# Remote Radio Frequency Sensing Based on 5G New Radio Positioning Reference Signals
## 2 5G Resource Grid, Waveform, and Positioning Reference Signal  
Fifth-generation mobile networks use OFDM modulation for radio communication purposes, as specified in [2]. The main idea of OFDM is to encode modulation symbols (e.g., QAM, QPSK) on orthogonal frequencies called subcarries at the same time so that they will not interfere with each other. In 5G, time is also divided into smaller pieces called symbols. Taking both subcarries and symbols, we can form a 5G grid in which we can insert data with different times and frequency resources, as illustrated in Figure 1.  
Figure 1: 5G NR Resource Grid. The smallest element of the NR grid that consists of one subcarrier of one OFDM symbol is called the Resource Element (RE). Twelve adjacent subcarriers create a Resource Block (RB), and the RB in a specific bandwidth part is called a Physical Resource Block (PRB). Fourteen OFDM symbols bundled together form a slot, which are then combined into subframes, ten of which make up an entire 5G frame. The number of slots per subframe (\(N_{Slots}^{Subframe,\mu}\)) and slots per frame (\(N_{Slots}^{Frame,\mu}\)) varies according to 5G numerology \(\mu\) as well as subcarrier spacing (SCS). There are seven numerologies in 5G NR, and their details are presented in Table 1. The whole 5G frame always has a duration time of 10 ms. The PRS pilots, which are used for radar sensing, are inserted into the RE of the 5G NR grid, together with user data. Therefore, the more pilots are used, the fewer data are transmitted; that is, the available communication bit stream is limited. For this reason, it is important to find a pilot configuration that allows for precise radar detection but does not limit transmission throughput too much. After pilot placement, the OFDM modulation is performed as follows: each OFDM symbol is converted to the time domain using the \(N_{fft}\)-point inverse fast Fourier transform (IFFT), after which the \(N_{cp}\) last samples of the symbol are copied to its beginning. This operation is called a cyclic prefix (CP) insertion. The CP length depends on the symbol number in a given subframe. The lengths of \(N_{fft}\) and \(N_{cp}\) are defined in Section 5.3 of [2]. Once the modulation is performed on all OFDM symbols, the time domain waveform is transmitted through the radio channel. On the receiver side, the cyclic prefix is removed, the \(N_{fft}\)-point Fast Fourier Transform (FFT) is performed, and the symbol is assigned to the 5G resource grid. For positioning tasks, the PRS is used as a pilot. One may wonder why pilots are necessary for radar sensing since the 5G NR base station knows exactly what it has sent through the radio channel in the downlink direction and can perform sensing on this basis. The answer is that the traffic on downlink channels is highly dependent on the current network conditions and the number of connected users, which implies high variability and sometimes (e.g., during night hours) a lack of downlink traffic at all. Therefore, the empty resource elements have to be interpolated, which might be time consuming depending on the number of empty REs. Pilots appropriately configured for this purpose are regular and deterministic, which allows us to skip the interpolation procedure. PRS is defined in 3 GPP TS 38.211 [2] in Section 7.4.1.7 and in 3 GPP TS 38.214 [35] in Section 5.1.6.5. PRS is composed from Gold sequences. This implies that the PRS sequence has good (high) auto-correlation characteristics and very low cross-correlation with sequences of other reference signals and data. There are many parameters that determine how PRS can be inserted into the 5G NR resource grid, making it more flexible than other reference signals and allowing for different occupation densities to be defined in the time/frequency domain. Moreover, the standard provides the possibility of configuration of more than one PRS resource. This feature is helpful in designing the PRS configuration for an OFDM-based radar and allows for beam-sweeping. The collection of multiple PRS resources is called