2.5 R ESIDUAL C ARRIER F REQUENCY O FFSET S YNCHRONIZATION
2.5.2 Residual CFO Tracking Loop Filter
In order to reduce the variation of the estimated residual CFO, a PI loop filter is utilized in our CFO synchronization design [20]. The PI loop filter is composed of two paths. The proportional path multiplies the estimated residual CFO by a proportional factor K . The P integral path multiplies the estimated residual CFO by an integral factor and then integrates the scaled value by using an adder and a delay element. The block diagram of the PI loop filter is shown as Fig. 2.13.
KI
KP
KI
+
Z-1+
Fig. 2.13 Block diagram of PI loop filter The transform function of the PI loop filter can be represented as
1
( ) 1
1
P I
H z K K Z
Z
−
= + −
− (2-26) For small loop delay and , the standard deviation of the steady-state tracking error is expressed as
I P P 1
K −K K
( ')e KP/ 2 ( )
σ = ⋅ eσ
K
(2-27) where e is the estimation error of the residual CFO estimator and e’ is the steady-state tracking error. The close-loop tracking time constant is approximately given by
loop 1/ P
T ≈ (2-28) So from (2-27) and (2-28) we can find that there is a tradeoff between steady-state tracking error and tracking convergence speed. In our proposed DVB-T/H platform, the loop parameter KP is chosen as a larger value to increase the convergence speed in the beginning of tracking, and then switched to a smaller value to reduce the steady-state tracking error variation.
Chapter 3 .
Simulation and Performance Analysis
In this chapter, the overall simulation platform built for DVB-T/H system will be illustrated first. The channel model and some other distortion source such as Doppler delay spread and SCO model will be discussed later. Finally, the performance analysis of the proposed CFO synchronization scheme and comparison with state of the art will be performed.
3.1 Simulation Platform
In order to verify the performance of the proposed CFO synchronization scheme, a complete DVB-T/H baseband simulation platform is constructed in Matlab. The block diagram of the overall simulation platform is shown as Fig. 3.1.
Scrambler Outer Coder Outer
Fig. 3.1 Overall DVB-T/H platform
As shown in Fig. 3.1, the blocks with dotted line is the specific function blocks for DVB-H system. By adding support of 4k IFFT/FFT, in-depth interleaving, and additional TPS information, the developed DVB-T system platform can share most of the function blocks with DVB-H system at the same time. The platform is composed of transmitter, channel, and receiver. A typical transmitter that receives data from MPEG2 encoder or IP datagram is completely established. The transmitter consist the full function of FEC blocks and OFDM modulation blocks. The coding rate, interleaving mode, constellation mapping mode, IFFT length, and guard-interval length are all parameterized and able to be selected while simulation. An oversampling and pulse shaping filter is added before data entering channel to simulate discrete signal as far as continuously. The oversampling rate is also parameterized and can be chosen according to the simulation accuracy. The roll-off factor of the pulse-shaping filter is chosen as a normal value α =0.15 because it is not defined in the DVB-T/H standard.
Various distortion models are adopted in the channel model to simulate real mobile environment such as multipath fading, Doppler spread, AWGN, CFO, and SCO. In practically, there are still some imperfect effects which contain co-channel interference, adjacent-channel interference, phase noise, and common phase error caused by imperfect front-end receiving.
However, the distortion of these imperfect effects is relatively smaller compared with effective time-varying channel response caused by Doppler spread, CFO, and SCO. Therefore these effects are neglected in our simulation platform.
Tuner A/D Inner Receiver De-mapping FEC decoder TPS Decoder
Mode GI
Mapping Hierarchy Alpha
Code Rate
to Source Decoder
Outer Receiver digital
analog
Fig. 3.2 The baseband receiver design
The baseband receiver in our system platform can be divided into inner receiver and outer receiver as Fig. 3.2 shows. The inner receiver includes all of the timing and frequency synchronization function, FFT demodulation, channel estimation, equalization, and pilot remove blocks. The outer receiver consists of other functional blocks that following the de-mapping. The transmission parameters extracted by TPS decoder such as constellation mapping mode and Viterbi code rate will be sent the relative blocks as control parameters.
Besides, the extracted TPS parameter such as guard interval length and IFFT/FFT mode should be checked all the time during online receiving to prevent synchronization error. Once TPS check fail occurs, the acquisition and tracking of inner receiver must be shut down and then restart all the synchronization schemes. As for bit-error-rate (BER) measurement, the DVB-T standard defines quasi error-free condition, which means less than one uncorrelated error event per hour, while the BER of the output of the Viterbi decoder is equal to 2 10× −4. Therefore, in order to verify the overall system performance, the BER after Viterbi decoder should be measured.
Resampler Mode/GI
Fig. 3.3 Functional blocks of inner receiver
Fig. 3.3 shows the detail functional blocks of the inner receiver. The main functional blocks consists of symbol timing offset synchronization, carrier frequency offset synchronization, SCO synchronization, channel estimation, and equalizer, respectively. The acquisition parts (gray color) only operate in the beginning of the receiving and then are turned off when the tracking parts work, and the tracking parts works all the time until the receiver is turned off or TPS check error occurs. In this thesis, we only focus on the performance analysis of the CFO synchronization scheme. The detailed discussion of other functional blocks such as timing synchronization and channel estimation will be neglected in this work and can be found in [21].
