CHAPTER 3 SIMULATION AND PERFORMANCE
3.3 P ERFORMANCE
3.3.1 Mode/GI Detection
The simulated flat peak area in Mode/GI detection block is depicted in Fig 3.10. Fig 3.10(a) shows the 2K mode detector and 8K mode detector respectively in the 8K mode transmission. As we can see, the flat peak area only occurs in 8K mode transmission after normalized maximum correlation. Similarly, 2K mode transmission is illustrated in Fig 3.10(b). After deciding proper threshold, the period of flat peak area can be estimated so that we can obtain the correct transmission mode and guard interval length.
1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4 1.45 1.5
Mode/GI Detection ( transmit 8K mode)
2K mode detector
Mode/GI Detection ( transmit 2K mode)
2K mode detector 8K mode detector
(b) 2K mode transmission
Fig 3.10 Flat peak area in Mode/GI detection
The performance of Mode/GI detection is depicted in Fig 3.11 in terms of false detection rate versus SNR. The definition of SNR is Es/ N0, where Es is the energy per channel symbol and N0/2 is the two-sided power spectral density of the AWGN. Both performances in 2K and 8K mode are shown in Fig 3.11. The transmission mode is 64-QAM and GI=1/8.
The simulation environment is Rayleigh fading channel, Doppler spread = 70 Hz, CFO=20ppm and SCO=20ppm. Since the Mode/GI detection is the first stage of acquisition mode, it has to bear all channel distortions without any compensation. As we can see, 8K mode has much lower false detection rate than 2K mode because of longer symbol duration.
Longer symbol duration makes the difference between possible values of period lager so that the possibility of false detection becomes small apparently. In general, error-free condition in 64-QAM can be achieved when SNR > 8db in 2K mode and >3db in 8K mode. As for other constellation mapping like 16-QAM or QPSK, required SNR of error-free condition is much smaller.
-2 -1 0 1 2 3 4 5 6
10-4 10-3 10-2 10-1 100
SNR
False Detection Rate
Mode/GI Detection @ 64-QAM GI=1/8
2K mode 8K mode
Fig 3.11 False Mode/GI detection rate versus SNR
3.3.2 Coarse Symbol Synchronization
As mentioned in Chapter 2, there are numerous algorithms of coarse symbol synchronization. The design target of coarse symbol synchronization is to find symbol boundary and ensure it lying ISI-free region. In order to analyze the performance of each algorithm, we take 650 OFDM symbols to estimate the resulting symbol offset and depict a histogram to show the statistic distribution. As a first acquisition stage of synchronization, coarse symbol synchronization has to tolerate severe channel distortions such as large CFO and large SCO before tracking operations. Therefore, we assume the simulated channel condition as Doppler spread 70 Hz, CFO=20ppm, SCO=20ppm and AWGN=10db. The three cases of Gaussian channel, Ricean channel (K=10db) and Rayleigh channel are shown below.
-10 -8 -6 -4 -2 0 2 4 6 8 10
MC coarse symbol synchronization @ Gaussian
-10 -8 -6 -4 -2 0 2 4 6 8 10
NMC coarse symbol synchronization @ Gaussian
(a) MC algorithm in Gaussian channel (b) NMC algorithm in Gaussian channel
MMSE coarse symbol synchronization @ Gaussian
(c) MMSE algorithm in Gaussian channel
Fig 3.12 Histogram of estimated symbol offset in Guassian channel
MC coarse symbol synchronization @ Ricean
-10 -5 0 5 10 15 20
NMC coarse symbol synchronization @ Ricean
(a) MC algorithm in Ricean channel (b) NMC algorithm in Ricean channel
MMSE coarse symbol synchronization @ Ricean
(c) MMSE algorithm in Ricean channel
Fig 3.13 Histogram of estimated symbol offset in Ricean channel
-10 -5 0 5 10 15 20 25 30 35 40
MC coarse symbol synchronization @ Rayleigh
-100 -5 0 5 10 15 20 25 30 35 40
NMC coarse symbol synchronization @ Rayleigh
(a) MC algorithm in Rayleigh channel (b) NMC algorithm in Rayleigh channel
-10 -5 0 5 10 15 20 25 30 35 40
0 20 40 60 80 100 120
Symbol offset (samples)
Symbols
MMSE coarse symbol synchronization @ Rayleigh
(c) MMSE algorithm in Rayleigh channel
Fig 3.14 Histogram of estimated symbol offset in Rayleigh channel
