## 4 Implementation of Joint Plans
### Joint Signal Design  
The FBMC chirp [40] and OFDM chirp [42] waveforms have been proposed in previous studies, employing the fundamental principle of modulating chirp signals onto distinct subcarrier groups. Due to the inherent orthogonality of subcarriers in OFDM and FBMC signals, signals on different subcarrier groups naturally satisfy orthogonality. This characteristic facilitates signal separation both at the transmitter and receiver ends. In order to achieve jamming functionality, UFMC signals are modulated with chirp signals, resulting in UFMC chirp. Note that the structure of UFMC chirp signals differs from that of pure OFDM chirp and FBMC chirp signals due to the inclusion of sub-band structures, along with the subcarriers in UFMC signals. This distinctive characteristic allows UFMC chirp signals to be flexibly applied to any sub-band, thus serving the dual purpose of multiple-target radar jamming and communication. Figure 4 illustrates the frequency-domain structure of the UFMC chirp signal, where the integrated signal symbols are shaped by two signals within each sub-band block. Multiplexing of the signal frequency bands is achieved by dividing the available sub-band blocks into multiple sub-bands, modulating the information to be sent to each subcarrier within each sub-band, and subsequently transmitting these signals simultaneously. Note that two orthogonal UFMC chirp waveforms are generated by zero interleaving and shifting of a single chirp spectrum as the input sequence. The proposed integrated signal technology in this study leverages the orthogonality of discrete frequency components, specifically subcarriers. Assuming the input sequence spectrum consists of \(N_{Rb}\) sub-band blocks, each sub-band block contains \(c\) discrete spectral components spaced apart by \(2\Delta f\). Initially, the input sequence is zero interleaved with \(c\) zeros, as depicted by \(X_{jam}\) in Figure 4. Next, the interleaved input sequence is shifted by \(\Delta f\) to obtain the second data sequence \(X_{com}\). These data sequences  
Figure 4: Integrated signal symbols for subcarrier modulation. the time domain through the IDFT operation with \(2c\) points. Note that both sets comprise \(2c\) subcarriers, with each set only utilizing \(c\) subcarriers to convey input data. If the spectrum of a chirp signal is employed for UFMC modulation, then the time-domain generation matrix of the UFMC chirp signal can be expressed as:  
\[\mathbf{S}= \begin{bmatrix}\mathbf{s}(0,0)&\mathbf{s}(0,1)&\cdots&\mathbf{s}(0, M-1)\\ \mathbf{s}(1,0)&\mathbf{s}(1,1)&\cdots&\mathbf{s}(1,M-1)\\ \mathbf{s}(2,0)&\mathbf{s}(2,1)&\cdots&\mathbf{s}(2,M-1)\\ \vdots&\vdots&\ddots&\vdots\\ \mathbf{s}(M-1,0)&\mathbf{s}(M-1,1)&\cdots&\mathbf{s}(M-1,M-1)\end{bmatrix}  \tag{6}\]  
where \(M\) is the number of product signals, \(s(m,n)=e^{j\pi k_{r}t^{2}}e^{j2\pi T\frac{n-m}{M}},t\in(0,T_{p})\), \(m\) is the row index of the matrix, \(n\) is the column index of the matrix, \(T_{p}\) is the pulse width of the chirp signal, and \(k_{r}\) is the frequency modulation slope of the chirp signal, expressed by the ratio of the signal bandwidth \(B\) to \(T_{p}\), (i.e., \(k_{r}=B/T_{p}\)). As shown by Equation (6), when generating \(M\) orthogonal signals, the pulse width will also increase by a factor of \(M\). In this paper, taking two orthogonal integrated radar jamming and communication signals as an example, the signal matrix is given by:  
\[\mathbf{S}_{1}= \begin{bmatrix}\mathbf{s}_{c}&\mathbf{s}_{c}\\ \mathbf{s}_{I}&\mathbf{s}_{I}\cdot e^{j\pi}\end{bmatrix}  \tag{7}\]  
where \(\mathbf{s}_{c}(t)=\mathbf{V}^{H} \begin{bmatrix}\left(\mathbf{s}_{1}\right)^{T },\left(\mathbf{s}_{2}\right)^{T},\cdots,\left(\mathbf{s}_{N_{Rb}}\right)^{T} \end{bmatrix} ^{T}\) is the communication signal to be modulated, \(\mathbf{s}_{p}\) is the modulation weight of the \(pth\) sub-band, \(\mathbf{s}_{p}= \begin{bmatrix}s_{p}[0],s_{p}[1],\cdots,s_{p}[c-1]\end{bmatrix}