Numerical Results
6.2 Comparison of Stall Avoidance Mechanisms in the Rayleigh Fading Channelthe Rayleigh Fading Channel
Figure 6.4 shows the gap-processing time of the timer-based stall avoidance mechanism in the Rayleigh fading channel with different Doppler frequencies. Let the timer expiry duration be 24 TTIs. From the figure, one can find that the average gap-processing time for the timer-based stall avoidance mechanism is longer in the Rayleigh channel with a lower Doppler frequency than that in the Rayleigh channel with a higher Doppler frequency. For example, when NEb
0 = 7 dB, the average gap-processing time for fd= 10 Hz and that for fd= 100 Hz are 39 and 30.6 TTIs, respectively. This phenomenon can be explained by the fact that a channel with a lower Doppler frequency causes a lower level crossing rate, thereby yielding a higher probability of having consecutive gaps.
Figure 6.5 compares the gap-processing time for the window-based method in the Rayleigh fading channel with a window size of 30 packets and Doppler frequencies equal to 10 Hz and 100 Hz. For NEb
0 = 7 dB, a faster varying fading channel (fd = 100 Hz) increases the gap-processing time to 74 TTIs as compared to 71.45 TTIs in the case
Figure 6.4: Effect of Doppler frequency on the gap-processing time for the timer-based stall avoid-ance mechanism with a 4-channel SAW HARQ in Rayleigh fading channels; where the Doppler fre-quency fd=10, 50, and 100 Hz.
of fd = 10 Hz. A faster varying fading channel usually has a higher packet error rate, thereby decreasing the probability of the detection window extending its size. That is, a faster fading channel may decrease the probability of the detection window being fully-booked. Consequently, in the Rayleigh fading channel with a higher Doppler frequency, the window-based stall avoidance mechanism takes longer time to detect a Type-II gap, which is different from the case in the timer-based stall avoidance mechanism.
In the Rayleigh fading channel with different Doppler frequencies (fd = 3, 10, 100 Hz), Figs. 6.6 and 6.7 show the gap-processing time performance of the indicator-based stall avoidance mechanism for the 4-channel SAW HARQ and that for the 12-channel SAW HARQ, respectively. Comparing these two figures, we find that Doppler frequency
Figure 6.5: Effect of Doppler frequency on the gap-processing time for the window-based stall avoidance mechanism with a 4-channel SAW HARQ in Rayleigh fading channels.
Figure 6.6: Effect of Doppler frequency and cycle duration on the the gap-processing time of the indicator-based stall avoidance mechanism with a 4-channel SAW HARQ in Rayleigh fading channels.
Figure 6.7: Effect of Doppler frequency and cycle duration on the the gap-processing time of the indicator-based stall avoidance mechanism with a 12-channel SAW HARQ in Rayleigh fading channels.
When the cycle duration of the multi-channel SAW HARQ is longer than the channel coherence time, all processes in the multi-channel SAW HARQ can ex-perience different channel conditions in different cycles. Hence, a process will not stay in a bad channel condition for a long period of time. This property is use-ful for the receiver to improve packet error rate performance in a multi-channel SAW HARQ process. On the contrary, when the cycle duration is shorter than the channel coherence time, the multi-channel SAW HARQ processes may en-counter a bad channel condition for several cycles, which will detain the receiver to receive a packet successfully. Thus, a shorter cycle duration decreases the success probability of all processes receiving packets, thereby increasing the gap-processing time. From [28], the channel coherence time can be calculated by
and 0.024 seconds, respectively. The cycle duration of the 4-channel SAW HARQ (0.008 seconds) is shorter than the coherence time (0.0596 and 0.0179 seconds) with fd = 3 and 10 Hz, respectively. Hence, the gap-processing time for fd = 3 and 10 Hz are worse than that of fd= 100 Hz, as shown in the Fig. 6.6. In Fig.
