## 2 System Model of NR-ODBR-DCSK
### 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. Figure 3: Sliding average filter schematic. 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 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  
\[s_{i,k}=\left\{ \begin{array}{cc}x_{i_{[}\frac{1}{\beta}]},&0<k\leq\beta\\ a_{k}x^{\prime}_{i_{[}\frac{1}{\beta}]-\beta}+b_{k}x^{\prime}_{i_{[}\frac{1}{ \beta}]-\beta},\beta<k\leq 2\beta\end{array} \right. \tag{9}\]