# Hybrid ARQ Scheme with Autonomous Retransmission for Multicasting in Wireless Sensor Networks
## 6 Simulation Results
Figure 4: Comparison of spectral efficiency when \(K=10\), MCS level is 8, and all users have the same downlink SINR. Figure 3: Comparison of spectral efficiency when \(K=10\), MCS level is 6, and all users have the same downlink SINR. Figures 6-8 indicate the performance of the proposed HARQ technique in the IEEE 802.16e downlink, when multicast users were randomly dropped within the coverage of a base station. To take into account the practical IEEE 802.16e communication environments, we performed the simulations in accordance with Section 2.4 of [24]. In SLS, the following parameters were used: 19 cells with 1 km radius; one antenna each at the transmitter and receiver sides; ITU-R path loss model for vehicular environment [22]; log-normal shadowing with a standard deviation of 8.9 dB and a cell-to-cell correlation coefficient of 0.5; and antenna height set to 10 m at the transmitter and 1.5 m at the receiver. Figures 6-8 compare spectral efficiencies when the MCS level was fixed at 4, 6, and 8, respectively. Given an MCS level, the multicast users were dropped so that the user with the worst downlink SINR had a PER less than 0.01. Furthermore, \(T=3\) was used for the proposed HARQ method considering the results in Figures 3 and 4. The proposed algorithm requires less ACK channel overhead than the conventional HARQ scheme. Therefore, the proposed algorithm exhibited better spectral efficiency than the conventional scheme. The performance of the proposed scheme relative to the conventional H-ARQ scheme increases with an increasing number of users, because the feedback overhead is proportional to the number of users. In addition, the feedback overhead is more influential when the modulation order product code rate (MPR) is high. Consequently, the proposed scheme achieved the highest spectral efficiency gain when MCS level 8 was used. As before, the performance of the proposed method was very similar to that of the autonomous method with optimal \(N\). Figure 9 shows spectral efficiency in the IEEE 802.16e downlink, obtained by SLS in accordance with Section 2.4 of [24]. The simulation was performed in a similar manner to the SLSs in Figures 6-8, except that the MCS levels were dynamically changed over 4-11 based on the downlink SINRs of multicast users. The MCS level of each drop was determined by considering the user with the worst SINR, so that the PER for multicast packets was less than 0.01. As before, the proposed method with \(T=3\) was used. The proposed algorithm presented better spectral efficiency than the conventional method, because it provides good tradeoff between the HARQ gain and the feedback overhead by properly adjusting the value \(N\). Since the feedback overhead is proportional to \(K\), the spectral efficiency gain increased with an increasing number of users. Overall, the spectral efficiency of the proposed algorithm was very similar to that of the autonomous method with theoretically optimal \(N\). Figure 5: An example of adaptation of \(N\) for different value of \(T\) in the simulation environments of Figure 4 at SINR = 11 dB. Figure 8: Comparison of spectral efficiency in the IEEE 802.16e downlink when the MCS level was fixed at 8. Figure 6: Comparison of spectral efficiency in the IEEE 802.16e downlink when the MCS level was fixed at 4. Figure 7: Comparison of spectral efficiency in the IEEE 802.16e downlink when the MCS level was fixed at 6. Another advantage of the proposed HARQ is power saving of the sensor nodes. The transmission power of the MSs is proportional to the amount of uplink resources for feedback. Figure 10 compares the sum of required uplink resource for ACK/NACK feedback and optimal \(N\) for different values of \(q_{m,k}\) when \(K=10\). It is assumed that all users have the same \(q_{m,k}\) for all HARQ transmissions. In the conventional HARQ, since the average number of ACK/NACK transmissions increases as \(q_{m,k}\) increases, the uplink feedback resources increase in proportion to the increase of \(q_{m,k}\).