System Level Modeling and Optimization of the LTE Downlink

D. Evaluation of Multi-User GainSimilar to the analysis in [63], this simulation extends the MIMO scenario describedin Table 5.1 (but without the addition of FFR). For these results, we compare thethroughput results with a log log fit. The reasoning for this fit is based on adaptingthe assumption that, for N TX transmit antennas at the eNodeB and N RX receiveantennas at each of the K UEs, cell capacity grown with N TX log log (KN RX ) [77,145, 146] to this cellular scenario in which each UE does not experience the sameSNR 1 .A metric a log log (K b) is adopted to quantify the maximum achievable MU gainin this scenario for different antenna configurations. Denoting as log log (K b 1×1 )the MU gain for the 1×1 case and accordingly normalizing, 2×2 and 4×4 CLSMconfigurations, shown in Figures D.2 and D.3 are compared to the SISO case. Weterm a as the multiplexing gain, while b is denoted as the multi-user gain flattening,as it depicts the reduction in the capacity of the scheduler to correctly extract multiusergain.Avg. cell throughput [Mbit/s]1401301201101009080706050400Throughput 2x25 10 15 20 25 30number of UEs/cellFairness of UE throughput10.90.80.70.60.50.40.30.20.100Fairness 2x25 10 15 20 25 30number of UEs/cellRound Robin Proportional fair Best CQI fitFigure D.2: 2×2 CLSM transmit mode multi-user gain results. Left: throughput results.Right: fairness results. Vertical lines mark the 95% confidence intervals.The values obtained from a log log MSE-minimizing fit are shown in Table D.1 forthe SISO and 2×2 CLSM and 4×4 CLSM cases.Table D.1.: log log fit results for the 1×1, 2×2, and 4×4 antenna configurations.1×1 2×2 CLSM 4×4 CLSMMultiplexing gain a - 1.55 2.67MU-gain flattening b 5.6 7.07 10.33While the potential throughput of 4×4 is double that of 2×2, such gains are not1 The original expression is derived for MU-gain derived from the channel distribution, rather thanthat of the channel and the cell pathloss/layout.98