System Level Modeling and Optimization of the LTE Downlink

3. Physical Layer Modeling and LTE System Level Simulationa decimation factor of six, which results in 2 · N RB SINR values for the whole LTEsystem bandwidth shown in Table 3.1. Additionally, due to the averaging nature ofthe rank and precoding feedback algorithms [51, 54], at least two subcarrier SINRvalues per RB are desirable.Table 3.1.: Number of calculated SINR samples for the different LTE bandwidths.Channel bandwidth (B channel ) [MHz] 1.4 3 5 10 15 20Number of SINR samples (2 · N RB ) 12 30 50 100 150 2003.1.1.1. Post-equalization SINR and Trace GenerationAs aforementioned, the complexity of the link quality model can be reduced byconsidering only a subset of the total post-equalization SINRs. For the calculation ofthe SINR itself, a simple linear receiver, the Zero Forcing (ZF) receiver, is considered.Since system level simulations are to be used where Multi-User (MU) diversity is alsoexpected to be exploited (for single-link simulations one would rather employ linklevel simulations), it can be argued that for a large number of users, the ZF receiverapproaches the average performance of the optimal receiver, since MU diversityeffect can compensate for poorly conditioned channel matrices [77].Assuming perfect channel knowledge, where the accent mark [ˆ] denotes a receiverestimate, the estimated received symbol vector ˆx can be expressed as()N∑intˆx = Gy = G H 0 x 0 + n + H i x i , (3.5)where G is the receive filter, which for the ZF receiver is calculated as the pseudoinverseof H and expressed asi=1H + = ( H H H ) -1H H , (3.6)where H H denotes the Hermitian transpose of H.For the cases where a spatial multiplexing (OLSM or CLSM) or TxD (based on theAlamouti STBC [41]) mode is employed, H denotes the effective channel matrix.For the SM cases, it can be calculated as the combination of the actual channelmatrix and the linear precoder W that maps the ν transmitted symbols 2 to theN TX transmit antennas. For TxD, the precoding-equivalent operation is shown for2 In the LTE standard, the number of simultaneously transmitted symbols is referred to as thenumber of layers, and is denoted as ν (see Chapter 2 and Section 2.2.2).29