSK System

In this section, Gaussian approximation (GA) is used to derive the bit error rate of the NR-ODBR-DCSK system under AWGN channel conditions, using the chaotic mapping as a normalized improved logistic mapping, which is a smooth chaotic sequence used as noise interference in the AWGN channel, with $n_i$ mean of 0, variance of $N_0/2$, and statistical independence.

Table 2. Math operators used in this chapter and their meanings.

Mathematical Symbol	Connotation
$Z_{i,1}$	Judgment signal
$E_b$	Signal energy
$E[\cdot ]$	Mean value operator
$Var[\cdot ]$	Variance operator
$erfc[\cdot ]$	Complementary error function
$\mathrm{Pr}ob[\cdot ]$	Probability function

is a compilation of several important mathematical symbols and the meanings they denote that are applied in this chapter.

Here, we only consider the BER performance of message $a_k$ and use it as a substitute for the BER performance of the whole system, so expanding $Z_{i,1}$ in Equation (11) yields

$$Z_{i,1}={\displaystyle \sum _{k=1}^{\beta /P}(\underset{required signal}{\underbrace{a_k{x}_i^2}}+\underset{\mathrm{int}ernal \mathrm{int}erference}{\underbrace{b_k{x}_i{x}^{\prime }+\frac{1}{P}{\displaystyle \sum _{p=1}^P{n}_i{x}_i}+a_k{x}_i\frac{1}{P}{\displaystyle \sum _{p=1}^P{n}_{i,P+k}}+b_k{x}_i^{\prime }\frac{1}{P}{\displaystyle \sum _{p=1}^P{n}_{i,P+k}}}}+\underset{noise}{\underbrace{\frac{1}{P}{\displaystyle \sum _{p=1}^P{n}_{i,P+k}\frac{1}{P}{\displaystyle \sum _{p=1}^P{n}_i}}}})}$$

(13)

From the signal frame structure format of the NR-ODBR-DCSK system, the signal energy within one frame can be expressed as

$$E_b=P{\displaystyle \sum _{k=1}^{\beta /P}E[x_i^2]}$$

(14)

If “+1” is transmitted for the lth user, (4) becomes

$$Z_{i,1}={\displaystyle \sum _{k=1}^{\beta /P}(\underset{required signal}{\underbrace{x_i^2}}+\underset{\mathrm{int}ernal \mathrm{int}erference}{\underbrace{b_k{x}_i{x}^{\prime }+\frac{1}{P}{\displaystyle \sum _{p=1}^P{n}_i{x}_i}+x_i\frac{1}{P}{\displaystyle \sum _{p=1}^P{n}_{i,P+k}}+b_k{x}_i^{\prime }\frac{1}{P}{\displaystyle \sum _{p=1}^P{n}_{i,P+k}}}}+\underset{noise}{\underbrace{\frac{1}{P}{\displaystyle \sum _{p=1}^P{n}_{i,P+k}\frac{1}{P}{\displaystyle \sum _{p=1}^P{n}_i}}}})}$$

(15)

Similarly, when sending “−1”, the required signal term becomes negative.

The means and variances of $Z_{i,1}$, given a “+1” or “−1” is sent, can be evaluated by numerical simulations. Denote the respective means and variances by $E[Z_{i,1}]$ and $Var[Z_{i,1}]$. Since $Z_{i,1}$ is the sum of a large number of random variables, we may assume that it is normally distributed. Hence, the approximate error probability of the ith transmitted bit is

$$\begin{array}{cc}BE{R}_{NR-ODBR-DCSK}& =2\mathrm{Pr}ob(a_k=+1)\times \mathrm{Pr}ob(Z_{i,1}\le 0\left|a_k=+1\right.)\hfill \\ & ={\displaystyle \frac{1}{2}}erfc[{\displaystyle \frac{E[Z_{i,1}\left|(a_k=+1\right.)]}{\sqrt{2Var[Z_{i,1}\left|(a_k=+1\right.)]}}}]\hfill \end{array}$$

(16)

In order to obtain the BER, we first obtain the values of the terms (expected values, variances and covariances) on the right side of Equation (15) by numerical simulations. Then, the values of mean and variance can be computed and substituted into (16) to obtain the BER. Since both numerical simulation and analytical method are involved in obtaining the BER, we refer to this method as a mixed analysis-simulation (MAS) technique.

