## 2 Signal Model  
Assume that \(S\) subcarriers are presented in the baseband DFRC OFDM signal, each consisting of \(N_{s}\) OFDM symbols, referred to as one-frame OFDM in this paper, included within a single pulse. After modulation, the OFDM signal for \(p\) pulses is described as  
\[s(t)=\sum\limits_{p=0}^{P-1}\sum\limits_{n=0}^{N_{s}-1}\sum\limits_{s=0}^{S-1}a_ {s,n,p}e^{|2\pi s\Delta f(t-nT_{s}-pT_{p})}rect[\frac{t-nT_{s}-pT_{p}}{T_{s}}], \tag{1}\]  
where \(a_{s,n,p}\) is communication information modulated on the \(s\)th subcarrier, with the \(n\)th OFDM symbol in the \(p\)th pulse; \(T_{s}\) is the length of a single OFDM symbol; and \(T_{p}\) is the length of a single pulse. \(S\) denotes the total number of subcarriers, and \(\Delta f\) denotes the subcarrier frequency spacing. \(rect[t/T_{s}]\) is a rectangular function defined such that, when \(0\leq t\leq T_{s}\), \(rect[t/T_{s}]\) equals 1; otherwise, it equals 0. The purpose of a cyclic prefix (CP) is to mitigate the inter-symbol interference (ISI) arising from multipath effects within the communication channel. The length of the CP must exceed the maximum delay time caused by multipath propagation, denoted as \(t_{d-\max}\). Specifically, the condition \(\max[t_{d-\max},2R_{I}/c|l=0,1,\ldots,L-1]<T_{g}\) must be satisfied. Therefore, the transmitted signal with the CP can be expressed as  
\[ \begin{array}{l}s_{CP}(t)=\sum\limits_{p=0}^{P-1}\sum\limits_{n=0}^{N_{s}-1} \sum\limits_{s=0}^{S-1}\{a_{s,n}e^{|2\pi s\Delta f(t-nT_{s}-nT_{cp}-pT_{p})} \\ \times rect[\frac{t-nT_{s}-nT_{cp}-pT_{p}}{T_{s}}]\},\end{array}  \tag{2}\]  
where \(T_{cp}\) is the duration after adding the CP. The transmitted OFDM-integrated radar and communication waveform is  
\[x(t)=s_{cp}(t)e^{|2\pi f_{c}t}, \tag{3}\]  
where \(f_{c}\) is the frequency of carriers. At the receiver, we observe the superposition of echoes reflected from all scatters within the detection area. The Taylor series expansion of the motion parameter \(R_{i}\) for the \(i\)th scattering point is given by  
\[R_{l}(t)=R_{l}+v_{l}t, \tag{4}\]  
where \(R_{l}\), \(v_{l}\) is the initial range and velocity of the \(l\) th target. Assuming that there are \(L\) targets in the environment, the multipath received signal in (4) is converted to the baseband signal as  
\[ \begin{array}{l}z(t)=\sum\limits_{l=0}^{L-1}\sum\limits_{p=0}^{P-1}\sum \limits_{n=0}^{N_{s}-1}\sum\limits_{s=0}^{S-1}\biggl{\{}\psi_{l}a_{s,n}e^{|2 \pi s\Delta f\left(t-nT_{s}-pT_{p}-nT_{cp}-\frac{2R_{l}(t)}{c}\right)}\\ \hskip 14.226378 pte^{-i2\pi f_{c}\frac{2R_{l}(t)}{c}}e^{i2\pi f_{d}t}rect\left[ \frac{t-nT_{s}-nT_{cp}-pT_{p}-(2R_{l}(t)/c)}{T_{s}}\right]\biggr{\}}\\ \hskip 14.226378 pt+n(t),\end{array}  \tag{5}\]  
where \(n(t)\) represents environmental noise, \(c\) is the light velocity, and \(\psi_{l}\) signifies the attenuation factor due to the propagation loss, scattering, and radar cross-section (RCS) of the \(l\)th target. Since OFDM is a narrowband signal, the frequency dependence of \(\psi_{l}\) can be neglected. Therefore, we assume that the attenuation factor \(\psi_{l}\) is frequency-independent in this paper. As the RCS of the \(l\)th target increases, the attenuation factor \(\psi_{l}\) also increases, thereby enhancing the estimation accuracy for the \(l\)th target.