3.2 Channel Model
The typical baseband equivalent channel model for DVB-T/H system platform is shown as in Fig. 3.4. The transmitted data will pass through multipath fading, Doppler delay spread, CFO, SCO, and AWGN in turn. The effects of co-channel interference, adjacent-channel interference, phase noise, and common phase error are neglected in our simulation. In the
following sections, the detailed effect of each channel distortion will be illustrated.
Fig. 3.4 Channel model of DVB-T/H system
3.2.1 Multipath Fading Channel Model
In wireless communication transmission, the multipath fading is caused by the reception through different paths with different time delay and power decay. In DVB-T standard, two types of multipath fading channel model are specified [3]. The fixed reception condition is modeled by Ricean channel (Ricean factor = 10dB) while the portable reception is modeled by Rayleigh channel. The full 20-tap Ricean and Rayleigh channel was used with floating point tap magnitude and phase values with tap delay accuracies rounded to within 1/2 of duration for practical discrete simulation. The channel models can be generated from the following equations where x(t) and y(t) are input and output signals respectively
Rayleigh: path, and τi is the relatively delay of the i-th path, respectively. The detailed value of these parameters is listed in table B.1 of [3]. The rms delay of Rayleigh and Ricean channel is 1.4426 sµ (about 13 samples) and 0.4491 sµ (about 4 samples). From the above two
equations, we can find that the major difference between Ricean and Rayleigh channel is the main path (the sight way). In Ricean channel, a main path is defined with the Ricean factor K (the ratio of the power of the direct path to the reflected path) and can be expressed as
2
However, there is no main path in Rayleigh channel. Hence the received signals consist of several reflected signals with similar power and bring serious synchronization error. The impulse response and frequency response of the two types of channel when K=10dB are shown in Fig. 3.5. As we can see there is a significant direct path in the impulse response of the Ricean channel. In the impulse response of the Rayleigh channel, there is no any direct path and all the paths have similar magnitude. Therefore, the frequency selective fading effect in the frequency response of the Rayleigh channel is more serious than that of the Ricean channel.
0 200 400 600 800 1000 1200 1400 1600 1800
0
(a) Impulse response of Rayleigh channel (b) Frequency response of Rayleigh channel
0 10 20 30 40 50
0 200 400 600 800 1000 1200 1400 1600 1800
0.3
(c) Impulse response of Ricean channel (d) Frequency response of Ricean channel Fig. 3.5 Channel response of Rayleigh and Ricean (K=10dB) channel
3.2.2 Doppler Spread Model
τ
(0)Fig. 3.6 Doppler spread model
In DVB-T/H system, the reception ability in mobile environment is necessary. Hence a mobile radio channel including Doppler spread must be constructed. A simplified Doppler spread model is shown in Fig. 3.6 [22]. In the beginning, we assume a channel with a known and fixed number of paths P such as Rayleigh or Ricean with a Doppler frequency fd( )k ,
attenuation ρ( )k ejθ( )k , and time delay τ( )k . All the parameters are fixed as described in section 3.2.1 except the Doppler frequency. Since each path has its own Doppler frequency, the decision of the statistic distribution of f is very important. There are two commonly d used Doppler frequency PDFs, uniform and classical, where the former exploits uniform distribution to model Doppler spread, and the later uses Jake’s Doppler spectrum [23], respectively. The PDF of the Jake’s Doppler spread can be expressed as
2
After transformation of random variable, each f can be obtained by the following equation d cos(2 (1)) max
d d
f = π⋅rand ⋅ f (3-5) The type of Doppler spread (uniform or Jake’s) affects the system performance enormously.
Because each path gets different f in each simulation case with different d fdmax, the value of fdmax should be fixed for each simulation and comparison.
3.2.3 Carrier Frequency Offset and Sampling Clock Offset model
The detailed signal model of CFO is already described in section 2.1.1 and will not be discussed repeatedly in this section. The model of SCO is built based on the concept of sinc interpolation. The input digital signals can be exploited to interpolate the intermediate value between two successive samples by using the shifted value of sic function. Assume that the sampling period is T and SCO is s ζ . Then the sampling phase can be represented as
received signal with perfect sampling, rADC( )⋅ is the received signal while SCO is ζ , respectively.
3.3 Performance Analysis
The performance analysis of the proposed CFO synchronization scheme is illustrated in this section. Except the verification of the proposed algorithms, some performance or computational complexity comparison between the conventional and the proposed approach is also made. Finally, the influence of the proposed CFO synchronization scheme to the overall system performance is presented.
