This thesis is organized as follows. In chapter 2, the signal models and the detailed algorithms of the proposed CFO synchronization scheme will be introduced. The simulation result and performance analysis will be discussed in chapter 3. Chapter 4 will introduce the design methodology, hardware architecture, and the chip summary of the proposed design.
Conclusion and future work will be given in chapter 5.
Chapter 2 .
Carrier Frequency Offset Synchronization Algorithms
In this chapter, we introduce the signal model and the effect of carrier frequency offset (CFO) in DVB-T/H system first. The algorithms of CFO synchronization in different synchronization categories will be illustrated in later sections. Some comparison and discussion between developed and the proposed algorithms are also made.
2.1 Introduction to Carrier Frequency Offset
OFDM is a bandwidth efficient signal scheme for digital communications. In OFDM systems, the spectrum of the individual subcarrier mutually overlaps and exhibits orthogonality to achieve optimum spectrum efficiency as shown in Fig. 2.1.
-4 -3 -2 -1 0 1 2 3 4
-0.4 -0.2 0 0.2 0.4 0.6 0.8 1
f(k) Fig. 2.1 Spectrum of five orthogonal subcarriers of OFDM systems
However, OFDM is very sensitive to the CFO introduced by the mismatch of oscillator frequency between transmitter and receiver. CFO causes linear phase error in time domain and shifts the subcarrier index in frequency domain, respectively. Once CFO exists, the orthogonality between subcarriers will be destroyed and the degradation of the system performance will be serious. Compared with other OFDM based system such as IEEE 802.11a, the subcarrier space of DVB-T/H system is relatively narrower and the tolerance of carrier frequency offset is also worse [3][5]. Hence the CFO synchronization is a very critical problem to be solved in DVB-T/H system.
2.1.1 Signal Model of Carrier Frequency Offset
Consider an OFDM system using an inverse fast Fourier transform (IFFT) of size N for modulation. Each OFDM symbol is composed of K (K<N) data subcarriers , where l denotes the OFDM symbol index and k (0
,
al k
k K
≤ < ) denotes the subcarrier index. After IFFT, a cyclic prefix composed of Ng samples is inserted to avoid the influence of multipath channel delay spread. So a transmitted symbol has Ns =N+ Ng samples with sample period T. The transmitted complex baseband signal of the l-th symbol can be expressed as
, where fc tx, is the central frequency of the transmitter RF oscillator, and is the subcarrier index relative to the centre frequency,
' k
' ( 1) /
k = −k K− 2.
Since the CFO f∆ (∆ =f fc tx, − fc rx, ) between transmitter and receiver RF oscillator can be expressed as a time-variant phase error, ej2π∆ft, the l-th received symbol after sampling with period T’ at time instants tn=(lNs+Ng+n)T’ and removing guard interval can be expressed as
r nl( )=ej2π∆ftn⋅s tl( )n ∗h t( , )n τ +w nl( ) complex-valued additive white Gaussian noise (AWGN). After demodulation via a fast Fourier transform (FFT), the l-th OFDM symbol at subcarrier k,
l( )
ICIl k is the inter-carrier interference noise due to carrier frequency offset. Likewise, is the channel frequency response on the k-th subcarrier of the l-th OFDM symbol with the assumption that the channel is stationary within at last one symbol, is a zero-mean stationary complex process as well.
,
Hl k
,
Wl k
2.1.2 Effect of Carrier Frequency Offset
As previous section shows, CFO introduces various imperfect effects to the received signal. From the viewpoint of time domain, the CFO can be expressed as a time-variant phase error. The rotated phase error is in proportion to the received sample time instants tn and can be expressed as
( ) 2 2 ( ) /
l n ftn lNs Ng n N
θ = ∆ =π πε + + (2-4) where θ is the phase rotation caused by CFO. Unlike other packet-based communication systems such as IEEE 802.11a, DVB-T/H is a continuous-data transmission system and the
receiving of data continues until the receiver is turned off. So the phase error will still be large even in very weak CFO environment when the receiver operates for a long time as shown in Fig. 2.2.
