## 3 Theoretical Background  
Mobile communication systems, also called mobile cellular systems, as networks are built with large numbers of base stations, where each base station covers some geographical zone. The zone is typically split into three cells. The fundamentals of telecommunications tell us that radio channel performance and capacity are driven by Signal to Noise and Interference Ratio (SINR). The signal level is driven by base station antenna radiated power, and signal propagation loss on the way from the base station to the mobile phone/modem. Noise is the thermal noise, driven by channel bandwidth. Interference is the received unwanted signal in the channel. Interference can be internal--from the same system but dedicated to other users--and external--from other systems. The downlink performance of mobile systems of the fourth and fifth generation--LTE and 5G NR--is mainly driven by internal interference. Both systems are based on OFDMA, where users in the same cell do not use the same part of the frequency band, unless there are multi-user Multiple Input Multiple Output (MIMO) techniques implemented. MIMO's impact on performance will be very limited, even in the coming years. Hence, the main source of interference is a received signal dedicated to other users, where the dominant component is inter-cell interference suffered from the neighboring cells. The quality of the radio channel in mobile systems is very different across cells, from close to the antenna to the cell edge, and dynamically changes in time, so LTE and 5G NR schedulers need to adjust parameters of connection to obtain the best possible user experience. This process is called Link Adaptation. In Link Adaption on a Time to Transmit Interval (TTI) basis with 1 ms granularity, the amount of data scheduled during TTI, and modulation and the MIMO scheme are selected to maximize the amount of data to be transmitted and the probability of the successful decoding of the data. The process is based on reports that the User Equipment (UE) sends to the base station (Figure 1), with information about the quality of a channel, defined by a 3 GPP standard as a Channel State Information report (CSI). It has three major components: a Channel Quality Indicator (CQI), Precoding Matrix Index (PMI), and Rank Indicator (RI). CQI is the most important from a link adaptation perspective, as it implicitly indicates a suitable downlink transmission data rate, i.e., the highest Modulation and Coding Scheme (MCS) value at which the UE will be able to properly demodulate and decode the downlink data at the target Block Error Rate (BLER) of 10%. CQI is measured in discrete values between 0 and 15, where index 15 indicates the best channel quality and index 0 indicates the poorest channel quality [10], while the mapping of CQI to the Modulation for the 256 QAM capable terminals, defined by 3 GPP, is presented in Table 1 (where the coder rates presented in the table are multiplied with factor 1024). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**CQI Index** & **Modulation** & **Code Rate \(\times\)1024** & **Efficiency** \\ \hline  & & Out of order & \\
1 & QPSK & 78 & 0.1523 \\
2 & QPSK & 193 & 0.3770 \\
3 & QPSK & 449 & 0.8770 \\
4 & 16 QAM & 378 & 1.4766 \\
5 & 16 QAM & 490 & 1.9141 \\
6 & 16 QAM & 616 & 2.4063 \\
7 & 64 QAM & 466 & 2.7305 \\
8 & 64 QAM & 567 & 3.3223 \\
9 & 64 QAM & 666 & 3.9023 \\
10 & 64 QAM & 772 & 4.5234 \\
11 & 64 QAM & 873 & 5.1152 \\
12 & 256 QAM & 711 & 5.5547 \\
13 & 256 QAM & 797 & 6.2266 \\
14 & 256 QAM & 885 & 6.9141 \\
15 & 256 QA & 948 & 7.4063 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Link adaptation and mapping of CQI to modulation for 256 QAM capable terminals. Figure 1: CQI reporting in a cell. The Rank Indicator is another important factor for spectral efficiency estimation, as depending on the MIMO performance, there will be roughly parallel streams in spatial multiplexing scenarios.