23 24 25 26 27 28
10-5 10-4 10-3 10-2
SNR (dB)
BER
0 0.0025 0.005 0.0075 0.01
Fig. 3.7 BER performance in different CFO error
In order to measure the estimator performance of the proposed CFO synchronization scheme, the tolerance ability to residual CFO error of the overall DVB-T/H system is measured as shown in Fig. 3.7. The simulation environment is 2k mode, GI=1/8, 64-QAM,
code rate=2/3, and Rayleigh fading channel without Doppler spread and SCO effect. The overall system performance is measured with the BER at Viterbi decoder output is equal to while different residual fractional CFO error occurs without compensation. We can find that when the residual CFO error is less than 0.0025, the system performance degradation is only 0.05dB and not very apparent. However, as the residual CFO error increases to 0.005 and 0.0075, the SNR loss is about 0.2dB and 0.4dB, respectively. Once the residual fractional CFO reaches 0.01, the SNR loss is up to 0.6dB. Therefore, the objective of the CFO synchronization is to make the residual CFO value less than 0.005 after one-shot acquisition and long time tracking to minimize the performance loss of the overall system.
2 10× −4
3.3.1 Fractional Carrier Frequency Offset Synchronization
As section 2.3 mentioned, the guard interval based fractional CFO estimation algorithm is very sensitive to the noise introduced by inter-symbol interference (ISI) in deep delay spread channel environment. In particular, the influence of multipath spread is more apparent when the length of guard-interval is shorter. As Fig. 3.5(a) shows, the impulse response of the Rayleigh channel still has two large delay paths near the 30-th sample. If the guard interval length is 1/32 in 2k mode, there are only 64 samples within the guard interval and almost half of them are distorted by the Rayleigh channel spread. Thus the estimator performance of the guard interval based algorithm degrades apparently in such condition. Fig. 3.8 shows the root mean square error (RMSE) performance of the conventional fractional CFO estimator in different guard interval length condition when all signal within guard interval are utilized for estimation. The simulation environment is 2k mode, 64-QAM, code rate=2/3, CFO=0.33 subcarrier space (2.94ppm), and Rayleigh fading channel without Doppler spread and SCO effect. As we can see from Fig. 3.8, the required SNR when RMSE is equal to 0.005 is only about 4dB when guard interval length is 1/4 of the symbol length. However, as guard interval
saturates near 0.01 when the guard interval length is 1/32 of the symbol length. In order to improve the performance of the guard interval based fractional CFO estimator, the ISI noise must be reduced by discarding some samples of the guard interval.
0 5 10 15 20
10-3 10-2
SNR (dB)
RM S E
GI=1/4 GI=1/8 GI=1/16 GI=1/32
Fig. 3.8 RMSE performance in different guard interval length
As previous mentioned the ISI noise caused by multipath delay spread degrades the performance of fractional CFO estimator apparently. Therefore in our proposed fractional CFO acquisition algorithm, the first y samples of guard interval are skipped during calculating the correlation of the cyclic prefix. The number of skipped samples y should be chosen carefully according to the multipath channel environment. In long delay spread condition, y should be chosen as large as possible to avoid the ISI distortion. However, if a large y is chosen, the remaining samples within guard interval for correlation may be too few to average the AWGN noise in short guard interval condition. For example, there are only 64 samples within the guard interval while 1/32 guard interval length in 2k mode, if the y is chosen larger
than 40, the number of remaining samples is less than 24 and can not average the AWGN noise effectively. In order to choose an appreciate value of y for different guard interval length spec among various channel condition, the most critical condition which includes 1/32 guard interval length in 2k mode and Rayleigh fading channel is considered and simulated as Fig.
3.9 shows. The simulation environment is 2k mode, GI=1/32, 64-QAM, code rate=2/3, CFO=0.33, and Rayleigh fading channel without Doppler spread and SCO effect. From Fig.3.9 we can see that as y increases, the RMSE of the estimator can be reduced effectively and achieves the 0.005 target when y=30 at 18.3 dB SNR. However, if y is chosen as 35, the remaining samples for correlation will be less than 29 and can not average the AWGN noise in low SNR environment effectively. So in our proposed fractional CFO acquisition algorithm, y is chosen as 30 to improve the estimator performance.
16 16.5 17 17.5 18 18.5 19 19.5 20
10-3 10-2
SNR (dB)
RM S E
y=0 y=5 y=10 y=15 y=20 y=25 y=30 y=35
Fig. 3.9 RMSE performance in different y
The RMSE performance comparison between the conventional and the proposed
fractional CFO acquisition is shown in Fig. 3.10. The improved SNR while RMSE is 0.005 is also listed in Table 3.1. The simulation environment is 2k mode, 64-QAM, code rate=2/3, CFO=-0.33, and Rayleigh fading channel without Doppler spread and SCO effect. As we can see the RMSE performance improvement is the most apparent when the guard interval length is the shortest. And the simulation result also proves that the proposed algorithm can eliminate ISI noise effectively.
0 5 10 15 20
10-3 10-2
SNR (dB)
RM S E
con, GI=1/4 con, GI=1/8 con, GI=1/16 con, GI=1/32 pro, GI=1/4 pro, GI=1/8 pro, GI=1/16 pro, GI=1/32
Fig. 3.10 RMSE performance comparison
Table 3-1 Performance comparison of fractional CFO estimator
1/4 1/8 1/16 1/32
Conventional 4.25 7.8 19 N.A.
Proposed 4 6.8 11.2 18.5
Improved SNR 0.25 1 7.8 N.A.
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
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