System Level Modeling and Optimization of the LTE Downlink

3. Physical Layer Modeling and LTE System Level Simulationcan be either a 2D or a 3D pattern. In the last case, it combines a horizontal andvertical component with an optional mechanical/electrical tilt [79].ˆ L pathloss : A distance-dependent pathloss between the transmitter and the receiver.ˆ L shadow : Shadow fading, which models slow-changing deviations from the averagepathloss values that model irregularities such as geographical features. Modeledas a zero-mean space-correlated lognormal distribution.ˆ |h r,t | 2 : Assumed to be a χ 2 distribution with a number of degrees of freedom Nof two, as the underlying distribution of h is assumed to be circular symmetriccomplex normal with an average power of one.As the macro-scale parameters are scalars applied to all of the entries of the MIMOchannel matrix, it can be trivially decomposed into a normalized 3 channel matrix Hmultiplied by the factors L pathloss , L shadow , and G antenna . Applying the link budgetof Equation (3.10) to Equation (3.9) we can rewrite Equation (3.9), expressing thesubcarrier post-equalization SINR for layer i asγ i =ζ i P ′ L,0ξ i P ′ L,0 + ψ iσ 2 n +N int ∑m=1θ i,m P ′ L,m, (3.11)where PL,m ′ = P L,m · G antenna,m · L pathloss,m · L shadown,m , and the index m denotes thetransmitting eNodeB (m = 0 for the target transmitter and m = 1, . . . , N int for theinterferers).Decomposing the combined fading experienced over the link into a slowly-changingposition-dependent macro-scale component and a faster-changing small-scale [80]enables to model the fading as two separate offline-computable components: oneposition-dependent and one time-dependent.3.1.1.2. On the Modeling of OLSM and the Block Fading AssumptionOver the course of this chapter, it has been stressed that block fading is assumed,i.e., unchanging channel conditions for the duration of a TTI, and this assumptionis applied to the calculation of the post-equalization SINR in Section 3.1.1.1.However, it is clearly mentioned in Section 2.2.1.2 that the OLSM transmit mode isbased on cyclically applying a set of precoders, as well as a shift of the signal, to eachmodulated symbol during one TTI. Thus, even if a constant channel is considered,the effective channel, i.e., the combination of the channel and the precoder is notconstant during a TTI due to the applied CDD and cyclical precoding.3 Through the course of this thesis, a normalized channel matrix refers to one in which all of itsentries have a mean power of one.31