Fig 3.12 shows the estimated symbol offset in the Gaussian channel. Since the Gaussian channel does not have the property of multipath fading, the mean excess delay is regarded as zero. As a result, the estimated symbol offset centralizes in the interval of [-4, 4]. Comparing the performances of MC, NMC and MMSE algorithm, we can find the difference between MC and NMC is very small. And MMSE algorithm has a slightly better performance than other two algorithms. The simulation result in the Ricean channel (K=10db) is depicted in Fig 3.13. Unlike Gaussian channel, Ricean channel has rms delay spread of 0.4491µ s (about 4 samples) so that the ISI effect is much heavier than Gaussian channel. The resulting estimated symbol offset is distributed in the larger interval of [-8, 8]. As shown in Fig 3.13 clearly, MMSE has a more centralized distribution and just in the interval of [-5, 5]. As for Rayleigh channel, the strong multipath fading degrades the performance of coarse symbol synchronization much due to severe ISI effect. Since Rayleigh channel has rms delay spread of 1.4426µ s (about 13 samples), the estimated symbol offset is distributed in the interval of [-5, 35] as shown in Fig 3.14. A large delayed peak causes large symbol timing offset.
Apparently, MMSE algorithm has better performance again. In summary, MMSE algorithm has an advantage of performance among these three algorithms. Concerning the hardware
implementation, MMSE has the highest hardware cost so that there exists a tradeoff between performance and hardware complexity.
In order to provide the reliable symbol boundary, the estimated delayed peak position must shift several samples in advance and set this shifted position as symbol boundary. As for how many shifted samples are enough, we have to consider the worst case of channel and ensure the symbol boundary being safe in this channel. In DVB-T system, ETSI standard [1]
defines a Rayleigh channel for portable reception so that we can assume it as the worst channel. To check Fig 3.14(c) again, MMSE algorithm has a largest 28-sample-delayed peak.
As a result, the symbol boundary must shift left 30 samples at least.
In order to detect the periodic peaks, an appropriate threshold must be decided. Since the power level of the correlation result varies depend on the channel characteristics. The severer channel yields the lower correlation power. Therefore, an adaptive threshold decision strategy has to be developed. We propose a simple peak detection algorithm. An adaptive threshold can be computed by
m K σ
Γ = + ⋅ (3.12)
where m denotes the mean of resulting correlation power and σ represents standard deviation. The definition of K depends on the amount of noise and the variation of signals.
For very noisy signals, it is best to lower it. In DVB-T system, K=1 is a suitable parameter value for peak detection algorithm. As a result, the coarse symbol synchronization has to spend some OFDM symbols to evaluate the mean and standard deviation of correlation power and therefore the peak can be correctly detected.
3.3.3 Scattered Pilot Mode Detection
As the last stage of acquisition mode, scattered pilot mode detection estimates the positions of scattered pilots prior to other operations in tracking mode like CFO/SCO tracking and fine symbol synchronization. The scattered pilot mode detection must have low
false-detection rate since the inaccurate scattered pilot position yields wrong operations of the downstream blocks in tracking mode. The scattered pilot mode detection must tolerate residual fractional ICI, large symbol offset and potentially large SCO. Therefore, we assume the simulation environment as 2K mode, GI=1/8, 64-QAM, Rayleigh channel, Doppler spread=70Hz, residual fractional CFO=0.02 (the ratio of carrier frequency offset to subcarrier spacing), and SCO=20ppm. The false detection rate versus SNR is depicted as Fig 3.15
-20 -15 -10 -5 0 5
10-3 10-2 10-1 100
SNR
False detection rate
Scattered Pilot Mode Detection
Fig 3.15 False detection rate of scattered piloted mode detection
The error-free condition can be achieved when SNR>5db and 8K mode will get better performance because of more subcarriers it has. In summary, the scattered pilot mode detection algorithm is strongly reliable in normal transmission.
In fact, this operation can probably be neglected if we disable tracking operations until TPS decoding is completed. Since the TPS bits contain frame information, the position of scattered pilots is able to be obtained as long as the TPS bits are decoded. However, the convergence of synchronization will delay a TPS frame, i.e. 64 OFDM symbols, at least.