6.7, it is also shown that the gap-processing time of fd = 3 Hz is longer than that of fd= 10 and 100 Hz because the cycle duration for the 12-channel (0.024 seconds) is shorter than the channel coherence time with fd= 3 Hz (0.0596 secs), but longer than that with fd = 10 (0.0179 secs) and that of 100 Hz (0.00179 secs).
2. Doppler effect:
(a) Case I: cycle duration < channel coherence time
In this case, we find that the higher the Doppler frequency, the shorter the gap-processing time. In Fig. 6.6, for Eb/N0 = 7 dB, the gap-processing time with fd=10 Hz is 24.7 TTIs, and the one with fd = 3 Hz is 60.8 TTIs. In this example, the changing rate of a Rayleigh fading channel with fd = 3 and 10 Hz is not fast enough for the 4-channel SAW HARQ to provide different channel conditions in adjacent cycles. Compared to fd = 3 Hz, the channel with fd = 10 Hz has a higher probability to provide different channel conditions in different cycles. Thus, the indicator-based stall avoid-ance mechanism can have shorter gap-processing time in the channel with fd= 10 Hz than that in the channel with fd= 3 Hz.
(b) Case II: cycle duration ≥ channel coherence time
In this situation, we find that the higher the Doppler frequency, the longer will be the gap-processing time. For Eb/N0 = 7 dB in Fig. 6.7, it is shown that the average gap-processing time with fd = 100 Hz is 50 TTIs, and the one with fd = 10 Hz is 38.7 TTIs. For the 12-channel SAW HARQ, the changing rate of a Rayleigh fading channel with fd = 10 and 100 Hz is always fast enough to provide different channel conditions in different
cycles. In this situation, a higher Doppler frequency may cause a higher packet error rate because an erroneous bit may corrupt a whole packet.
When the cycle duration is longer than the channel coherence time, the average gap-processing time in a channel with a higher Doppler frequency is therefore longer than that in a channel with a lower Doppler frequency.
From the above physical/MAC cross-layer investigation, we can suggest a design prin-ciple for the indicator-based stall avoidance mechanism to determine the number of processes of the channel SAW HARQ as follows: (the cycle duration of the multi-channel SAW HARQ ≈ the multi-channel coherence time of the Rayleigh fading multi-channel).
Figure 6.8 compares the gap-oriented goodput performance between the enhanced indicator-based stall avoidance mechanism and the traditional indicator-based stall avoidance mechanism in a Rayleigh fading channel. We consider a data burst with 150 packets. For the case with fd = 100 Hz and Eb/N0 = 7 dB, we find that the gap-oriented goodput of the enhanced indicator based stall avoidance mechanism is 0.49, while the gap-oriented goodput of the traditional indicator based method is 0.37.
In the considered case, the short-term goodput performance of the proposed enhanced indicator based stall avoidance mechanism is 32% better than that of the conventional indicator-based method. Note that both stall avoidance mechanisms have the similar average gap-processing time.
Figure 6.8: Comparison of gap-oriented goodput between the enhanced indicator-based and the traditional indicator-based stall avoidance mechanisms with a 4-channel SAW HARQ in the Rayleigh fading channel.
Chapter 7 Conclusions
In this report, we have investigated the performance of four stall avoidance mechanisms for the WCDMA system with HSDPA in both the AWGN channel and the Rayleigh fading channel. By analysis and simulation, we show that the indicator-based stall avoidance mechanism performs better than the timer-based and the window-based stall avoidance mechanism in terms of gap-processing time. Furthermore, we propose an enhanced indicator-based scheme to improve the short-term goodput performance for the current indicator-based scheme.
More importantly, we have derived analytical expressions for the gap-processing time of the considered stall avoidance mechanisms in the AWGN channel. From a physical/MAC cross-layer investigation, we observe that it is important to take the physical layer impact into account when implementing the multi-channel SAW HARQ.
Specifically, we suggest that for the indicator-based stall avoidance mechanism, the number of parallel processes of the multi-channel SAW HARQ can be simply decided by the ratio of the coherence time of a Rayleigh fading channel over the transmission