# Cross-Cycled Uplink Resource Allocation over NB-IoT
## 2 System Model and Problem Formulation  
### System Model  
This paper considers that a cell needs to meet the uplink data requests of the NB-IoT UEs with high channel qualities, i.e., the UEs are near the cell. Figure 2 shows the NB-IoT frame structures, which adopt orthogonal frequency-division multiple access (OFDMA). The bandwidth of an uplink and a downlink channel is 180 kHz, and a radio frame is 10 ms long and contains ten subframes, each 1 ms long. In addition, an uplink subframe has 12 or 48 subcarriers, and we consider the former because it is mandatory in NB-IoT. NPRACHs and NPUSCH share the same uplink radio resources in an uplink frequency, and devices should execute the random access procedure in NPRACHs, which can be repeated with the smallest period of 40 ms and up to 2560 ms. The period can be adjusted based on traffic loading. The subcarrier space of NPRACHs is 3.75 kHz, and this paper considers that NPRACHs are predetermined. NPUSCH is used for UEs to transmit data to the cell. A cell can provide four resource unit types occupying different subcarriers in the frequency domain and subframes in the time domain: 12 subcarriers (tones) with 1 ms, six subcarriers with 2 ms, three subcarriers with 4 ms, and a subcarrier with 8 ms. A resource unit is the smallest allocable unit. A cell should decide which NB-IoT UE uses one unit type to transmit its data. To avoid interference, each subcarrier can be used by only one UE or channel. In NB-IoT systems, the data transmission of each UE must follow the control instructions, namely downlink control indicators, from the cell. The channel carrying DCIs is called the NPDCCH. Each UE should periodically monitor its NPDCCH, which is known as its search space, to decode a DCI. A UE should monitor a common search space before the random-access procedure and can monitor a specific search space after the random access procedure. This paper considers that the UEs have high channel qualities at the first CE level and monitor the same common search space. Nevertheless, this paper can also be applied directly to specific search spaces. As shown in Figure 2, the NPDCCH period of a UE consists of a series of NPDCCH subframes and a series of narrowband physical downlink share channel (NPDSCH) subframes. The number of NPDCCH subframes is determined by the parameter \(R_{max}\), and the NPDCCH period can be set by the two parameters, \(R_{max}\times G\), for a UE, where \(G\) is a system parameter [1] (Readers can refer to [13] for background about the NPDCCH period, signals in the frame structures, and CE level determination). Here, we assume that the UEs' NPDCCH period (i.e., the common search space period) has been determined. A cell should determine four parameters for a UE to use uplink radio resources: resource unit type, modulation, and coding scheme (modulation for short), scheduling delay, and resource assignment. A DCI carries these four parameters. The used unit type, modulation, signal-to-noise ratio (SNR), and amount of transmitted data will affect the required data repetition number of a UE to achieve the required transmission reliability. Therefore, some unit type and modulation combinations are not usable for a UE if the required number of repetitions is higher than the maximum repetition number. Specifically,  
Figure 2: Resource allocation protocol in NB-IoT frames. if a UE has a better channel quality, the cell can have more combination selections of a unit type and a modulation-coding scheme for the UE. Similarly, a cell transmitting a DCI for a UE should also apply a DCI repetition number to meet the reliability. After determining the above two parameters, the cell should allocate the other parameters for a UE: resource assignment and scheduling delay value. The resource assignment field is the number of units that do not include the repetition number assigned to a UE. Then, the resource assignment field and the modulation-coding index used can determine the number of bits (i.e., the transport block size (TBS)) the UE can transmit.