# Remote Radio Frequency Sensing Based on 5G New Radio Positioning Reference Signals
## 4 OFDM Radar Sensing Method  
### Monostatic OFDM Radar Sensing  
The principle of the OFDM-based radar is explained in Figure 7. Let us define \(RG_{TX}\) as the transmitted resource grid and \(RG_{RX}\) as the received resource grid, obtained via OFDM demodulation of the received signal. Therefore, estimation of the channel frequency response \(H(k_{p},l_{p})\) can be obtained as follows:  
\[H(k_{p},l_{p})=\frac{RG_{RX}(k_{p},l_{p})}{RG_{TX}(k_{p},l_{p})}, \tag{12}\]  
where \(k_{p}\) denotes the \(k\)-th subcarrier used by the PRS pilot, \(l_{p}\) denotes the \(l\)-th symbol used by the PRS pilot, and the pair \((k_{p},l_{p})\) denotes the particular resource element in the resource grid. For the sensing task, all resource elements of \(H(k,l)\) that do not contain PRS pilots are zeroed. Then, the channel impulse response (CIR) is calculated from the already estimated channel frequency response (CFR) by performing an inverse FFT on all spectra of OFDM symbols that contain PRS pilots. Next, the Doppler frequency shifts are found by performing an FFT upon time-varying CIR weights, separately, tap by tap. In this way, the resultant delay-Doppler (range-velocity) matrix (DDM/RVM) is obtained.  
Since CIR cannot be longer than a longer cyclic prefix (CP), the CIR matrix can be limited to the \(N_{cp}^{long}\) or \(N_{pilots}^{symbol}\) first rows, depending on which is smaller, where \(N_{cp}^{long}\) denotes the size of the longer 5G CP and \(N_{pilots}^{symbol}\) denotes the number of PRS pilots in one OFDM symbol. Let \(N_{pilots}^{sc}\) be the number of all PRS pilots placed on a subcarrier. Since the FFT spectrum of any CIR weight is periodic (i.e., repeated by \(N_{pilots}^{sc}\) columns due to repeating blocks of zeros in the CFR matrix of the PRS pilots), we should consider only the first \(N_{pilots}^{sc}\) columns of the DDM matrix. By performing a circular shift of the columns of the resulting DDM matrix by \(\frac{N_{pilots}^{sc}}{2}+1\) elements to the right, the \(0\ Hz\) Doppler frequency shift is placed in the center of the DDM matrix. The delay-Doppler matrix can be easily transformed to the range-velocity matrix by converting delay to distance and Doppler shift to velocity (by applying Equations (16) and (20) to the row and column indices, respectively). An exemplary range-velocity matrix that was obtained after all the operations described above is presented in Figure 8. In the center of this figure, a strong clutter component is seen, originating from motionless objects in (10). In this study, \(\chi_{TX}(t)\) plays the role of a disturbed (see (11)). On the right side of the clutter, we see the peak originating from a moving object. It is significantly higher than in field measurements [31, 32, 33] and in the performed simulations in order to show its spectral side-lobes better and to visualize a risk of masking a weak echo with a strong one. In this study, we consider scenarios with only one moving object at the same time, i.e., the HST. The influence of motionless clutter can be reduced by any clutter removal algorithm (for example, by the extensive cancellation algorithm ECA-PLUS [36]); however, this topic is not addressed in this study.  
Figure 7: Principle of the OFDM-based radar exploiting PRS.