Fig. 2.2 Phase rotation in time domain for long time reception when ε=0.01
-4 -3 -2 -1 0 1 2 3 4
Fig. 2.3 Spectrum of five subacrriers in carrier frequency offset environment
CFO results in different effects in frequency domain. It not only reduces the amplitude but also shifts the phase of the demodulated signal. Further more, the second term of (2-3)
,
ICIl k degrades the system performance strongly because it destroys the orthogonality within each subcarrier in OFDM symbols, and can be expressed as
~
Because the subcarrier space of DVB-T/H system is very narrow (about 0.7~4.5 KHz), we can divide the normalized CFO value into integral part and fractional part, and can be expressed ass
I F
ε ε= +ε (2-6) From Fig. 2.3, we can find that CFO causes inter-carrier interference noise within each subcarrier and makes the orthogonality of spectrum lost. Once the integral part of CFO εI is not zero, all of the subcarriers will shift circularly. The shift of subcarrier index will make the channel estimator receive wrong pilot sequence at the pre-defined pilot index and then the calculated channel frequency response will be not reliable. Also the TPS decoder can not receive correct TPS pattern to decode the correct system parameter. All of these imperfect effects in different domain should be corrected by the aid of CFO synchronization to obtain good receiving performance.
2.2 Carrier Frequency Offset Synchronization Scheme
From previous section, we can know that the imperfect effects caused by CFO degrade the system performance enormously. Besides, the DVB-T/H system is very sensitive to the CFO because of its narrow subcarrier space and continuous-data transmission scheme. So the synchronization of CFO is a very important factor and must be handled carefully. In our system platform, the CFO synchronization is divided into acquisition stage and tracking stage.
As the beginning of receiving data, the acquisition stage estimates the CFO value roughly with the first 3 received symbols. After acquisition stage finishes, the integral CFO value
ε
^ Iand most of the fractional CFO value
ε
^ F should be estimated and compensated. Thetracking stage then turned on to track the residual fractional CFO value εR (εF =
ε
^F + ) εR left by the acquisition stage until the receiver is turned off.The objective of CFO synchronization is to establish subcarrier orthogonality as fast and accurately as possible (acquisition) and then maintain orthogonality as well as possible at all times during online reception (tracking). However, a CFO acquisition algorithm alone can not be both fast and sufficiently accurate, because
1. Pre-FFT algorithms allow only fast acquisition of the fractional CFO but no acquisition of the integral CFO.
2. Post-FFT algorithms allow fast acquisition of the integral CFO but, due to lack of orthogonality, acquisition of fractional CFO is very complicate.
Both fast and accurate acquisition can be attained by adopting a multi-stage synchronization strategy with two one-shot acquisition stages (one pre-FFT and the other post-FFT) followed by tracking. In DVB-T/H system, the data format provides for training is only for frequency domain (continual and scattered pilots) but not for time domain. Hence, pre-FFT non-data-aided acquisition and post-FFT data-aided acquisition and tracking algorithms are suitable. This leads to the overall CFO synchronization and compensation scheme as shown in Fig. 2.4.
Fig. 2.4 Overall CFO synchronization and compensation scheme
The control loops of the three-stage synchronization subsystem operate in a
per-OFDM-symbol basis. When the CFO acquisition or tracking stage has generated an estimation of CFO value, the CFO compensator will calculate the effective compensation value before the beginning of the next pre-FFT OFDM symbol, and then start to compensate the updated CFO value when the next pre-FFT OFDM symbol comes.
2.3 Fractional Carrier Frequency Offset Synchronization
The estimation of fractional CFO was first proposed by Moose in 1994 [9]. This approach utilizes maximum likelihood estimation (MLE) of differential phase between two repeated training symbols in frequency domain to estimate the fractional CFO value. The estimation range is limited within±0.5 subcarrier space, and can be expressed as
/ 2 1
In WLAN IEEE 802.11a system, similar idea is exploited but different training patterns are utilized [10]. The estimation of CFO is accomplished by the aid of pre-defined short preamble and long preamble in time domain and achieves wider estimation range than Moose’s approach. However, there is no any pre-defined training sequence except the continual and scattered pilots in DVB-T/H system. The former two data-aided algorithms are both not suitable solutions for our application.
From section 2.1.2, we can know that the phase of the received signal in time domain is rotated by CFO linearly according to the sample time instant tn as (2-4) shows. When the difference of sample time instant between two received signals is equal to FFT length N, the phase error difference caused by CFO between them can be expressed as
( ) ( ) 2 2
l n N l n ftn N ftn
θ + −θ = ∆π + − ∆ π
2 (πε lNs Ng n N) /N 2 (πε lNs Ng n) /N
= + + + − + +
2πε 2 (π εI εF)
= = + . (2-8) Since the phase rotation of multiples of 2π can be ignored, the phase error between and is just equal to
l( ) r n
( )
r nl +N 2πεF and in proportion to the fractional CFO value. This phase error feature will be utilized in our proposed fractional CFO synchronization. In the proposed DVB-T/H system platform, however, no any useful training symbol can be used in time domain. So if we want to exploit the phase error feature between and
, the guard interval based algorithm is the most suitable solution.
l( ) r n
l(
r n+ )N
In order to prevent the influence of multipath channel spread and inter-symbol interference (ISI), a cyclical prefix is inserted in front of each symbol. The cyclical prefix must be composed of partial signal in the back of the symbol, and its length has to be longer or equal to the multipath delay spread as shown in Fig. 2.5.
