CHAPTER 1 INTRODUCTION
1.3 T HESIS O RGANIZATION
This thesis consists of 5 chapters. The reader is assumed to be familiar with OFDM theory and thus we’ll just focus on timing synchronization of DVB-T system. The effect of timing error and the corresponding synchronization algorithms will be introduced in chapter 2.
Chapter 3 provides the overview of simulation platform and we will explain the main blocks and the channel model. The simulation results and comparisons will be presented in this chapter. In chapter 4, we present the architecture design and discuss the considerations about hardware implementation. Finally, conclusion and future work are made in chapter 5.
Chapter 2
Timing Synchronization Algorithms
2.1 Introduction to Timing Offset
In OFDM system, timing offset would cause inter-symbol interference (ISI) which destroys the orthogonality of subcarriers. The timing offset can be divided into two parts:
symbol timing offset and sampling clock offset. The symbol timing offset occurs when symbol synchronization finds incorrect OFDM symbol boundary, and sampling clock offset is caused by the difference between the sampling frequencies of the digital-to-analog converter (DAC) and the one of the analog-to-digital converter (ADC). Sampling clock offset can also lead to symbol timing drift. Unlike other packet based communication system such as 802.11a, DVB-T system is a continuous-data transmission. Therefore, sampling clock offset is a critical problem to be solved.
2.1.1 Effect of Symbol Timing Offset
The symbol synchronization of the OFDM system is to find the start of OFDM symbol, i.e. the FFT window position. Just as what is shown in Fig 2.1, we call ∆ the ISI-free region.
If the estimated start position of OFDM symbol is located within the ISI-free region, data will not be affected by inter-symbol interference (ISI). The effect of phase rotation caused by symbol timing offset can be easily corrected after FFT.
Fig 2.1 ISI-free region
where k represents the subcarrier index, n denotes sample index in time domain, and N is the number of subcarriers in an OFDM symbol. Note the last term ei2πkε/N in Eq(2.4), which exhibits the phase rotation. Therefore, we can conclude that the effect of symbol timing offset in the ISI-free region is phase rotation and unchanged magnitude of subcarrier, which can be compensated by equalizer completely. The phase rotation effect is shown in Fig 2.2. Fig 2.2(b) depicts the condition of symbol timing offset ε = 2 while Fig 2.2(c) shows the condition of
ε = 5. As symbol timing offset ε is lager, the phase variation is severer. The additional variance of channel response due to timing error will increase the difficulty of channel estimation. In order to ease the load of channel estimation unit, the symbol timing effect should be as small as possible even the phase rotate effect can be completely corrected in
theory.
(a) Symbol timing offset ε in the ISI-free region
0 200 400 600 800 1000 1200 1400 1600 1800
-4
Phase rotation with symbol timing offset=2
0 200 400 600 800 1000 1200 1400 1600
-3
phase rotation of symbol timing offset=5
(b) Phase rotation due to symbol timing offset=2 (c) Phase rotation due to symbol timing offset=5 Fig 2.2 Phase rotation of symbol timing offset ε=2 and ε=5
On the other hand, if the estimated start position locates out of ISI-free region, the sampled OFDM symbol will contains some samples that belong to previous symbol or following symbol, which leads to the dispersion of signal constellation (ISI) and reduce system performance much. Therefore, the objective of symbol synchronization, first of all, is to avoid the estimated symbol boundary lying in ISI region and subsequently reduce the symbol timing offset as far as possible. The relative mapping constellations are depicted in Fig 2.3. Fig 2.3(a) shows the phase rotation effect due to symbol timing offset of 5 samples while Fig 2.3(b) shows the ISI effect which destroys the signal constellation heavily.
(a) Symbol offset 5 samples in the ISI-free region (b) Symbol offset 5 samples in the ISI region Fig 2.3 Mapping constellation
2.1.2 Effect of Sampling Clock Offset
The sampling clock errors include the clock phase error and the clock frequency error.
The effect of clock phase error is similar to the effect of symbol timing offset and hence we can regard the clock phase error as a fractional part of symbol timing offset. The major impact of sampling clock error is clock frequency error which causes phase rotation in frequency domain and symbol timing drift in time domain. We call the sampling clock frequency error
“sampling clock offset (SCO)”.
Sampling clock offset causes sampling timing change at every sample interval as shown in Fig 2.4. For example, if the sampling clock frequency is 8MHz, sampling clock offset is 10ppm, then the symbol timing has a drift of about 80 samples per second. Obviously, SCO is an important issue in broadcasting transmission system like DVB-T. Ignoring sampling clock synchronization would lead to severe timing drift.
Fig 2.4 Sampling clock offset
Similar to symbol timing offset, sampling clock offset causes phase rotation in frequency domain. Furthermore, the amount of phase rotation is monotonous increasing as the symbol is conveying as shown in Fig 2.5.
