Ranging Techniques for IEEE 802.16e OFDMA
3.3 Floating-Point Simulation
3.3.4 Simulation Results
Some floating-point simulation results are shown in this section. Note that the signal-to-noise ratio (SNR) used in our simulation means the ratio of the variance of ranging signal samples to that of the noise samples. The detection thresholds h4, h1, h2 and H we have chosen are 4.3, 3, 1.55, 12. The value of h4 is determined by the weighted-cost method mentioned in previous subsection. The determination of h1, h2 and H is also based on the similar idea but is more complex. Thus, we decide them by many times of simulations. In addition, the number of simulation runs are from 2000 to 5000, depending on the simulated case. For simulations with the SUI-3 channel, 2000 runs are enough to observe more than
1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 0.35
0.4 0.45 0.5 0.55 0.6 0.65
Threshold (h4)
Weighted cost (md:fa=2:1)
Weighted cost with cost of md:fa=2:1, single user single−path fading, method−2
Figure 3.7: Weighted cost for rmd: rf a = 2 : 1.
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0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55
Threshold (h4)
Weighted cost (md:fa=1:1)
Weighted cost with cost of md:fa=1:1, single user single−path fading, method−2
Figure 3.8: Weighted cost for rmd: rf a = 1 : 1.
1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6
Weighted cost with cost of md:fa=1:2, single user single−path fading, method−2
Figure 3.9: Weighted cost for rmd: rf a = 1 : 2.
Weighted cost with cost of md:fa=1:3, single user single−path fading, method−2
Figure 3.10: Weighted cost for rmd : rf a = 1 : 3.
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Ranging failure rate, miss detection rate and false alarm rate
Ranging failure rate, miss detection rate and false alarm rate (AWGN, 1 user)
ranging failure rate, method 1 miss detection rate, method1 false alarm rate, method1 ranging failure rate, method 2 miss detection rate, method2 false alarm rate, method2
Figure 3.11: Ranging failure rate, miss detection rate and false alarm rate in AWGN channel with one ranging user.
100 detection failures. But for simulations with the AWGN channel, we need up to 5000 runs.
Figures 3.11, 3.12 and 3.13 show the total failure rate, missed detection rate and false alarm rate of ranging code detection with detection method 1 and method 2 in AWGN channel. The total failure rate here means that either missed detection or false alarm occurs.
We can see that method 1 obviously has better performance than method 2, especially at low SNR. This is reasonable since method 1 uses the detection metric that is somewhat similar to signal-to-interference ratio (SIR). Another observation is that the main ranging failure comes from false alarm. This is also intuitively reasonable since the peak norm value when the code matches is large in AWGN so we can always detect the desired ranging user. But, noise will cause some false alarm at low SNR.
Figure 3.14 shows the average successful detection rate of each user, which is always very
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Ranging failure rate, miss detection rate and false alarm rate
Ranging failure rate, miss detection rate and false alarm rate (AWGN, 2 users)
ranging failure rate, method 1 miss detection rate, method1 false alarm rate, method1 ranging failure rate, method 2 miss detection rate, method2 false alarm rate, method2
Figure 3.12: Ranging failure rate, miss detection rate and false alarm rate in AWGN channel with two ranging users.
Ranging failure rate, miss detection rate and false alarm rate
Ranging failure rate, miss detection rate and false alarm rate (AWGN, 3 users)
ranging failure rate, method 1 miss detection rate, method1 false alarm rate, method1 ranging failure rate, method 2 miss detection rate, method2 false alarm rate, method2
Figure 3.13: Ranging failure rate, miss detection rate and false alarm rate in AWGN channel with three ranging users.
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Average detection rate per user
Average detection rate per user (AWGN, method 1)
1 user 2 users 3 users
Figure 3.14: Average success rate of each user with method 1 in AWGN channel.
close to 1 here. Figure 3.15 depicts the average root mean square error (RMSE) of timing offset estimation. We see that the estimation is perfect as long as SNR is larger than 5 dB.
The total failure rate, missed detection rate and false alarm rate of ranging code detection with detection method 1 and method 2 in SUI-3 channel are depicted in Figures 3.16, 3.17 and 3.18. As in the AWGN case, method 1 has better performance than method 2. We observe that in a multipath channel like SUI-3, the failure rate is mainly determined by the number of users and less influenced by SNR. As long as the SNR is high enough, there exists a performance floor. That is, the performance does not improve any more when SNR gets larger.
Figure 3.19 shows the average successful detection rate of each user. Note that the prod-uct of each user’s failure detection rate is the missed detection rate since the transmission of each user is independent. Figure 3.20 depicts the average RMSE of timing offset estimation.
The RMSE ranges roughly from 1.9 to 3 samples over the range of SNR considered.
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Average RMSE (AWGN, method 1)
1 user 2 users 3 users
Figure 3.15: RMSE of timing offset estimation in AWGN channel.
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Ranging failure rate, miss detection rate and false alarm rate
Ranging failure rate, miss detection rate and false alarm rate (SUI−3, 1 user)
ranging failure rate, method 1 miss detection rate, method1 false alarm rate, method1 ranging failure rate, method 2 miss detection rate, method2 false alarm rate, method2
Figure 3.16: Ranging failure rate, miss detection rate and false alarm rate in SUI-3 channel with one ranging user.
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Ranging failure rate, miss detection rate and false alarm rate
Ranging failure rate, miss detection rate and false alarm rate (SUI−3, 2 users)
ranging failure rate, method 1 miss detection rate, method1 false alarm rate, method1 ranging failure rate, method 2 miss detection rate, method2 false alarm rate, method2
Figure 3.17: Ranging failure rate, miss detection rate and false alarm rate in SUI-3 channel with two ranging users.
Ranging failure rate, miss detection rate and false alarm rate
Ranging failure rate, miss detection rate and false alarm rate (SUI−3, 3 users)
ranging failure rate, method 1 miss detection rate, method1 false alarm rate, method1 ranging failure rate, method 2 miss detection rate, method2 false alarm rate, method2
Figure 3.18: Ranging failure rate, miss detection rate and false alarm rate in SUI-3 channel with three ranging users.
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Average detection rate per user
Average detection rate per user (SUI−3, method 1)
1 user 2 users 3 users
Figure 3.19: Average success rate of each user with method 1 in SUI-3 channel.
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Average RMSE (SUI−3, method 1)
1 user 2 users 3 users
Figure 3.20: RMSE of timing offset estimation in SUI-3 channel.
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CFO effect (SUI−3, method 1, 1 user)
ranging failure rate (CFO=0) ranging failure rate (CFO=0.1)
Figure 3.21: Comparison of the failure detection rates under no CFO and CFO=0.1 in SUI-3 channel with one ranging user.