Therefore, there exists a tradeoff between hardware complexity and convergence speed.
3.3.4 Fine Symbol Synchronization
As illustrated in Chapter 2, fine symbol synchronization exploits IFFT to estimate the effective channel impulse response. Time-dimension interpolated scattered pilots are used to assume as sub-sampled channel frequency response. After zero padding, IFFT generates the effective channel impulse response with resolution of 3/2. To estimate the path delay can yields the symbol timing offset caused by inaccurate coarse symbol synchronization or sampling clock offset. The performance of path delay estimation depends on the channel type such as Gaussian, Ricean and Rayleigh. Furthermore, Doppler spread also dominates the accuracy of symbol timing offset estimation. We discuss these simulation performances in different channel condition respectively.
(1) Static Gaussian channel
In the static Gaussian channel, the first path is also the strongest path. Therefore, path delay can be easily estimated by detect the maximum S^k as shown in Fig 3.16
0 5 10 15 20 25 30
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
IFFT index
Square of magnitude
Estimated CIR @ Gaussian channel
^
S
maxFig 3.16 Estimated channel impulse response in Gaussian channel
The simulation environment is 2K mode, 64-QAM, GI=1/8, residual CFO=0.02 (ratio of actual CFO to subcarrier spacing), SCO=20ppm and AWGN=10db. The detected path delay
of S^max can reliably represent the symbol timing offset by restoring the resolution of estimated CIR. After multiplying by 2/3, the actual path delay caused by symbol timing offset can be obtained. Fig 3.17 shows the path delay estimation in the case of SCO=20ppm without timing recovery. X-axis denotes the timing drift caused by sampling clock offset. We calculate the actual symbol timing offset as depicted in dotted line. And the estimated symbol timing drift by IFFT path delay estimation is shown in solid curve. The solid curve appears in a shape of stair since the resolution of estimated CIR is not infinite. For increasing the resolution, we can pad more zeros to the channel gain and use more points of IFFT. As Fig 3.17 is depicted, the estimated symbol timing offset is very close to actual symbol timing offset so that the fine symbol synchronization can be achieved in Gaussian channel.
0 100 200 300 400 500 600 700 800
0 5 10 15 20 25 30 35
Symbol index
Timing drift (samples)
Fine symbol synchronization
Estimated symbol timing drift Actual symbol timing drift
Fig 3.17 Path delay estimation in Gaussian channel
(2) Ricean channel with Doppler spread 70 Hz
Similar to Gaussian channel, Ricean fading channel (K=10db) has a main path as shown
in Fig 3.7(a). After applying Doppler spread, the channel has time-variant channel impulse response. The time-variant CIR can probably cause the error of path delay estimation. Fig
3.18 shows the estimated CIR and then we can detect S^max which yields path delay.
0 10 20 30 40 50 60 70 80
0 0.05 0.1 0.15 0.2 0.25
IFFT index
Square of magnitude
Estimated CIR @ Ricean channel (K=10db)
^
S
maxFig 3.18 Estimated channel impulse response in Ricean channel
The estimation result is depicted in Fig 3.19. Comparing to Fig 3.17, the accuracy of estimation is slightly worse in some symbol index. The inaccurate path delay estimation is caused by time-variant CIR due to Doppler spread. However, the estimation error is tolerable if we take some samples in safe region that means we can define several sample offset like 5 samples as the target of symbol synchronization instead of complete synchronization.
0 100 200 300 400 500 600 700 800
Fine symbol synchronization @ Ricean channel & Doppler 70Hz
Estimated symbol timing drift Actual symbol timing drift
Fig 3.19 Path delay estimation in Ricean channel
(3) Rayleigh channel with Doppler spread 70 Hz
Unlike Gaussian or Ricean channel with a direct path, Rayleigh fading channel has no main path as shown in Fig 3.7. Therefore, the previous criterion of maximum detection is not suitable for Rayleigh channel since the peak probably occurs during a large interval.
Considering the Doppler spread, time-variant CIR causes the false estimation of path delay.
As a result, another criterion has to be used in Rayleigh channel. Instead of finding the
maximum S^k, we first set a threshold and select the first strong path whose energy must exceed the threshold value Γ . Hence, the estimated path delay is
{ }
^ 2 ^
min | , 0, , 1
3 k Sk k M
δ = > Γ = − (3.13)
where the M-point IFFT is used and δ is the estimated symbol timing offset.
