# Hybrid ARQ Scheme with Autonomous Retransmission for Multicasting in Wireless Sensor Networks
## 6 Simulation Results  
In this section, the performance of the proposed HARQ scheme is compared with that of the conventional HARQ scheme through system level simulations (SLSs) for multicast transmission in the IEEE 802.16e downlink [21]. Although 3 GPP LTE is more popular than IEEE 802.16e system, since 3 GPP LTE has more complex structure of HARQ operation, IEEE 802.16e is easier to apply the proposed autonomous retransmission without changing the current standard than LTE. So, we chose IEEE 802.16e for performance evaluation. Note that the proposed autonomous retransmission-based HARQ transmission can be applied to various future standards for wireless multicast. We used MATLAB for simulator development. To generate time-correlated fading channels, the ITU-R Pedestrian B channel with 10 km/h velocity was used [22]; the carrier frequency was 2.5 GHz; the bandwidth was 10 MHz with 1024 subcarriers; the sampling rate was 11.2 MHz; and the frame duration was 5 ms. For a HARQ operation, multicast packets with 384 bits were transmitted to the downlink partial use of subcarriers (PUSC) zone; \(R_{u}\) was set to 24 (a half slot in the uplink); \(M_{\max}\) was 4; four independent HARQ processes were used; the convolutional turbo code (CTC) with a code rate of 1/2 was used; Chase combining was employed at the receivers; update interval \(N\) for the proposed method was set to 100 frames; and the downlink SINR was assumed to be available to the transmitter through feedback. For random packet error generation, we used MCS levels in Table 1 and the downlink PER curves shown in [23]. Each point of the simulation results was obtained by averaging the spectral efficiency metrics over more than 200 random drops of mobile users and corresponding fading channels. In Figures 3 and 4, the spectral efficiency of the proposed method is compared to that of the conventional method when the number of multicast users is 10 (\(K=10\)) and all users have the same downlink average SINR. We used QPSK and 16 quadrature amplitude modulation (16 QAM) in Figures 3 and 4, respectively. For comparison, the spectral efficiency of transmission without the HARQ scheme (\(N=3\)) was also presented. In the low SINR regime, the number of autonomous retransmissions for the proposed HARQ method is increased to reduce feedback overhead resulting from high PER. Thus, the proposed method performs better than the conventional HARQ scheme. Since the number of autonomous retransmissions for the proposed method is decreased to avoid unnecessary autonomous retransmission in the high SINR regime, the proposed scheme achieves higher HARQ gain than the non-HARQ approach. The performance of the proposed scheme improves \begin{table}
\begin{tabular}{c c c c} \hline \hline
**MCS Level** & **Modulation** & **Code Rate** & **Spectral Efficiency (Bits/Symbol)** \\ \hline
1 & QPSK & 1/12 & 0.167 \\
2 & QPSK & 1/8 & 0.250 \\
3 & QPSK & 1/6 & 0.333 \\
4 & QPSK & 1/4 & 0.500 \\
5 & QPSK & 1/3 & 0.667 \\
6 & QPSK & 1/2 & 1.000 \\
7 & QPSK & 2/3 & 1.333 \\
8 & 16 QAM & 2/5 & 1.600 \\
9 & 16 QAM & 1/2 & 2.000 \\
10 & 16 QAM & 2/3 & 2.667 \\
11 & 64 QAM & 2/3 & 4.000 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: MCS levels. with increase in the update interval, \(T\). When \(T=3\), the proposed method performs very similarly to the autonomous method with the optimal \(N\) determined by (17), which is the theoretical upper limit. If the exact value of PER for all users in the multicast group is known at the transmitter, the optimal \(N\) can be determined by (17), but it is not possible in real situations due to the continuous change of channel conditions of multiple users. Therefore, the number of autonomous retransmissions, \(N\) is calculated using the procedure in Section 5. Figure 5 shows an example of adaptation of \(N\) with the different value of \(T\) in the simulation environment of Figure 4 at \(SINR=11\) dB. The optimal \(N\) calculated from (17) is two, and when \(T=3\), the difference between the estimated \(N\) and the optimal \(N\) is minimized.