# On the Evaluation of the NB-IoT Random Access Procedure in Monitoring Infrastructures
## 2 State of the Art
### NPRACH and Random Access Procedure  
The NPRACH has been completely redesigned [20]. In fact, the traditional LTE PRACH alone occupies a much greater bandwidth than the entire NB-IoT carrier (e.g., 1.05 MHz vs. 180 kHz). Moreover, since the LTE PRACH symbols are based on Zadoff-Chu sequences, the related signal has a non-zero peak-to-average power ratio, that reduces coverage while increasing the energy footprint. Differently, NPRACH only uses the _Single-Tone_ configuration and 3.75 kHz subcarrier spacing, hence occupying between 45 kHz and 180 kHz, according to the number of subcarriers. The NB-IoT random access preamble is shown in Figure 2. It is mainly characterized by four symbol groups, each of them comprising five OFDM symbols plus the cyclic prefix. In particular, the network configures the preamble format (i.e., the duration of the cyclic prefix), depending on the cell size. A single NPRACH preamble lasts either 5.6 ms or 6.4 ms, when Format 0 or Format 1 is applied, respectively. A pseudo-random frequency hopping algorithm offers as different preambles the number of subcarriers allocated to the NPRACH. Consequently, selecting different subcarriers at the beginning of the transmission ensures hopping schemes which never overlap. In addition, different NPRACH resource configurations can be deployed in a cell, each corresponding to a different coverage class. Each one is described through periodicity, the number of repetitions, starting time, frequency location, and the number of subcarriers, as depicted in Figure 3. Generally, an NPRACH resource is called Random Access Opportunity (RAO). Figure 1: Time–frequency structure of NB-IoT uplink channels. Figure 2: NPRACH preambles. In contrast, LTE PRACH structure is defined by predefined configuration indexes, which are broadcasted by System Information as well. In the time domain, the LTE PRACH occupies one, two or three subframes (i.e., 1, 2 or 3 ms, respectively) and it is periodically scheduled by the base station, while in the frequency domain it needs exactly six LTE RBs. The PRACH always consists of a set of 64 orthogonal sequences. Typically, the PRACH is scheduled every 5 ms and 54 preambles are dedicated to the contention-based access, while the other 10 are reserved for contention-free access. On the other hand, NB-IoT random access procedure is per se contention based [30] and entails the exchange of four messages, as depicted in Figure 4:  
1. The device finds the first available RAO and then transmits a random preamble, chosen among the available ones. Let \(s\) be the number of the available subcarriers. Then, the end device starts the RAR window, \(W\). 2. Upon preamble reception, the base station transmits an RAR that explicitly instructs the user on which uplink resources have to be utilized for the transmission of the next message. If this message is not received, the user keeps waiting for it until the expiration of \(W\). 3. Exploiting the scheduled resources, the user transmits its identity and other important information; this message is also known as Msg3. Subsequently, the terminal starts the Contention Resolution Timer
4. The base station performs the contention resolution and sends back to the devices the identity of the winning users through the Contention Resolution Message. If this message is not received, users keep waiting for it up to the Contention Resolution Timer expiration. The procedure fails when either the RAR or the Contention Resolution Message is not correctly received by mobile terminals in the proper windows. Henceforward, a worst-case scenario is assumed. Particularly, overlapping preambles always destructively interfere, therefore the base station never detects them. In other words, if two or more devices send the same preamble in a single RAO, each user fails the procedure. Each collided user may retransmit a preamble after a backoff time \(b\), chosen uniformly and at random within the interval \([0,B]\).