Fig 2.5 Phase rotation between consecutive OFDM symbols
To prove the phase rotation of SCO, we consider an OFDM system using IFFT with N-points. Each OFDM symbol consist of K (K < N) data subcarrier, al,k , where l denotes the OFDM symbol index and k denotes the subcarrier index, -K/2≤ k ≤ K/2-1, T is the sampling clock period and Ng is the number of guard interval samples. Then one OFDM symbol has total Ns samples, Ns is equal to N + Ng. The transmitted complex baseband signal for l-th symbol can be described by
2 ( ( ) )
The l-th received symbol after sampling with the sampling clock T’ and removing the guard interval can be represented as
2 ( ( ) ) received samples via FFT yields the data symbol in frequency domain, zl,k.
1 2 /
In acquisition process, the residual CFO has been estimated and pre-compensated in the time-domain. The ICI produced by the remaining CFO is smaller compared to Gaussian noise, which can be considered as a complex zero mean Gaussian noise. α is an attenuation factor which is close to 1. Considering the frequency selective fading channel and neglecting the As we can see, the phase rotation occurs. The rotated phase is
( ) 2 ( )(1 ) 2 ( ) H( )
l g s g s l
k f N l N T k N l N k
N
ϕ = ∆π + ⋅ +ζ + π + ⋅ ζ φ+ (2.11)
where φlH(k) is the phase of fading channel Hl(k).
If the channel is a slowly fading channel (φlH(k)≈φlH−1(k)), the difference of rotated phases between two adjacent symbols is represented as
'( ) ( ) 1( ) indicates, CFO causes mean phase error as well as SCO causes linear phase error between two adjacent symbols.
Fig 2.6 Phase rotation due to timing drift
Fig 2.6 demonstrates the phase rotation of timing drift due to sampling clock offset. In the former symbols, the total amount of phase rotation is limited in 2π (rads) since the drift point is less than one sample. After symbol timing drift exceeding one sample, phase rotation becomes severer increasingly. Regardless of the case of symbol timing drifting into ISI region, the violent phase variation still reduce the performance of channel estimation. If symbol timing drifts out of ISI-free region, inter-symbol interference is produced and hence system performance degrades much.
2.2 Symbol Synchronization
The purpose of symbol synchronization is to find the correct position of symbol boundary. Received symbol should synchronize to the first arriving path in order to take full advantage of the useful guard interval for the pre-FFT acquisitions. The inaccurate symbol timing caused by symbol synchronization error and sampling clock offset can induce ISI (inter-symbol interference) which destroys the orthogonality of subcarriers. The symbol synchronization process contains three parts: mode/GI detection, coarse symbol synchronization and fine symbol synchronization. In the first stage of synchronization flow, blind mode/GI detection must be done prior to the following synchronization operations since the receiver has no information about transmission mode and guard interval length of the received data. In general, to get precise symbol timing, we must divide the symbol synchronization into two parts: coarse symbol synchronization and fine symbol synchronization.
The goal of coarse symbol synchronization is to detect a coarse symbol boundary in the time domain before the FFT operation. After mode/GI detection, the transmission mode and guard interval (GI) length are well know and thus the cyclic property of GI can be adopted in coarse symbol synchronization. However, the coarse symbol synchronization is not exact enough so that the fine symbol synchronization of post-FFT operation is required in the frequency domain. Fine symbol synchronization is not only to estimate more accurate symbol timing but to ensure that the symbol timing do not drift into ISI region.
2.2.1 Mode / GI Detection
In order to perform timing and frequency synchronization as well as channel estimation, both the guard interval length and the correct number of subcarriers have to be determined.
Consequently, Mode/GI detection must be done prior to synchronization and channel estimation. In fact, there are few approaches to blind Mode/GI detection in the relative materials. That’s probably because the transmission mode and GI length are assumed to known information in their researches. In particular, [5] proposes a blind Mode detection using variation-to-average ratio of moving sum but lacks GI detection. We therefore propose a joint Mode/GI detection method for the case of blind reception. Mode/GI detection can exploit the cyclic property of guard interval and then use maximum correlation method with minimum parameter GI = 1/32. Maximum correlation algorithm correlates cyclic prefixed part and useful part (where the guard interval is copied from) and then applies a moving window to seek the peak of moving sum. In order to ease the threshold decision, the normalization process is adopted in maximum correlation algorithm. The original correlation result divides its own power in addition. As a result, the normalized maximum correlation algorithm is derived as Eq(2.13).
1 interval of [0, 1]. The example of 2K moving sum operation is illustrated in Fig 2.7.
