System Level Modeling and Optimization of the LTE Downlink

4. Extensions to the L2S ModelTo accomplish this, the subcarrier SINR vectors γ 0,...,M of each (re)transmission arestacked into a vector γ of length (M + 1) · N SCsγ = vec (γ 0 , γ 1 , . . . γ M ) , (4.5)which is then compressed into an effective SNR value γ eff by means of MIESM:γ eff (γ) = I −1n()1 ∑I n (γ(M + 1) N i ) , (4.6)SCswhere, N SCs is the total number of subcarriers. Adapting Equation (4.4), the outageprobability ε can be calculated as:⎡⎢ε = P ⎣ G IRn· I (n Nmrep · γ eff (γ) )} {{ }γ AWGNi⎤⎥< D⎦ , (4.7)where γ AWGN is denoted as the AWGN-equivalent SINR of the combined TB includingthe repetition gain.In order to consider the non-ideal behaviour of the channel coding and the loss inperformance due to the rate matching process, AWGN BLER curves are employedinstead of the outage probability. Thus, ε is approximated as:ε ≈ BLER AWGN (r m , n, γ AWGN ) . (4.8)In LTE, the values for r m cannot simply be obtained from the final code rate appliedby the rate matching [45]. However, by using the implementation of the rate matcherin [98], the equivalent puncturing matrices applied to the mother code of rate r c =1/3 can be extracted and employed to obtain the outer turbo coding rate r m andthe inner repetition coding rate 1/Nrep m for each of the HARQ retransmission indexand MCS value pairs.For each MCS and retransmission index m, the obtained effective turbo code rates(r m ) and repetition rates (Nrep) m are shown in Figure 4.5. The r m code rates requiredfor each of the modulations defined for the LTE data channel are listed in Table 4.1.Model accuracy is evaluated by means of link level simulations with the Vienna LTEsimulator [98] for both AWGN and time-correlated ITU Pedestrian-B channels [114–116].For each of the 15 LTE MCSs, the BLER curves from the simulation and from theproposed model are compared at the 10% BLER point, which is known to lead tonear-optimal performance [113] and is thus also the target BLER for link adaptation.55