## 3 Dual-PRF Waveform Design and Signal Processing  
In this section, we first design two types of nonuniform sensing timings under uplink-flexible and uplink-fixed mode, respectively. And then we verify the theory performance by some experiments. At last, we detail the sensing signal processing for the designed waveform.  
According to the nonuniform of the 5G NR communication system, we propose a dual-PRF waveform design, which realizes sensing by reusing the hardware and OFDM waveform of an existing 5G NR communication base station. First, the sensing waveform and communication waveform work under time division mode. Hence, the two cannot interfere each other; that is, the sensing waveform does not impact the quality of the communication service. Second, in the 5G NR communication system, each symbol lasts for a very short time with the millimeter wave band. Hence, utilizing a small number of symbols in one frame for sensing within the millimeter wave band has very little effect on communication efficiency. More precisely, we allocate only one OFDM symbol for sensing in one time slot at most to deduce the impact on communication efficiency.  
Furthermore, according to the 5G NR communication protocol, there is some uplink slots in one frame. And one uplink slot in every five consecutive communication slots can satisfy the max uplink demand. The uplink slot can be set in any slot or fixed position among the five consecutive slots. In order to adapt the two uplink communication modes, we designed a sensing waveform under uplink-flexible mode and uplink-fixed mode, respectively. The uplink-flexible mode is called when the uplink position is flexible in every five consecutive slots. On the contrary to flexible mode, if the uplink position is fixed in one slot of every five consecutive slots, we call it uplink-fixed mode.  
As we know, if we estimate vehicle parameters by applying DFT to (8) and (9), the range resolution \(\Delta r\) can be computed by  
\[\Delta r=\frac{c}{2B}=\frac{c}{2N_{c}\Delta f} \tag{12}\]  
where \(B\) denotes the bandwidth. Then, the maximum unambiguity range \(r_{u}\) can be computed by  
\[r_{u}=\frac{c\tau_{u}}{2}=\frac{c}{2\Delta f}. \tag{13}\]  
In this paper, we take for example subcarrier interval \(\Delta f\) = 120 kHz and \(B\) = 400 MHz. Then, we can obtain the range resolution \(\Delta r\) = 0.375 m and the maximum unambiguity range \(r_{u}\) = 1.25 km. Generally, \(T_{frame}\) = 10 ms, and considering \(f_{c}\) = 26 GHz, we can compute the velocity resolution \(\Delta v\) as  
\[\Delta v=\frac{c}{2f_{c}}\Delta f_{d}=\frac{c}{2f_{c}}\frac{1}{T_{frame}}=2.0 8\ \mathrm{km/h}. \tag{14}\]  
Furthermore, according to the above parameters, the unambiguity velocity \(v_{u}\) of the uniform sensing timing can be computed as  
\[v_{u}=\pm\frac{c}{2f_{c}}f_{du}=\pm\frac{c}{2f_{c}}\frac{1}{2T_{r}}=\pm 83.08 \ \mathrm{km/h}. \tag{15}\]  
Obviously, the uniform sensing timing can satisfy the vehicle sensing by applying DFT conveniently under urban traffic scenarios. According to the descriptions of TD-ISAC,above all it can be seen that the nonuniform sensing timing does not change the uniform structure of (8). Hence, in one communication frame, it can also satisfy the vehicle sensing parameter of \(\Delta r\), \(r_{u}\) and \(\Delta v\) except \(v_{u}\). Therefore, we mainly consider the timing design of the nonuniform sensing pulse corresponding to\(f_{d}\) of the reflected object.