# Performance Analysis of Downlink 5G Networks in Realistic Environments
## 4 Capacity Bounds Analysis
### Multiservice Capacity Bounds  
Unlike a single-service case, in a multiservice case, different radio link services, \(k\), will be requested by the user, and different spreading factors, \(SF_{i}\), different signal-to-noise ratios, \(SNR_{i}\), and therefore different service factors, \(Sk_{i}\) parameters, will be requested by the user. A simplified calculation model is suggested in this analysis, which is based on the following assumptions:  
1. \(n_{k}\) is the number of active users requiring the same radio service (\(k\)) with identical service factor values, \(S_{k}\). 2. The non-orthogonality factor, \(\varepsilon_{ij}\), is equal for different user signals \(i\) and \(j\) using the same service factor, \(S_{k}\). 3. The inter-class interference between users due to the non-orthogonality of the codes for a single-service type \(k\) is assumed to be \(\varepsilon_{k}\). In contrast, the inter-class interference factor, \(\varepsilon_{k}\), is between all users \(i\) of service \(l\), and all users \(j\) of service \(k\) are assumed to be the same. 4. The received power, \(P_{Ri}\), required at node B is assumed to be the same for all user signals using the same service, \(S_{k}\). In this case, the received power at node B is denoted by \(P_{Rk}\). Similarly to previous generations of mobile networks, in 4G networks, the power budget of the uplink differs from that of the downlink. The uplink power budget is based on the transmitted signal of the UE, whereas in the downlink, it is based on the capability of Node B. Considering the uplink power budget, each user transmits a signal with a given transmitted power, \(P_{S}\), calculated by the UE, to Node B with less power due to path loss. Consider applying the coding principle at Node B; the user's signals generate noise due to the non-orthogonality of the codes, which is referred to as the non-orthogonality factor \(\varepsilon_{ij}\). In other words, the interference \(I_{i}\) observed at Node B for user \(i\) signal is the sum of the received power of all other users \(j\) multiplied by the non-orthogonality factor \(\varepsilon_{ij}\). The interference \(I_{i}\) observed at Node B for user \(i\) signal is the sum of the received power of all the other users \(j\) multiplied by the non-orthogonality factor. In this case, there is thermal noise, \(N_{t}\), and the interference from the neighboring cells, \(\chi(\mathbf{n})\) where \(\mathbf{n}=(n_{2},\ldots,\ n_{m})\)is the number of active users in the neighboring cells. Therefore, interference \(I_{i}\) can be reformulated as follows:  
\[I_{i}=N_{t}+\chi(\mathbf{n})+\sum_{j=1,\ j\
eq i}^{n_{1}}V_{j}\cdot P_{Rj}\cdot \varepsilon_{ij} \tag{19}\]  
In Equation (19), the activity factor, \(V_{j}\), for user \(j\), which depends on the type of service user \(j\) requests, is introduced. It is also called the service activity factor. Service activity means the continuous use of some service in a cell. Monitoring voice/data activity in a cell is an important technique to reduce interference or to increase the capacity as each transmitter is switched off during the period of no activity, and these periods can be used for other data flow without losing the quality of service (QoS). Based on the spreading technique, the data symbol of a given user spreads on a certain number of chips; therefore, the spreading factor, \(SF_{i}\), is defined as the number of chips on which the data symbol spreads, creating something called the spreading gain of the signal. The more chips the signal spreads on, the higher the spreading gain, but the lower the symbol data rate is. Considering this principle, the received signal power of user \(i\) after dispreading is expressed as follows:  
\[C_{i}=SF_{i}\cdot P_{Ri} \tag{20}\]  
After decoding the signal at Node B, given the required bit error ratio (BER), a certain signal-to-noise ratio (SNR, i.e., \(E_{b}/N_{0}\)) should be satisfied for each user signal to guarantee the required quality of service (QoS).