Fig 2.7 Periodic flat peak area
As we can see, the moving sum of applying moving window with GI = 1/32 causes a flat peak area if the mode selection is correct. Nevertheless, If 2K moving window is used in 8K transmission data, there would be no peak area appeared. The period of flat peak area in 2K mode can be either 2K*(1+1/4), 2K*(1+1/8), 2K*(1+1/16) or 2K*(1+1/32). To estimate the period of the peak area can obtain the information of GI length. First of all, a proper threshold has to be decided and then find the rising edge of flat peak area. The proper threshold would depend on channel if we do not use normalization. That’s why the normalization process is introduced in Mode/GI detection. As a result, we calculate the period of rising edge and determine which case is rather close to the resulting estimated period. In summary, the blind Mode/GI detection is divided into two stages. First stage is 2K mode detection. If the peak area is detected, the transmission mode is therefore 2K and GI length can be derived by estimating the period of peak area. If no peak area appeared in first stage, the second stage of 8K mode detection following turns on. Similarly, the period of flat peak area in 8K mode is either 8K*(1+1/4), 8K*(1+1/8), 8K*(1+1/16) or 8K*(1+1/32).
The probability of false period determination is very small because the four cases of candidate periods have large difference of at least 64 samples with respect to others. In the multipath fading channel, the position of flat peak area will delay several samples and depend on the mean excess delay of multipath delay profile. However, the delay position will not
affect the determination of period so that this algorithm can be robust even in the strong multipath fading channel with low SNR condition.
2.2.2 Coarse Symbol Synchronization
The true design goal for coarse symbol synchronization is not to achieve the highest possible accuracy, but to meet the requirements of following operation such as AFC (automatic frequency control) and clock recovery process with a minimum implementation cost and fastest process time. The consideration for choosing suitable algorithm is to detect a coarse symbol boundary lying ISI-free region and to be tolerable to large frequency offset and potentially large sampling clock frequency deviations during acquisition. There are a lot of algorithms concerning coarse symbol synchronization. Almost all of algorithms exploit cyclic correlation based method such as maximum correlation [3], minimum mean square error [4], modified maximum likelihood [7] and double correlation [10]. In [8], a simple estimator of the minimum power difference is adopted. A joint coarse symbol synchronization and frequency acquisition is proposed in [9]. Three major synchronization algorithms of maximum correlation (MC), maximum likelihood (ML) and minimum mean square error (MMSE) are exhaustively analyzed in [6]. There are three algorithms to be discussed and compared as below.
a) Maximum Correlation (MC)
1 *
0
arg max Ng ( ) ( )
est k i
K − r k i r k i N
=
= − ⋅ − − (2.14)
Similar to Mode/GI detection, first algorithm of coarse symbol synchronization uses correlation method based on guard interval, which is denoted by Maximum Correlation algorithm. This algorithm is commonly used in GI-based symbol synchronization or frame synchronization of other transmission systems. Unlike Mode/GI detection, the length of the moving sum is the same as the length of guard interval in order to get best performance. The
operation is illustrated in Fig 2.8.
Fig 2.8 Delayed peak of moving sum
Due to multipath fading channel, the peak of moving sum will locate at a delayed position corresponding to mean excess delay of channel. The delayed position will cause the symbol boundary lie in ISI region. Therefore, a number of samples must be reserved for shifting forward while we decide the symbol boundary. Considering the Rayleigh channel specified by standard, which has a mean excess delay of 13 samples as a worst case, the shifting number of 20~30 samples should be applied in order to ensure the symbol boundary is safe in various types of channel. This maximum correlation method can resist the effect of large CFO and SCO so that the performance is acceptable. The major advantage is minimum implementation cost.
b) Normalized Maximum Correlation (NMC)
1 * moving window length is applied in coarse symbol synchronization. The full guard interval length is taken as moving window length in place of Eq(2.13). The advantage of this algorithm is easy to set threshold for finding maximum peak because the moving sum is
normalized to 1. The accuracy is close to maximum correlation algorithm.
c) Minimum Mean Square Error (MMSE)
This algorithm is simplified from Maximum Likelihood (ML) algorithm [6]. The ML
where w and k,1 w are parameters corresponding to the characteristics of transmitted data k,2 and channel. The basic concept of ML algorithm is to derive the log-likelihood function and obtain the ML solutions in an approximation value. The detail demonstrations can refer to [6].
Since ML algorithm requires known channel characteristic in advance, the MMSE algorithm approximates the parameters to a practical form. In fact, wk,1 is close to 1 as well
as wk,2 is close to 1/2 so that the resulting algorithm can be rewritten as correlation power. Note the value of K is negative so that the perfect estimation value is 0. est These three algorithms will be compared in Chapter 3.
