System Level Modeling and Optimization of the LTE Downlink

4. Extensions to the L2S ModelThe expression can be simplified by omitting the Tr () term [118], obtainingMSE = ( σ 2 eσ 2 x 0+ σ 2 v) ( ˜H H 0 ˜H 0) −1(4.16)N∑int[+i=1˜H −1 (0 σ2xiH i W i Wi H H H i) ( ) ] H˜H −10 , (4.17)where, assuming all of the entries of H i to have an average power of one, σ xi is theaverage receive power over all antennas for the i-th user (i.e., the transmit powerdivided by the pathloss).For the purpose of model validation, a fixed value for σ 2 e could be used. This settingwould, however, not be realistic. As the quality of the channel estimation varieswith the quality of the pilot symbols from which the estimation is achieved, it istherefore a function of the signal level of the pilots. Adapting from [120], we expressthe channel estimation error σ 2 e as:()σe 2 = c N∑inteσx 2 σn 2 + σx 2 i, (4.18)0i=1where a typical value for c e would be 0.0544 [120, 121] 2 .4.2.1. Model AccuracyThe model is validated in two scenarios: (i) over a SNR range, where no interferersare present and the noise level is varied and (ii) with six interferers placed on ahexagonal grid layout with omnidirectional antennas and evaluating the results onthe points corresponding to the center cell, so as to avoid border map artifacts.In both cases, the model is validated for 2×2 and 4×4 antenna configurations employingCLSM and the standard-defined precoding codebook [39]. The model isvalidated for all the possible number of spatial layers for each antenna configuration,which comprise ν = {1, 2} for the 2×2 case and ν = {1, 2, 3, 4} for the 4×4 case.As the switching between number of layers RI needs to be performed at run-time,it is not in the scope of validating the accuracy of the model to show the combinedperformance when dynamically changing the number of employed layers rather thanto evaluate whether the prediction for any possible rank choice, whichever that onemay be, is accurate.In both cases, the channel matrix is obtained from an implementation of the WinnerPhase II channel model [122], and the precoding matrix chosen so as to maximize2 Assumes a pedestrian simulation and an LMMSE channel estimator.60