Based on the statistical properties of chaotic sequences and signal energies, it is not difficult to conclude that

$$E[Z_{i,1}\left|(a_k=+1)\right.]=2{\displaystyle \sum _{k=1}^{\beta /P}E[x_i^2]}=2{\displaystyle \frac{E_b}{P}}$$

(17)

$$Var[Z_{i,1}\left|(a_k=+1)\right.]={\displaystyle \frac{4E_b{N}_0}{P^2}}+{\displaystyle \frac{\beta N_0^2}{4P^3}}$$

(18)

Substituting Equations (17) and (18) into Equation (16) yields the theoretical BER equation for NO-ODBR-DCSK under AWGN:

$$BE{R}_{NR-ODBR-DCSK}={\displaystyle \frac{1}{2}}erfc[{({\displaystyle \frac{2N_0}{E_b}}+{\displaystyle \frac{\beta N_0^2}{8P{E}_b^2}})}^{-\frac{1}{2}}]$$

(19)

4. Simulation Design of NR-ODBR-DCSK System Based on USRP

The software versions used in this design are LabVIEW 2021 and MATLAB 2022a, and the USRP device models used are the NI USRP-2920 and the NI USRP-2954R. In order for the LabVIEW software to be able to control the USRP devices, it is also necessary to install the NI-USRP Driver, the LabVIEW-FPGA modulation program and the NI Modulation Toolkit. The host computer communicates with the USRP device over a Gigabit Ethernet cable, and information transmission between the two USRP devices can be performed wirelessly or wired. Wireless transmission is used in this experiment, and the communication distance between the devices is set to one meter considering the limitation of the experimental site. The transmitter and receiver are equipped with two RF antennas of model VERT900, which are connected to TX1 of RF0 port and RX2 of RF1 port of USRP-2920, and TX1 of RF0 port and RX2 of RF1 port of USRP-2954R. Figure 6 shows a schematic of this experiment.

As shown in the figure, the basic flow of the experiment is as follows: first, the modulation side uses MATLAB software to generate the NR-ODBR-DCSK modulation data and saves it as a text file. Subsequently, the saved modulation data are transmitted to LabVIEW software, which processes the received data and sends the signal through the USRP-2954R device at the transmitter side. The signal is transmitted over a wireless channel, adding noise during transmission, and is finally received by the USRP-2920 device at the receiving end. The LabVIEW software at the receiving end is responsible for receiving the signal from the USRP-2920 device and generating a text file. Finally, the text file is transferred to the MATLAB software at the demodulation end for signal demodulation. Figure 7 shows the setup of the experimental scenario.

4.1. USRP-Based NR-ODBR-DCSK Transmitter

The design idea of the NR-ODBR-DCSK communication system in this section is to organize the chaotic signals generated by MATLAB simulation into the form of text, and then write the text signals into the USRP device through the LabVIEW program. The USRP device processes the text signals into the digital baseband signals, and then upconverts the signals into IF through digital up-conversion and transmits the signals into the real channel through the operations of digital-to-analog conversion, filtering and amplification. Then, the signal is transmitted to the real channel through digital-to-analog conversion, filtering and amplification, etc. The following Figure 8 shows the schematic diagram of the NR-ODBR-DCSK system transmitter through USRP:

Enter the name of the user’s USRP device in the Device Name dialog box on the front panel. By marking the name of the user’s device, the transmission of the RF signal is realized, and parameters such as the IQ sampling rate, carrier frequency, and gain are set at the same time. I and Q represent the in-phase and quadrature components of the signal data, respectively, which are divided into two paths, and the operation of the digital upconverter in the USRP is controlled by controlling the IQ rate, which in turn converts the sampling rate of the baseband IQ signal into a digital IF signal. The IQ rate is used to control the operation of the digital upconverter in the USRP, which in turn controls the sampling rate of the quadrature baseband data and upconverts the baseband IQ signal into a digital IF signal. In the front panel, the text signal data are imported into the text path, the data information in the text file is read, the text signal data are converted into a double-precision two-dimensional array, the data in the array are stored in a subset of the array, and then each signal is indexed, and the time domain waveform of the signal is displayed on the waveform graph. The channel parameters are set as follows, the transmit gain is 15.6 dBm, and its reference range is 0~35 dBm, the receive gain is 50 dBm, and its reference range is 0~99 dBm, the SNR is 20 dB, and the effective path loss is 24.4 dB. The following Figure 8 shows a diagram of the LabVIEW front panel, which sets the parameters of the transmitter as shown below.

The display waveform of an oscilloscope connected to the transmitting signal is shown in Figure 9.

In this section of the transmitter side design, the signal data are continuously written to the USRP device, so the USRP device transmits the RF signal uninterruptedly, and after stopping the running program, it releases the memory occupied by the transmitter side program while running.