2.2.3 Scattered Pilot Mode Detection
Before fine symbol synchronization and other operations in tracking mode, another acquisition operation has to be proceeded, which is scattered pilot mode detection. It is known that the distribution of scattered pilots has four modes.
min 3 ( mod 4) 12 | int , 0, [ min; max]
k K= + × l + p p eger p≥ k∈ K K (2.18)
The four scattered pilot modes are drawn in Fig 2.9.
Fig 2.9 Four modes of scattered pilot position
The proposed scattered pilot mode detection exploits the property of boosted power level scattered pilots. Since the power level of scattered pilots is 16/9 while other data subcarrier is 1, we take one OFDM symbol and divide the subcarriers into 4 groups. Afterward, we accumulate the power of subcarrier belong to each group respectively as shown in Eq(2.19)
/12 1
* 0
arg max N (3 12 ) (3 12 ) 0,1, 2,3
k i
SP − z k i z k i k
=
= ⋅ + ⋅ ⋅ ⋅ + ⋅ = (2.19)
Although the power of each subcarrier is possible larger than 16/9 such as maximum power level of 7/3 in non-hierarchical 64-QAM, many times of accumulations make the false detection rate almost reduce to zero.
2.2.4 Fine Symbol Synchronization
Since the coarse symbol synchronization is not able to provide the accuracy needed, a rather exact algorithm must be adopted in frequency domain. The algorithm requires that sampling and carrier frequency are already synchronized. Hence fine timing will be the last task in the synchronization scheme.
After the coarse symbol synchronization, the residual symbol timing offset ε becomes small and the symbol boundary locates in ISI-free region. We can assume this timing error is introduced by the physical channel whose first path time delay is ε⋅T. The effect of path delay is illustrated in Fig 2.10.
Fig 2.10 Effective channel impulse response due to inaccurate FFT window
As Fig 2.10 is depicted, the symbol timing offset in ISI-free region causes path time delay of effective channel impulse response. We assume that the signal is transmitted over multipath fading channel characterized by
1 0
( , ) L l( ) ( l)
l
hτ t − h t δ τ τ
=
= ⋅ − (2.20)
where hl(t) are the path complex gains, τl are the path time delay, and L is the total number of paths. Then the effective channel model due to symbol timing offset changes to be
1
( , ) lL0 l( ) ( l )
hτ t = =− h t ⋅δ τ τ ε− + ⋅ T (2.21) Therefore, the fine symbol timing can be maintained by acquiring the effective channel impulse response (CIR) and then estimating the main path delay. The path delay estimation task utilizes the channel frequency response (CFR) estimated by channel estimation unit and subsequently performs an IFFT to transform the CFR to CIR.
Before detail discussion of path time delay in CIR estimation, channel estimation should be introduced in advance. In channel estimation design, 2-D interpolation is generally used because of its robustness for mobile time-variant channel caused by Doppler spread. In 2D interpolation, channel gain estimations at scattered pilots are first interpolated over
time-dimension so that three OFDM symbols must be kept in buffers. Then linear
interpolation is adopted in two adjacent symbols with same scattered pilot modes for
estimating the channel gain of scattered pilot within the interval. Afterward, all other channel responses are obtained by frequency-dimension interpolation. This 2-D interpolation method deserves to be applied in DVB-T system even though large memory requirement. The time-dimension interpolation can overcome the severe time-variant channel and channel frequency response can be estimated effectively.
After time-dimension interpolation, a total of Kmax/3+1 sub-sampled channel gain of scattered pilots are available. To provide a sufficiently accurate estimation, a zero padded IFFT of size N/2 must be used. The operations of fine symbol synchronization are illustrated in Fig 2.11.
Fig 2.11 Structure of fine symbol synchronization
Fig 2.11 shows the process of fine symbol synchronization including zero padding, N/2 IFFT and peak decision. The fine symbol synchronization utilizes the CFR of Kmax/3+1 scattered samples after the time-dimension interpolation and then performs zero padding to size N/2. The changes of spectrum due to downsampling and zero padding are drawn in Fig 2.12 and Fig 2.13 respectively.
Fig 2.12 Downsampling of channel frequency response
Fig 2.13 zero-padding of channel frequency response
Fig 2.12 shows a basic concept of downsampling in frequency domain. The resulting time domain response after sampling in frequency domain is CIR duplication. Then downsampling causes CIR expansion so that the original CIR can be computed with a little aliasing. It has been known that low pass filtering has to be done prior to downsampling for avoiding aliasing. However, the effect of aliasing is slight because the power of CIR usually centralizes in the prior paths and hence the low pass filtering can be neglected if the downsampling rate is not too large.
Fig 2.13 illustrates the effect of zero-padding. We can assume the zero padding in frequency domain as the spectrum compression and hence CIR expands according to the ratio
Fig 2.13 illustrates the effect of zero-padding. We can assume the zero padding in frequency domain as the spectrum compression and hence CIR expands according to the ratio