# A Survey of Resource Allocation Techniques for Cellular Network's Operation in the Unlicensed Band
## 5 Fairness
A stochastic geometry-based approach for performance analysis of LTE-U and Wi-Fi has been presented in [64; 65]. The impact of number of users and SCs on the fairness of the system is evaluated in [64; 65], respectively. A stochastic geometry-based framework has been considered in [66] to analyze the throughput and fairness issues in Wi-Fi and LTE-U's coexistence. A discrete Markov chain-based analysis of the LAA-LBT based system is considered in [67; 61] that shows fair co-existence with an increasing number of users and SCs, respectively. In [68; 69; 70; 71], the fairness of LAA-LBT based LTE-U with respect to existing Wi-Fi users has been considered. However, the impact of increasing number of users, SCs, and operators needs to be further studied. The number of studies that analyze the fairness of LAA-LBT based channel access mechanism are larger than a similar number of studies for CSAT based channel access. However, a comprehensive study that analyzes LAA-LBT based LTE-U's fairness towards Wi-Fi with varying number of users, SCs, and operators is required. A comprehensive summary of the various studies on the fairness of CSAT and LAA-LBT based channel access mechanisms along with various channel selection schemes is presented in Table 1. Next, we explore the existing studies from the perspective of coverage, capacity, and coordination in LTE's operation in the unlicensed band. Dynamic uplink radio access selection scheme between scheduling and random access for LAA uplink transmission has been proposed in [72]. In order to exploit optimum performance, an optimization game of the uplink radio access selection has been formulated. The optimum solution of the game is proved to exist by potential game theory. The comparison of fairness between LBT and CSAT has been performed in [73]. The fundamental trade-off of co-channel interference (CI) in a licensed spectrum and collision probability on the unlicensed spectrum has been analyzed by developing a power allocation rule with double water-filling lines, and the complete set of Pareto-optimal solution has been achieved by the weighted Tchebycheff method in [22]. In [74], the LTE-U sum-rate maximization has been addressed using a cooperative Nash bargaining game for fair coexistence and a one-sided matching game for a resources allocation problem in the LTE-U system. The two games are repeated until convergence is achieved in [74]. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & & **Scale with users** & **Scale with APs/BSs** & **Scale with Operators** & **References** \\ \cline{3-5}  & & ✓ & ✓ & ✓ & [35; 53] \\ \cline{3-5}  & & ✓ & X & X & [19; 31; 54; 55] \\ \cline{3-5}  & & x & ✓ & X & [48] \\ \cline{3-5}  & & ✓ & ✓ & X & [39; 50; 66] \\ \cline{3-5}  & & & Not specified & & [49; 58] \\ \cline{3-5}  & & ✓ & ✓ & X & [27; 28] \\ \cline{3-5}  & & X & ✓ & ✓ & \\ \cline{3-5}  & & ✓ & X & X & [6; 21; 42; 61; 62; 64] \\ \cline{3-5}  & & X & ✓ & X & [23; 25; 63; 65; 67; 73] \\ \cline{3-5}  & & & Not specified & & [20; 26; 33; 41; 68; 69; 70; 71] \\ \hline \hline \end{tabular}
\end{table} 
Table 1: A summary of fair co-existence analysis of LTE with WiFi on the unlicensed band.