4.2. USRP-Based NR-ODBR-DCSK Receiver

At the receiving end of the NR-ODBR-DCSK communication system, the RF signal from the transmitting antenna is first received via the USRP receiving antenna. The received signal is processed by a filter to limit the signal to a fixed bandwidth while filtering out some of the noise components. Next, the signals are orthogonally mixed using a mixer to obtain two orthogonal signals. Then, the analog signals are converted to digital signals by an analog-to-digital converter (ADC), and the frequency of the signals is down-converted to a range that can be processed by the host computer by digital down-conversion. The digital signals after these processes are transmitted over a network cable to the LabVIEW software, which stores the received data as a text file. Subsequently, the signal data in the text file are imported into MATLAB, and the original information code elements at the transmitting end can be recovered by running the demodulation program. The flowchart of the receiving end of the NR-ODBR-DCSK communication system is shown in Figure 10.

After running the LabVIEW program, the front panel control interface is opened as shown below, which is the USRP parameter setting program. This program is used to control the transmit parameters in the front panel, which mainly include parameters such as I/Q sampling rate, carrier frequency, antenna gain, and transmit antenna channel. The front panel schematic of the receiver side is also shown below, demonstrating the configuration of each parameter and the signal reception status of the receiver side.

After the transmission is completed, the received signal data are imported into MATLAB, and by comparing the transmitting and receiving code elements in Figure 8 and Figure 11, it can be clearly seen that the receiving code elements are exactly the same as the original information code elements at the transmitting end, indicating that the chaotic communication experiment is successful. This experiment verifies the feasibility and effectiveness of the communication schemes in the chaotic communication system through the semi-physical simulation platform.

5. Experimental Simulation Analysis

5.1. Energy Efficiency of the NR-ODBR-DCSK System

For ease of reading and understanding, this section begins with a definition of the symbols that need to be applied, as shown in

Table 3. Several signal energy representations.

Mathematical Symbol	Connotation
$E_{b-NR-ODBR-DCSK}$	NR-ODBR-DCSK signal energy
$E_{ref}$	NR-ODBR-DCSK reference signal energy
$E_{data}$	NR-ODBR-DCSK information signal energy
$DBR$	Ratio of transmitted data energy to transmitted bit energy

below.

In NR-ODBR-DCSK, the length of the reference signal in the current symbol period is $\beta$, the length of the information signal is $\beta$, and the specific equation for the bit energy transmitted in one codeword period is

$$E_{b-NR-ODBR-DCSK}=E_{ref}+E_{data}={\displaystyle \sum _{k=1}^{\beta /P}{x}_{i,⌈\frac{k}{P}⌉}^2}+{\displaystyle \sum _{k=1}^{\beta /P}{(a_k{x}_{i,⌈\frac{k}{P}⌉-\beta }^{\prime }+b_k{x}_{i,⌈\frac{k}{P}⌉-\beta }^{\prime })}^2}$$

(20)

where E denotes the signal energy, $E_{b-NR-ODBR-DCSK}$ is the NR-ODBR-DCSK signal energy, $E_{data}$ is the NR-ODBR-DCSK information signal energy, and $E_{ref}$ is the NR-ODBR-DCSK reference signal energy.

The ratio of the transmitted data energy to the transmitted bit energy of NR-ODBR-DCSK within a frame, DBR, is given by Figure 2.

$$DB{R}_{NR-ODBR-DCSK}={\displaystyle \frac{E_{data}}{E_{b-NR-ODBR-DCSK}}}=1$$

(21)

The specific equation for the signal energy of DCSK in a frame is

$$DB{R}_{DCSK}={\displaystyle \frac{E_{data-DCSK}}{E_{b-DCSK}}}={\displaystyle \frac{1}{2}}$$

(22)

where $DB{R}_{DCSK}$ is the ratio of transmitted data energy to transmitted bit energy, $E_{data-DCSK}$ is the DCSK information signal energy, and $E_{b-DCSK}$ is the DCSK signal energy.

Table 4. Comparison of DBR performance of different DCSK systems.

Names of Different Modified DCSK Systems	DBR
NR-DCSK	1
SR-DCSK	${\displaystyle \frac{\beta -R}{\beta +R}}$
RSST-SR-DCSK	${\displaystyle \frac{P+1}{P+4}}$
HE-DCSK	${\displaystyle \frac{1}{2}}$
NR-ODBR-DCSK	${\displaystyle \frac{1}{2}}$

below compares the NR-DCSK system proposed in reference [18], the SR-DCSK proposed in reference [6], the RSST-SR-DCSK system proposed in reference [26] and the HE-DCSK system proposed in reference [8]. Among them, the NR-DCSK system mainly improves the noise immunity performance, the SR-DCSK system improves the information transmission rate, the RSST-SR-DCSK system improves the information transmission security, and the HE-DCSK system provides the information transmission double-speed transmission performance.