Symbol (N) GI(Ng)
copy channel impulse
response
Fig. 2.5 Guard interval insertion and multipath channel spread
Because all the samples in guard interval are copied from the rear part of the symbol, the received sample r nl( ) in guard interval and r nl( +N) in the symbol’s tail are exactly identical when there is no any distortion exists such as multipath delay spread or CFO. As previous sections mentioned, the difference of rotated phase error between and
is in proportion to the fractional CFO value
l( ) r n
l(
r n+ )N εF. We can conclude that the tail
received sample and its cyclical prefix show the same property except for a phase rotation error which is exactly 2πεF. The estimation of fractional CFO value can be accomplished with the MLE of differential phase between guard interval and the tail of symbol [11], and can
be expressed as range of the fractional CFO synchronization is also limited within ±0.5 subcarrier space. In the proposed CFO synchronization scheme, the rough estimation of fractional CFO is calculated with the first symbol after symbol boundary is decided. And then the estimated fractional CFO value
ε
^F will be sent to the CFO compensator before data being sent to FFT demodulator as Fig. 2.4 shows.If AWGN is the only external distortion, the accuracy of the fractional CFO synchronization will be very excellent because the correlation of guard interval and tail of symbol can average the noise induced by AWGN. However, the DVB-T/H system is an outdoor wireless communication application and robust ability to long delay spread of multipath channel is necessary. As Fig. 2.5 shows, the delay spread of multipath channel will affect the data of the front portion of the guard interval directly especially when the length of guard interval is relatively short (2k mode, Ng /N =1/ 32). In order to reduce the effect of multipath delay spread, several beginning samples of the guard interval must be discarded, and (2-9) can be rewritten as
1
where y is the number of discarded samples. However, discarding too many samples will also degrade the averaging performance. The optimal value of y will be shown by simulation result in chapter 3.
2.4 Integral Carrier Frequency Offset Synchronization
From previous section, we can know that the time domain guard interval correlation algorithm can only deal with the rotated phase error caused by the fractional CFO value. The imperfect effect caused by the integral CFO should be monitored and synchronized in frequency domain. Thanks to the compensation of
ε
^F , the residual fractional CFO εR is relatively smaller (εR ≤0.02) and the ICI noise is also neglected. In essence, the k-th transmitted subcarrier shows up at FFT output bin with subcarrier index k+ as Fig. 2-3 (b) εI shows. The subcarrier index shift, which is just equal to the integral CFO εI, must now be detected by using the pre-defined training sequence (continual and scattered pilots) or the null subcarriers. In later sections, some different algorithms of integral CFO synchronization will be illustrated and discussed.2.4.1 Conventional Pilots Based Approach
The DVB-T/H standard defines continual and scattered pilots for synchronization and equalization in frequency domain [3]. The signal power of the two kinds of pilots is at boosted power level and larger than the data and null subcarriers. The only difference between continual and scatter piloted is their subcarrier index. The continual pilots locate at fixed subcarrier index and do not shift as OFDM symbol number increases. However, scattered
pilots are inserted every 12 subcarriers and have an interval of 3 subcarriers in the next adjacent symbol. In general, the continual pilots based integral CFO synchronization algorithms are the most widely used because of its good performance in low SNR and mobile environment [12][13]. The main idea of this approach is based on the MLE theory. In the first step, the correlation between two continual pilots at the same subcarrier index for two successive symbols in the frequency domain based on shifting the pilot positions is calculated, and can be expressed as
* are the positions of the subcarriers to be correlated in two successive symbols, and m is the estimation range. The integer CFO value εI is then estimated by detecting the offset position i where the value Ci is maximized as
Fig. 2.6 shows the received signal according to the subcarrier in frequency domain when the integral CFO is equal to 1 subcarrier space. In DVB-T/H 2k mode, the positions of continual pilots should be 0, 48, 54, 87…. Accordingly, if the maximum value of is obtained from subcarriers 1, 49, 55, 88…, the estimated integral CFO is 1 because the position of maximum correlation is achieved one subcarrier position away from the original continual pilots. Because the continual pilots are transmitted at boosted power level, the power difference of correlation values is still apparent and not affected by strong noise even in low SNR and deep delay spread channel condition. The total number of multiplication when the acquisition of integral CFO is finished can be expressed as
Ci
(2 1) ( 4 2)
M = m+ ⋅ P⋅ + (2-13) where M is the total number of multiplication, and P is the number of correlated pilots, respectively. In DVB-T/H system, P is 45, 89, and 177 for 2k, 4k, and 8k mode. Apply (2-13) we can see that as the search range increases, if all of the continual pilots are used for estimation, the total number of multiplication will increase enormously. For example, if the desired search range m is 60 for 2k mode when using all continual pilots, the number of multiplication will raise up to 22022. For low power consideration, such large number of multiplication should be avoided. The tradeoff between estimator performance and power consumption has become an important task for the integral CFO acquisition.
