System Level Modeling and Optimization of the LTE Downlink

4. Extensions to the L2S Model4.1.2. HARQ ModelingIn this section, the concepts presented in Section 3.1.2 for the calculation of theeffective post-equalization SINR (γ eff ) are extended to the modeling of the combininggain due to the use of HARQ in constant channels. The model is based on a MIbasedinterpretation of HARQ combining and adapts the MIESM SINR averagingprocedure to take into account the total MI of the combined TB [109].As detailed in Section 4.1, the combined HARQ TB combines both repeated andnewly-transmitted bits. This combining of new and repeated information can beexpressed in terms of Accumulated Mutual Information (ACMI) [110, 111], whichwe denote as I ∗ .In the CC case, as the same bits are retransmitted M times, it can be interpretedas an increase in the receive SNR. With every retransmission, energy is added, butno new information is sent. Thus, the CC ACMI of a set of M retransmissions sentover SNR γ, can be expressed as( M)∑I∗CC (γ) = I n γ , (4.1)m=0where m denotes the m-th retransmission (m = {0, 1, . . . , M}, with m = 0 correspondingto the initial transmission) and I n denotes the BICM capacity for theemployed MCS which n bits per symbol [72], shown in Equation (3.22).For IR, if only new parity bits are sent in subsequent retransmissions, the result isan increase in the amount of information, thus increasing the ACMI such thatI IR∗ (γ) =M∑I n (γ) . (4.2)m=0For the combined CC-IR HARQ scheme employed in LTE, we define G HARQ =(M + 1) G as the total number of received bits after M retransmissions and separateinto G CC and G IR , which represent the set of repeated and non-repeated bits,respectively, where G HARQ = G CC + G IR . In this case, I ∗ results in a combinationof Equations (4.1) and (4.2), which we denote as I∗LTE (γ):I∗LTE (γ) = G ((IRn · I n 1 + G ) )CC· γ , (4.3)G HARQas G IR unique bits are sent, repeated on average(1 + G )CCtimes.G HARQ53