3.3 P ERFORMANCE A NALYSIS
3.3.2 Integral Carrier Frequency Offset Synchronization
In order to acquire correct subcarrier index for the following channel estimator and TPS decoder, the estimation result of the integral CFO acquisition must be accurate perfectly.
Hence the estimation failure rate is used for evaluating the performance of the integral CFO synchronization. In our integral CFO synchronization scheme, the integral CFO estimator is composed of 2 stages, where the first stage detects whether the integral CFO is positive or negative, and the second stage finds the accurate integral CFO value, respectively. Both of the two stages should achieve acceptable performance even in critical channel condition to acquire accurate estimation result. We will analysis the performance of the two stages, and then illustrate the overall estimator performance and make some comparison with conventional algorithms in order.
The first stage of the proposed integral CFO estimator utilizes both sides of the boundary between data and guard band subcarriers as searching window to detect the shift direction caused by integral CFO. Hence the window width is the most important parameter of this stage. A wider window width can achieve better performance in low SNR condition but leads to more number of multiplication. The trade-off between estimation performance and computational complexity should be decided and simulated as Fig. 3.11 shows. The simulation environment is 2k mode, GI=1/8, 64-QAM, code rate=2/3, CFO=10 (89.2ppm), and Rayleigh fading channel without Doppler spread and SCO effect. The estimation failure rate is acquired by applying 1200 OFDM symbols for simulation and then calculating the ratio of the number of failure estimation to total number of simulated symbols. As we can see from Fig. 3.11, when the target estimation failure rate is set as 0.001, the window width which is equal to 5 can satisfy both target estimation performance at 8.8dB SNR and lower computational complexity at the same time. Therefore, the window width of the first stage of the proposed integral CFO acquisition is chosen as 5 in the future simulation results.
w1
w1
4 5 6 7 8 9 10 11 12 10-4
10-3 10-2 10-1
SNR (dB)
Failure rate
w1=2 w1=3 w1=4 w1=5 w1=6
Fig. 3.11 Performance of the first stage with different window width
Fig. 3.12 shows the performance of the first stage of the proposed integral CFO estimator in different channel models. The simulation environment is 2k mode, GI=1/8, 64-QAM, code rate=2/3, CFO=10, and SCO=0ppm. The simulated channel models are Gaussian channel, Ricean channel, static Rayleigh channel, and mobile Rayleigh channel, respectively. From Fig.
3.12 we can see that when the estimation failure rate is equal to 0.001, the SNR loss of Ricean channel is only 1dB compared with the AWGN only condition because the frequency selective fading effect of the Ricean channel is relatively weaker than that of the Rayleigh channel as Fig. 3.5 shows. In the case of mobile Rayleigh channel, the maximum Doppler frequency is chosen as 70Hz which is corresponding to velocity of 150km/h to achieve practical mobile situation. As we can see the SNR loss caused by Doppler spread compared with the static Rayleigh channel is about 4dB. Hence the time-varying frequency selective fading affects the estimator performance obviously.
-4 -2 0 2 4 6 8 10 12 14 10-4
10-3 10-2 10-1 100
SNR (dB)
F a ilu re ra te
Gaussian Ricean Rayleigh
Rayleigh+fd 70Hz
Fig. 3.12 Performance of the first stage in different channel models
In the second stage, two algorithms are proposed for searching the shift index caused by integral CFO according to the direction detected by the first stage. The first algorithm is based on the reduced number of continual pilots. The number of correlated continual pilots affects the estimation performance and computational complexity directly. Fig. 3.13 shows the estimator performance of the proposed reduced continual pilots approach while correlating different number of pilots. The simulation environment is 2k mode, GI=1/8, 64-QAM, code rate=2/3, CFO=10, and Rayleigh fading channel without Doppler spread and SCO effect. As we can see, the number of correlated continual pilots can be chosen as 15 to provide error-free estimation when SNR is larger than 4dB and consume about only 1/3 number of multiplication compared with the conventional continual pilots based algorithm which correlates all 45 continual pilots.
-6 -4 -2 0 2 4 6 10-4
10-3 10-2 10-1 100
SNR (dB)
Failure rate
CP=45 CP=30 CP=15 CP=10
Fig. 3.13 Continual pilots based approach with different number of pilots
The other proposed algorithm for the second stage of the integral CFO acquisition is based on the guard band moving window algorithm. Similar to the first stage, the moving window width is an important parameter of this algorithm. Fig. 3.14 shows the estimator performance of the proposed guard band based algorithm for the second stage with different moving window width. The simulation environment is 2k mode, GI=1/8, 64-QAM, code rate=2/3, CFO=10, and Rayleigh fading channel without Doppler spread and SCO effect. As we can see the window width can be chosen as 10 to provide error-free estimation while SNR is larger than 15dB in Rayleigh fading channel. If the constellation mode is simpler such as QPSK in Rayleigh channel, the required SNR for quasi error-free condition (BER after Viterbi decoder is equal to ) may be near the required error-free SNR of the proposed guard band based approach. Therefore we must check the result of scatter pilot mode detector or TPS decoder to assure the estimation result of this algorithm is correct in such condition.
w2
2 10× −4
10 11 12 13 14 15 10-4
10-3 10-2 10-1 100
SNR
Failure rate
w2=6 w2=8 w2=10 w2=12
Fig. 3.14 Proposed guard band based approach with different window width
In order to evaluate the performance of the proposed integral CFO estimator, the two stages should be combined together in the later simulation results. The related parameters of the proposed integral CFO estimator are shown in Table 3-2.
