# Integrated Communication and Measurement System with BOC-Assisted OFDM
## 2 The Transmitting and Receiving System for the Composite Signal
### Signal Model  
The composite signal designed in this paper consists of two parts: the BOC signal and the OFDM signal. The BOC signal is applied for measurement, and the OFDM signal is applied for communication. The main idea of the BOC signal is to modulate a square-wave subcarrier via spread spectrum modulation to shift the power spectrum from the central frequency to both sides [23; 24]. Consequently, the BOC signal is equivalent to a pseudorandom code sequence multiplied by a square-wave subcarrier. Moreover, the BOC signal energy is concentrated at the edges of the frequency band, thus making full use of the frequency band resources [25]. Mathematically, the BOC signal is expressed as Equation (1):  
\[S_{BOC}(t)=PRN(t)\cdot S_{sc}(t) \tag{1}\]  
where \(PRN(t)\) denotes the pseudorandom code signal and \(S_{sc}(t)\) denotes the modulated square-wave subcarrier signal. There are two types of square-wave subcarrier signals: sine and cosine [13]. Their time-domain expressions are as follows:  
\[S_{sc}(t)=\left\{ \begin{array}{ll}sign[\sin(2\pi f_{sc}t)]&(\text{Sin}- \text{BOC})\\ sign[\cos(2\pi f_{sc}t)]&(\text{Cos}-\text{BOC})\end{array} \right. \tag{2}\]  
where \(sign(\cdot)\) is the sign function and \(f_{sc}\) is the square-wave subcarrier frequency. The main idea of the OFDM signal is that the channel is divided into orthogonal subchannels and data are transmitted on the subchannels in a parallel/orthogonal manner. The OFDM modulation process is as follows. First, the serial data bits are encoded, interleaved, and digitally modulated, after which the pilot is inserted to obtain the symbol vector \(S_{k}=[S_{k}(m)]=[S_{k}(0),S_{k}(1),\ldots,S_{k}(M-1)]\), where \(S_{k}(m)\) represents the kth symbol transmitted on the mth subcarrier, with \(k=0,1,2,\ldots,\infty\) and \(m=0,1,2,\ldots,M-1\). Second, serial to parallel (S/P) conversion is executed to obtain parallel subdata bits. Finally, the inverse fast Fourier transform (IFFT) is applied to the parallel subdata bits to generate the OFDM signal. Here, each data symbol output through the IFFT is generated via the superposition of all subcarrier signals. Mathematically, the discrete-time OFDM symbol is expressed as Equation (3):  
\[S_{OFDM}(t)=\frac{1}{M}\sum_{m=0}^{M-1}S_{k}(m)\cdot e^{j2\pi km/M}=IFFT[S_{k}(m)] \tag{3}\]  
In this paper, the proposed composite signal makes use of the orthogonality of the OFDM subcarriers and the spectral characteristics of the BOC signal, and BOC modulation and OFDM modulation are combined through power control. A block diagram of the transmitting system is shown in Figure 1.  
The composite signal transmission process is as follows. First, the ranging message is modulated by the spread spectrum and square-wave subcarrier methods to generate the fundamental frequency BOC signal. Second, the serial data \(S_{k}\) are obtained by inserting the pilot after the communication message is encoded, interleaved, and digitally modulated. Convolutional coding is  
Figure 1: Transmitting system for the composite signal. adopted for coding, and quadrature phase shift keying (QPSK) modulation is adopted for digital modulation. Third, parallel subcarriers \(S_{BOC}^{\prime}\) and \(S_{k}^{\prime}\) are obtained through the S/P conversion of \(S_{BOC}\) and \(S_{k}\), respectively. Note that the parallel subcarriers both need to be subjected to the fast Fourier transform (FFT) before power control, as shown in Equation (4):  
\[ \begin{split} F_{BOC}(u)&=FFT\big{[}S_{BOC}^{ \prime}\big{]}=FFT\big{[}S_{b}(u)\big{]}\\ &=\sum_{u=0}^{U-1}S_{b}(u)\cdot e^{-\beta\pi bu/U}\end{split}  \tag{4}\]  
where \(S_{b}(u)\) denotes the \(u\)th symbol transmitted on the bth subcarrier, with \(b=0,1,2,\ldots,\infty\) and \(u=0,1,2,\ldots,U-1\). This is designed to ensure that the BOC signal at the transmitter is not compromised by the following IFFT. Moreover, to facilitate power control, the numbers of subcarriers and symbols should be consistent with those of OFDM, namely, \(b=k\), \(u=m\), and \(U=M\).