Besides the continual pilots based approach, another algorithm based on both continual and scattered pilots (CP+SP) was also proposed [14]. This algorithm calculates the correlation between possible 4 types of CP+SP patterns with the shifted received symbol in frequency domain. By detecting the peak value of the correlation result among the 4 CP+SP patterns, the integral CFO and the scattered pilot mode can be estimated at the same time, and can be expressed as
where P’ is the total number of CP+SP, is the z type CP+SP sequence, and z is the subcarrier index pattern of 4 possible types of CP+SP, respectively. Although this approach can acquire the scattered pilot mode and the integral CFO at the same time, the computational complexity also rises to about 4 times of the continual pilots based one and leads to more power consumption.
,
Yz k
2.4.2 Conventional Guard Band Based Approach
In DVB-T/H system, the number of subcarriers K within an OFDM symbol is chosen smaller than the symbol length N to provide that so-called “guard bands” at the edges of the transmission spectrum are left free. Hence all the subcarriers within guard-bands are composed of null subcarriers and the transmitted signal power is zero. According to the DVB-T standard, the signal power of the useful data subcarrier is normalized to 1, and the power of the reference pilots is 16/9 [3]. By exploiting the feature of power difference, a guard band power detection based algorithm for integral CFO acquisition was proposed by Kim in 1997 [15]. This algorithm utilizes the guard bands in both sides of spectrum as a moving window to search the subcarrier index shift value caused by the integral CFO. The main idea is that when the useful signal component (data or pilot subcarriers) is not within the moving window, the total component power within the moving window includes only noise component. So when the power of the moving window reaches minimum, the shift value of the window is equal to the shift value of signal spectrum due to the integral CFO, and can be expressed as where w is the width of the moving window at both sides of the guard band and is set as 5.
Kmin Kmax N−1
Fig. 2.7 Received symbol in frequency domain when CFO is -2
Fig. 2.7 shows the received symbol spectrum in frequency domain according to subcarrier index when the integral CFO is -2 subcarrier space. As we can see the minimum power appears in the moving window where i is -2 because it does not include any data or pilot component. The total number of multiplication M required for the acquisition of integral CFO can be expressed as
( 2 )
M = w+ m ⋅ 4 (2-16) From (2-16), we can find that the number of multiplication M could be reduced effectively by using small moving window width w. However, small w may lead this algorithm to worse performance in low SNR and deep frequency selective fading environment. So the trade-off between w and M should be treated very carefully.
In order to improve the performance of the conventional guard band power detection based algorithm, another modified guard band power detection method was proposed [16].
This algorithm modifies the structure of the symbol spectrum and inserts additional null subcarriers within the useful subcarriers to reduce the influence from ICI noise and deep frequency selective fading. However, the modification conflicts with the DVB-T/H standard
and can not be applied for our system platform.
2.4.3 Proposed 2-stage Approach
From previous sections, we can conclude that neither the continual pilots based algorithm nor the guard band power detection based algorithm can satisfy good performance and low computational complexity at the same time. Besides, the number of multiplication of all these algorithms is in proportion to the search range. If we want to let the integral CFO estimator work in low SNR and deep frequency selective fading environment and search large range CFO with low computational complexity, none of these algorithms is the best choice. In order to solve this problem, a 2-stage integral CFO acquisition algorithm is proposed as Fug 2.8 shows. The objective of the first stage is to recognize whether the integral CFO value εI is positive or negative (i.e. to find whether the direction of subcarrier shift due to integral CFO is right or left) with a low complexity guard band based algorithm. Once the first stage
From previous sections, we can conclude that neither the continual pilots based algorithm nor the guard band power detection based algorithm can satisfy good performance and low computational complexity at the same time. Besides, the number of multiplication of all these algorithms is in proportion to the search range. If we want to let the integral CFO estimator work in low SNR and deep frequency selective fading environment and search large range CFO with low computational complexity, none of these algorithms is the best choice. In order to solve this problem, a 2-stage integral CFO acquisition algorithm is proposed as Fug 2.8 shows. The objective of the first stage is to recognize whether the integral CFO value εI is positive or negative (i.e. to find whether the direction of subcarrier shift due to integral CFO is right or left) with a low complexity guard band based algorithm. Once the first stage