Table 3-2 Parameters of the proposed integral CFO estimator
Search range m 60
Window size of Con GB w 5
Window width of the first stage w1 5
Window width of the second stage w2 10
Index of the 15 correlated continual pilots in Pro CP
0 48 141 255 282 432 531 759 918 942 1101 1110 1140 1323 1704
The performance comparison between the conventional and the proposed integral CFO estimators will be illustrated in different channel conditions. Fig. 3.15 shows the performance of the two conventional and two proposed integral CFO estimators in Gaussian channel model.
The simulation environment is 2k mode, GI=1/8, 64-QAM, code rate=2/3, CFO=10, fd=0Hz, and SCO=0ppm. Where the Con indicates the conventional, Pro is the proposed, GB is the guard band based, and CP is the continual pilots based, respectively. As we can see the conventional continual pilots based approach requires the lowest SNR for 0.001 estimation failure rate. However, the number of multiplication of this algorithm is also the largest among the four approaches. The proposed continual pilots based algorithm is about 6dB higher but consumes much lower computational complexity than the conventional continual pilots based one. As for the two guard band based algorithms, the proposed one achieves about 2dB lower than the conventional one because of its three symbols summation scheme.
-5 0 5 10
10-4 10-3 10-2 10-1 100
SNR (dB)
F a ilu re ra te
Con, CP Con, GB Pro, CP Pro, GB
Fig. 3.15 Performance of different integral CFO estimators in Gaussian channel
Fig. 3.16 shows the performance comparison in Ricean channel model (K=10dB). The simulation environment is 2k mode, GI=1/8, 64-QAM, code rate=2/3, CFO=10, fd=0Hz, and SCO=0ppm, respectively. We can find that the simulation result is very similar to that in Gaussian channel because the Ricean channel model has a main path which leads to flatter channel frequency response in frequency domain. The required SNR for 0.001 estimation failure rate is also in inverse proportion to the number of multiplication.
-6 -4 -2 0 2 4 6 8 10 12
10-4 10-3 10-2 10-1 100
SNR (dB)
F a ilu re ra te
Con, CP Con, GB Pro, CP Pro, GB
Fig. 3.16 Performance of different integral CFO estimators in Ricean channel
The performance comparison among the four integral CFO estimators in static Rayleigh channel is shown in Fig. 3.17. The simulation environment is 2k mode, GI=1/8, 64-QAM, code rate=2/3, CFO=10, fd=0Hz, and SCO=0ppm, respectively. Because the serious frequency selective fading effect caused by the Rayleigh channel model distorts the signals in frequency domain, the required SNR for 0.001 failure rate increases apparently except the conventional continual pilots based approach due to its high computational complexity. Compared with Fig.
3.13, the performance of the proposed continual pilots based approach degrades because the first stage performs worse than the second stage in static Rayleigh channel model. Hence the performance of the proposed two stage scheme is dominated by the stage which performs worse than the other one.
-5 0 5 10 15 20
10-4 10-3 10-2 10-1 100
SNR (dB)
F a ilu re ra te
Con, CP Con, GB Pro, CP Pro, GB
Fig. 3.17 Performance of different integral CFO estimators in static Rayleigh channel As for time-varying environment, the performance comparison among the four integral CFO estimators in mobile Rayleigh channel is shown in Fig. 3.18. The simulation environment is 2k mode, GI=1/8, 64-QAM, code rate=2/3, CFO=10, fd=70Hz, and SCO=0ppm, respectively. As we can see in mobile environment, the frequency selective fading effect becomes time-varying and brings more distortion to the signals in frequency domain than the time-invariant condition. The error-free SNR of the conventional guard band based approach even exceeds 30dB and degrades about 15dB compared with the static Rayleigh channel. The conventional continual pilots based algorithm still keeps the lowest
error-free SNR as the previous simulation results. The performance degradation of the two proposed algorithms due to time-varying Rayleigh channel is not as serious as the conventional guard band based algorithm.
-5 0 5 10 15 20 25 30 35
10-4 10-3 10-2 10-1 100
SNR (dB)
F a ilu re ra te
Con, CP Con, GB Pro, CP Pro, GB
Fig. 3.18 Performance of different integral CFO estimators in mobile Rayleigh channel From above simulation results we can see that the computational complexity affects the performance of the integral CFO estimator directly. The more number of multiplication is utilized, the lower error-free SNR is achieved. The number of multiplication of the four algorithms in 2k mode according to the simulation parameters which is shown in Table 3-2 is listed in Table 3-3. As we can see although the conventional continual pilots based approach requires the lowest SNR in various channel condition, it consumes much more number of multiplication than the other three algorithms. Because the difference between the quasi error-free SNR of the overall system and the error-free SNR of the conventional continual pilots based algorithm is very large, it is not necessary to consume such huge computational
complexity by exploiting this approach. If the most economical conventional guard band based approach is utilized, its error-free SNR is even larger than the quasi error-free SNR of the system in QPSK constellation when the channel model is more critical such as Rayleigh channel. Therefore, considering the trade-off between computational complexity and estimator performance, the proposed two algorithms may be better solutions to balance it.
Table 3-3 Number of multiplication comparison
Con, CP Con, GB Pro, CP Pro, GB
# of multiplication 22022 500 4132 940
scale 100% 2.28% 18.76% 4.27%