# Spectrum Demand Forecasting for IoT Services
## 4 Spectrum Forecasting Model
### Adjustments  
Some technologies for IoT have not achieved a full grade of maturity, but are crucial for wireless communications and will have an important impact on improving spectral efficiency in the coming years. For this reason, it is unlikely that these technologies could provide spectrum savings (before allocation) but instead, they will simply generate a more efficient use of any of the bands used in the future IoT. In this paper, we consider two technologies that require adjustments to the calculated spectrum (MIMO and NOMA). Additionally, collisions in excessively congested scenarios will also harm spectral efficiency. We propose to quantify these impacts as follows:  
* MIMO: Multiple-input multiple-output systems have been widely used in the last decade. They provide gains in multiple important variables in wireless communications such as: reducing error probability, increasing coverage, increasing the number of served users, or increasing the total capacity (by means of an increase in the spectral efficiency). With recent advances in Massive MIMO technologies and reduced antenna hardware, more IoT devices will benefit in the future. Massive MIMO systems are especially useful for eMBB and multimedia services such as real-time high-resolution video. When MIMO systems are included in any technology (notice that many wireless technologies already include MIMO in their high transmission rates), the new (area) spectral efficiency \(\bar{\eta}^{a}_{w,i}\) for the \(i\)-th scenario should be modified as:  
\[\bar{\eta}^{a}_{w,i}=\alpha\bar{\eta}^{a}_{w,i}+(1-\alpha)\bar{\eta }^{a}_{MIMO} \tag{9}\] \[\bar{\eta}^{a}_{MIMO}=\beta\min(N_{t},N_{r})\bar{\eta}^{a}_{w,i}, \tag{10}\]  
where \(\alpha\) is the fraction of traffic using a MIMO link, \(0<\beta<1\) is the spatial correlation factor that depends on antenna separation and reduces the multiplexing gain, and \(N_{t}\) and \(N_{r}\) are the numbers of transmitting and receiving antennae. * NOMA: Non-Orthogonal Multiple Access has been long known to be optimal in some situations (Multiple Access and Broadcast Channels in Information Theory) and in general more efficient than regular orthogonal mechanisms such FDMA or TDMA, or even better than interference-limited mechanisms such CDMA. Recently, several companies have put research efforts to propose NOMA schemes and implement them on the new 5G cellular networks [47; 48]. It is likely that in some years some of these NOMA schemes will be fully deployed, especially for mMTC scenarios, where 3 GPP expects densities of one million devices connected in a square km. NOMA schemes could materialize in important gains of spectrum efficiency. An upper-bound expression to quantify these gains is proposed in [49] as follows: \[G_{NOMA}=\beta_{NOMA}\Gamma,\] (11) \[\Gamma=1+\log_{2}\left(\frac{[\prod_{i=2}^{N-1}\frac{Ni-i}{Ni-N}][1+\frac{2(N -1)p}{N}]}{N\log_{2}\left(\frac{1+Np}{1+(N-1)p}\right)}\right),\] (12) therefore: \[\bar{\eta}^{i}_{w,i}=\alpha\bar{\eta}^{a}_{w,i}+(1-\alpha)\bar{ \eta}^{a}_{NOMA}\] (13) \[\eta^{a}_{NOMA}=G_{NOMA}\eta^{a}_{w,i},\] (14) where \(N\) is the number of devices using the channel simultaneously and \(p\) is the received power for each device. The constant \(0<\beta_{NOMA}<1\) expresses how effective the NOMA gain is and \(\alpha\) is again the fraction of users using the NOMA scheme. * Collisions: Many low-power devices and sensors will not be able to handle complex access protocols or advanced receivers that help reduce the interference, hence, neither MIMO nor NOMA schemes are suitable for them. These devices will normally transmit non-urgent information at very low rates, and re-transmissions will be their best option to guarantee reliability. High-density scenarios will undoubtedly generate collisions and channel congestion.