5. Performance Evaluation <strong>of</strong> Fractional Frequency Reuse in <strong>LTE</strong>peak UE throughput results shown in Figure 5.8 are obtained.SINR threshold [dB]20151050Mean throughput gain (%) Edge throughput gain (%) Peak throughput gain (%)151501051000−550−10−150−20−25−50−300.9 0.7 0.5 0.3 0.1 0.9 0.7 0.5 0.3 0.1 0.9 0.7 0.5 0.3 0.1100−10−20−30−40−50Figure 5.8: From left to right: Mean, edge, <strong>and</strong> peak throughput gain (%). Depicted is only<strong>the</strong> area where fairness is improved compared to <strong>the</strong> reuse-1 case.Constraining fairness ensures that <strong>the</strong> plotted points have a throughput distributionthat is at least as fair as <strong>the</strong> one <strong>of</strong> reuse-1. Overall, <strong>the</strong> results show that in orderto improve edge throughput, one has to sacrifice from <strong>the</strong> peak UEs <strong>and</strong>, less butalso to some extent, average throughput.Out <strong>of</strong> <strong>the</strong> fairness-enhancing set, our interest lies in showing how optimal <strong>the</strong> trade<strong>of</strong>fbetween mean throughput <strong>and</strong> fairness can be: i.e., maximizing <strong>the</strong> fairness gainwhile minimizing mean throughput loss. Thus, we are interested in finding <strong>the</strong>points where: (i) fairness is maximum relative to mean throughput loss, <strong>and</strong> (ii) <strong>the</strong>maximum achievable fairness is obtained without incurring in mean throughput loss.Figure 5.9 depicts this trade-<strong>of</strong>f between fairness <strong>and</strong> mean throughput gain/loss.Considering <strong>the</strong> FFR points depicted in Figure 5.8 (i.e., FFR configurations in whichfairness is improved with respect to <strong>the</strong> reuse-1 case), a set <strong>of</strong> points with <strong>the</strong>following components is obtained: (i) β FR , (ii) Γ thr , (iii) J FFR , (iv) mean throughput,(v) edge throughput, <strong>and</strong> (vi) peak throughput.Plotting <strong>the</strong> relation between fairness <strong>and</strong> mean throughput yields <strong>the</strong> plot in Figure5.9. Only <strong>the</strong> FFR combinations improving fairness are considered, thus <strong>the</strong>lowest (y-axis-wise) point with a 0% mean throughput gain corresponds to <strong>the</strong> reuse-1 case. The envelope <strong>of</strong> scatterplot points corresponds to <strong>the</strong> FFR configurationsin which <strong>the</strong> trade-<strong>of</strong>f between mean throughput <strong>and</strong> fairness is optimum (markedred), with <strong>the</strong> following three significant performance points highlighted: (i) optimumtrade-<strong>of</strong>f between fairness <strong>and</strong> mean throughput, (ii) no mean throughput loss,but increased fairness, <strong>and</strong> (iii) no fairness loss, but increased mean throughput.Additionally, edge <strong>and</strong> peak throughput performance are also evaluated over meanthroughput performance gain, which is shown in Figure 5.10. There, <strong>the</strong> red pointsmark <strong>the</strong> same FFR configurations marked in Figure 5.9, i.e., <strong>the</strong> optimum trade-<strong>of</strong>fFFR configurations between mean average throughput <strong>and</strong> fairness. Combining <strong>the</strong>74
5. Performance Evaluation <strong>of</strong> Fractional Frequency Reuse in <strong>LTE</strong>results shown in Figures 5.8 <strong>and</strong> 5.9, <strong>the</strong> following conclusions are drawn:ˆ Without losing any mean throughput or fairness with respect to <strong>the</strong> reuse-1 case,it is possible to obtain obtain an additional 15% average throughput, 50% edgethroughput, <strong>and</strong> 10% peak throughput.ˆ Constrained to not losing any mean throughput, fairness can be improved to 0.85,which doubles edge throughput at <strong>the</strong> cost <strong>of</strong> a 20 % loss <strong>of</strong> peak throughput.ˆ It is possible to maximally increase fairness up to 0.93 by sacrificing 15% mean,<strong>and</strong> 45% peak throughput, as well as a being able to set fairness to a variety <strong>of</strong>points in-between.fairness0.950.90.850.8optimum trade-<strong>of</strong>f betweenfairness <strong>and</strong> mean throughputno mean throughput loss,increased fairness0.750.7−30 −25 −20−15 −10 −5 0 5 10 15Mean throughput gain (%)2.4 2.6 2.8 3 3.2 3.4 3.6 3.8Mean throughput (Mbit/s)no fairness loss,increased mean throughputFigure 5.9: Trade-<strong>of</strong>f between fairness <strong>and</strong> mean throughput for round robin scheduling.Red: optimum fairness-to-mean-throughput trade-<strong>of</strong>f envelope.Edge throughput (Mbit/s)1.81.61.41.210.80.60.40.2Edge throughput gain (%)150100500−50Edge-Mean throughput trade-<strong>of</strong>f−30 −25−20−15−10 −5 0 5 10 15Mean throughput gain (%)2.4 2.6 2.8 3 3.2 3.4 3.6 3.8Mean throughput (Mbit/s)Peak throughput (Mbit/s)87.576.565.554.543.5Peak throughput gain (%)100−10−20−30−40−50Peak-Mean throughput trade-<strong>of</strong>f−30−25−20−15−10 −5 0 5 10 15Mean throughput gain (%)2.4 2.6 2.8 3 3.2 3.4 3.6 3.8Mean throughput (Mbit/s)Figure 5.10: Left: Trade-<strong>of</strong>f between edge throughput <strong>and</strong> mean throughput (round robinscheduling). Left: Trade-<strong>of</strong>f between peak throughput <strong>and</strong> mean throughput.Marked red: optimum fairness-to-mean-throughput trade-<strong>of</strong>f.75