Comparing the DBR of the NR-ODBR-DCSK with that of other DCSK systems, it can be seen firstly that the energy efficiency of the NR-ODBR-DCSK is higher than that of the DCSK and NR-DCSK systems, secondly, that it is higher than that of the SR-DCSK system in certain cases, which is dependent on the length of the half-spreading factor of the SR-DCSK system, and lastly, that the NR-ODBR-DCSK system has the same DBR as the HE-DCSK system. This is due to the fact that HE-DCSK itself also provides a double-speed information transfer rate, but HE-DCSK has not been improved in any other way except for the increased information transfer rate.

5.2. Comparison of BER Performance of Different DCSK Systems

In order to compare the BER performance of different systems, this section compares the BER performance of four modified DCSK systems, including the DCSK system, under different spreading factor conditions. The four systems are DCSK, NR-DCSK, NR-ODBR-DCSK, and RSST-SR-DCSK. The following figure shows the simulation results.

From the two Figure 12a,b, it can be seen that both the NR-ODBR-DCSK and NR-DCSK systems exhibit better bit error rate (BER) performance than the conventional DCSK and RSST-SR-DCSK systems for different $\beta$ values ($\beta =64$ and $\beta =128$). As the SNR increases, the BER of all systems decreases, but the NR-ODBR-DCSK system always exhibits the lowest BER, especially at high SNR. Comparing the cases of $\beta =64$ and $\beta =128$, it can be seen that the BER performance of the systems improves as the $\beta$-value increases; especially, the NR-ODBR-DCSK system has the lowest BER at $\beta =128$. This indicates that increasing the $\beta$-value can further improve the noise immunity of the system, and the NR-ODBR-DCSK system exhibits significant performance advantages at different $\beta$-values. Therefore, the NR-ODBR-DCSK system exhibits good BER performance under both low and high $\beta$ conditions and is especially suitable for applications in communication scenarios with different signal-to-noise ratios and noise environments.

5.3. The Impact of Different Replication Times P on the System

In order to investigate the effect of different numbers of replications P on the BER performance of the NR-ODBR-DCSK system, two sets of comparative experiments are performed in this section, one for the comparison of the system performance simulation when the number of replications is taken as 1, 5, 10, and 20 and beta is 300, as shown in Figure 13a below, and the other for the comparison of the system performance simulation when the number of replications is taken as 1, 5, 10, and 20 and beta is 100, as shown in Figure 13b below.

The figure shows that the bit error rate (BER) of the NR-ODBR-DCSK system decreases significantly as the SNR increases. The curves at different P values show that increasing the P value can effectively reduce the BER, and when P = 20, the system has the best BER, the lowest BER and the best performance at high SNR. When P = 1, the system is equivalent to a DCSK system, with significantly higher BER and relatively poor system performance. Therefore, increasing the P value can improve the noise immunity of the NR-ODBR-DCSK system and enhance the reliability of the communication system. Specifically, when P is increased from 1 to 10, the BER decreases significantly; however, when p is increased to 20, the magnitude of the performance improvement becomes smaller, indicating that P = 10 is the most effective choice to improve the system performance, and further increases in P have limited effect on the improvement in BER. Therefore, around P = 10 is the best balance point for system performance optimization, and further increasing p on this basis has less effect on BER.

6. Conclusions

In order to address the problems of low transmission rate and noise effects of DCSK system, this paper proposes a differential chaotic shift keying (NR-ODBR-DCSK) communication system based on noise suppression and orthogonal double rate. The system superimposes two mutually orthogonal signals by Walsh orthogonalization at the transmitter side to achieve double the information transmission rate while avoiding the problem of chaotic synchronization. At the receiving end, the properties of orthogonal signals are utilized to not only increase the information transmission rate, but also reduce the bit error rate (BER), which significantly improves the performance of the system.

In the NR-ODBR-DCSK system, the noise suppression transmission mechanism is used to effectively reduce the noise variance in the received signal. By analyzing the signal structure of the system, the structure of the transmitter and receiver are designed and theoretically analyzed and simulated in an additive white noise (AWGN) channel. The results show that the NR-ODBR-DCSK system not only has a low bit error rate (BER), but also achieves a good data energy to bit energy ratio (DBR) and exhibits superiority in terms of energy efficiency and transmission performance.

Finally, this paper verifies the experimental feasibility of the NR-ODBR-DCSK system by performing simulation tests of a semi-physical communication system using two USRP devices. The simulation and analysis results show that the NR-ODBR-DCSK system possesses a higher data transmission rate and lower BER under specific signal-to-noise ratio (SNR) conditions compared with the conventional DCSK and SR-DCSK systems.