How to choose Γ is an important issue. In order to make Γ less sensitive to noise, an adaptive threshold is needed. We define the threshold as
^ max/16
Γ =S (3.14)
The parameter of 16 is determined by simulation and is also feasible for hardware
implementation. The resulting path delay estimation is depicted in Fig 3.20. In fact, this criterion can be applied in either Gaussian channel or Ricean channel and a slightly smaller path delay will be detected. The smaller path delay will not affect the fine symbol synchronization much.
0 20 40 60 80 100 120 140 160 180 200
0 0.02 0.04 0.06 0.08 0.1 0.12
IFFT index
Square of magnitude
Estimated CIR @ Rayleigh channel & Doppler 70Hz
^
Smax
^ max/16 Γ =S
Fig 3.20 Estimated channel impulse response in Rayleigh channel
The simulation performance is shown in Fig 3.21. As we can see, the estimated symbol timing error is apparently larger than the case of Gaussian and Ricean fading channel. Similar to Ricean channel, the strategy of symbol timing adjustment can not be a complete synchronization. Fine symbol synchronization has to provide a buffer zone of about 5 samples for avoiding estimation error. Note the major target of fine symbol synchronization is to ensure that the symbol timing do not drift to ISI region due to residual SCO.
0 100 200 300 400 500 600 700 800 0
5 10 15 20 25 30 35
Symbol index
Timing drift (samples)
Fine symbol synchronization @ Rayleigh channel
Estimated symbol timing drift Actual symbol timing drift
Fig 3.21 Path delay estimation in Rayleigh channel
We have designed different criteria for different channels to detect the path delay. The criterion of maximum detection works for the Gaussian and Ricean fading channel. The criterion of Eq(3.14) works for the Rayleigh fading channel as well as the Gaussian and Ricean channel. The simple criterion of maximum detection can be used if the receiver knows in advance that channel has a direct path such as the Gaussian or Ricean channels. In practical situations where the operating environment varies widely, the receiver may not know the type of channels. In such situation, we can always use the criterion of Eq(3.14) for the multipath Rayleigh fading channels.
It’s obvious that the fine symbol synchronization with N/2 IFFT method dominates the complexity of overall synchronization system. Therefore, we proposed a low complexity design of fine symbol synchronization. In order to reduce the size of IFFT, we first downsample the estimated channel frequency response and hence the IFFT with fewer points can be adopted. Nevertheless, Downsampling causes the estimation error due to aliasing. The performances of fine symbol synchronization with varied downsampling rate in 2k mode are shown in Fig 3.22.
Fig 3.22 Fine symbol synchronization
As we can see, the 1024-IFFT achieves the best performance which keeps the symbol timing during 0 and 1. The larger downsampling rate is adopted, the larger estimation error is generated. Note the estimation will fail as the downsampling rate exceeds 8, i.e. 64-IFFT in 2k mode, because of huge aliasing. In 2k mode, the smallest size of IFFT can be adopted in fine symbol synchronization is 128-point. However, the large variance of estimation results is not reliable enough. Hence, we apply a method using 16-point average window as a lowpass filter prior to downsampling by 16. The aliasing effect can be eliminated so that the estimation variance is reduced. The performance of proposed fine symbol synchronization with N/32 IFFT is depicted in Fig 3.23. The proposed method can keep the symbol timing offset less than 3 samples. The comparisons between proposed method, conventional method and downsampled conventional method are listed in Table 3.2. The root mean square error of proposed method is between N/4 IFFT and N/8 IFFT. However, the complexity reduction is up to 26.67 times from N/2 IFFT to N/32 IFFT.
Fig 3.23 Proposed low complexity fine symbol synchronization
RMSE (sample) Complexity in 2K mode Complexity reduction ratio ( Radix-2)
N/2 IFFT [3] 0.3556 1024-IFFT 1
N/4 IFFT 0.3686 512-IFFT 2.22
N/8 IFFT 0.4845 256-IFFT 5
N/16 IFFT 0.5320 128-IFFT 11.43
Proposed N/32 IFFT
0.4548 64-IFFT + 16-point average window
26.67
Table 3.2 Comparisons between proposed and conventional fine symbol synchronization