CHAPTER 2 TIMING SYNCHRONIZATION ALGORITHMS
2.2 S YMBOL S YNCHRONIZATION
2.2.4 Fine Symbol Synchronization
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 of compression in spectrum. In our design, the channel gain of subcarrier is zero-padded from N/3+1 to N/2. In terms of spectrum, we can regard as spectrum compression with a ratio of
2/3 and thus CIR will expand with a ratio of 3/2. Therefore, the resolution of estimated CIR is 2/3. The resulting sampling resolution is
' 2 / 3
3 est
T T N T
= N = (2.22)
In order to promote the peak detection, the square operation is performed with the resulting estimated CIR. After the square operation, the difference between channel impulses will be more apparent and hence the probability of wrong peak detection can be reduced. As a result, the expression of peak detection can be represented as
^ 2
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 solution of fine symbol synchronization. The size of IFFT can be reduced by downsampling the estimated channel frequency response. However, the aliasing will occur if the downsampling rate is too large. In order to eliminate aliasing, we apply a 16-point average window as lowpass filter in advance. We then downsample the CFR by 16 so that the complexity can be reduced substantially. The proposed low complexity fine symbol synchronization design is depicted as Fig 2.14. The simulation results will be shown in
Fig 2.14 Proposed low complexity fine symbol synchronization