System Level Modeling and Optimization of the LTE Downlink

5. Performance Evaluation of Fractional Frequency Reuse in LTEput) is distributed over N users. It is defined as( ∑Ni=1 x i) 2J (x) =N ∑ , (5.1)Ni=1 x2 iwhere x is a vector of length N containing the resources obtained by each of theN users. Applied to the results shown in Figure 5.6, fairness can be interpretedas either the steepness of the throughput ecdf or alternatively the flatness of theSINR-to-throughput mapping.Figure 5.7 depicts, employing the same visualization as in Figure 5.5, the obtainedfairness for all of the simulated β FR and Γ thr FFR value pairs, as well as the UEthroughput ecdf associated the following three points of interest in the plot: (i)reuse-1, (ii) reuse-3 (its closest FFR approximation, where β FR = 0.01), and (iii)β FR = 0.34, Γ thr = 10 dB, where a high fairness gain relative to reuse-1 is achieved.Empirical CDF0.91 reuse-10.80.70.60.50.40.30.20.100 1 2 3 4 5 6 7 8 9UE throughput [Mbit/s]SINR threshold [dB]20151050(i)0.90.7Fairness0.5(iii)0.30.1(ii)0.90.80.70.60.50.40.30.20.1Empirical CDFEmpirical CDF0.91 reuse-30.80.70.60.50.40.30.20.100.5 1 1.5 2 2.5 3 3.5 4UE throughput [Mbit/s]0.910.80.70.60.50.40.30.20.100 2 4 6 8 10UE throughput [Mbit/s]Figure 5.7: FFR fairness results employing round robin scheduling. The associated UEthroughput ecdf is shown for the (i) reuse-1 case, (ii) reuse3 case, and (iii)β FR = 0.34, Γ thr = 10 dB case.Ideally, an operator of an LTE network would find it desirable to obtain a fairnessgain (or at least not lose any fairness so as to avoid starvation of some UEs),while maintaining or ideally improving average throughput. Thus, ensuring that cellthroughput (i) is not reduced and (ii) is shared optimally among UEs.With this constraint, a fairness increase while maintaining average throughput impliesa throughput gain for the UEs with poor channel conditions, and vice versa.For the case depicted in Figure 5.6, a degradation in fairness from 0.69 (reuse-1fairness) to 0.32 was observed, which indicates that the observed throughput gain isdue to a more biased throughput distribution.If just the area where J FFR > J reuse1 is taken into account, the mean, edge, and73