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 .
Synchronization Algorithms
2.1 Introduction to Unsynchronous Problems
In OFDM system, unsynchronous problems can be divided into two parts: timing and frequency. Timing unsynchronous problems concludes sampling clock offset (SCO) and symbol timing 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.
Frequency unsynchronous problems are carrier frequency offset (CFO) and phase mismatch in time axis. Phase mismatch problem is happened when symbol timing offset changed in the system with 2-D linear interpolation in channel estimation. The phase rotation difference in the same carrier index between adjacent symbols causes interpolation error in time axis is called phase mismatch. And in OFDM system, the spectrum of the individual subcarrier mutually overlaps and exhibits orthogonality to achieve optimum spectrum efficiency. However, CFO would make inter carrier interference (ICI). CFO is also introduced by the mismatch of oscillator frequency between transmitter and receiver. 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][7]. Hence the CFO synchronization is a very critical
problem to be solved in DVB-T/H system.
2.1.1 Effect of Carrier Frequency Offset and Sampling Clock 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 al,k, where l denotes the OFDM symbol index and k (0 ≤ 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
, be expressed as a time-variant phase error, ej2πΔft, 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 complex-valued additive white Gaussian noise (AWGN).
After demodulation via a fast Fourier transform (FFT), the l-th OFDM symbol at subcarrier k, R is as follows l k,
1 2 ' /
ICI is the inter-carrier interference noise due to carrier frequency offset. Likewise, l k H is l k, 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, W is a zero-mean l k, stationary complex process as well.
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 = Δ =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 2.1.
0 2 4 6 8 10
Fig 2.1 Phase rotation in time domain for long time reception when ε=0.01
-4 -3 -2 -1 0 1 2 3 4
Fig 2.2 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)
,
ICI degrades the system performance strongly because it destroys the orthogonality within l k
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),
expressed ass
I F
ε ε= +ε (2-6) From Fig. 2.2, 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.
The difference of rotatedphases between two adjacent symbols is represented as:
indicates, CFO causes mean phase error as well as SCO causes linear phase error between two adjacent symbols.
Fig 2.3 Phase rotation due to timing drifts
In Fig 2.3, it 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.
2.1.2 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 2.4, we call Δ 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 2.4 ISI-free region
Assume x(n) represents received data in time domain, X(k) is subcarrier after FFT operation
for x(n) with perfect symbol timing, and ˆ ( )X k denotes subcarrier after FFT operation with symbol timing offset ε in the ISI-free region. The detail equations are demonstrated as follows.
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 (2-8), 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 2.5. Fig 2.5(b) depicts the condition of symbol timing offset ε = 2 while Fig 2.5(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 in the ISI -free region
(b) Phase rotation due to symbol timing offset=2
(c) Phase rotation due to symbol timing offset=5
Fig 2.5 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 2.6. Fig 2.6(a) shows the phase rotation effect due to symbol timing offset of 5 samples while Fig 2.6(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 2.6 Mapping constellation
2.1.3 Effect of Carrier Phase Mismatch
The problem of carrier phase mismatch comes from the different phase rotation of post-FFT symbols by using 2-D channel equalization (2-D CE). To observe the carrier phase mismatch problem, we should discuss from fine symbol synchronization, SCO tracking and 2-D channel interpolation.
First, we discuss fine symbol synchronization. Fine symbol synchronization scheme in DVB-T/H system is the function of precisely monitoring the time symbol boundary to prevent ISI occurring in serious frequency selective fading channel. If we don’t use fine symbol synchronization, the carrier phase rotation would be too large and the phase between pilots to pilots would make the interpolation error, as shown in Fig 2.7. The performance would decrease very seriously.
Re Im
ˆp
θ H kp( )
( 1) H kp +
{
H k( )}
{ }
H kˆ ( )Fig 2.7 the influence of frame position error to interpolations
In our simulation, we choose IFFT method to be the algorithm of fine symbol synchronization. IFFT based method is the most popular algorithm in DVB-T/H system as shown in [1], [2]. Observing the channel impulse response (CIR) in time domain we can obtain the residual symbol timing offset information as shown in Fig 2.8.
N
N-2
N-5
Channel Impulse Response FFT Window
Cyclic prefix
Fig 2.8 Relative CIR due to inaccurate FFT window
As we know, fine symbol synchronization of IFFT based method uses the channel frequency response (CFR) of pilots in frequency domain. It goes through IFFT operation and then gets CIR. The source of CFR is calculated from 2-D linear interpolation as shown in Fig 2.9.
Frequency axis
Time axis
Fig 2.9 Interpolation of 2D channel estimation
2-D channel interpolation [8], usually used to resist severe multi-path and mobile environment, includes time and frequency axis interpolations. The first step is to store the previous 3 post-FFT symbols and use the pilot information producing the time axis interpolation. Then, in frequency axis it interpolates the total CFR Hl,k of previous 3-th post-FFT symbol. Before the frequency axis interpolation and after time axis interpolation, we take the interpolated (K/3) pilots to IFFT for obtaining CIR. And we must pad zeros to (N/2).
The decision equation express as
{
max}
After fine symbol updating, it remains phase rotation between pilots’ CFR, as shown in Fig 2.10. And the previous and current post-FFT symbols have different phase rotation. In 2-D linear interpolation algorithm, the previous symbols and pilots are stored in memory in order to time axis interpolation. At the same subcarrier index between previous and current
symbols, the different phase rotation makes phase mismatch. It would cause the performance degradation. The carrier phase mismatch is shown as
2 /
where Hp-pre(k) and Hp-cur(k) respectively means CFR of k-th pilot in previous symbols and current symbol in f-domain. H(k) means CFR of k-th subcarrier in f-domain symbol. Ĥ(k) means the estimated value.
Fig 2.10 the phase rotation of pilots’ CFR caused by different symbol timing offset
When the multi-path fading spread changes seriously, the channel impulse response would also changes, as shown in Fig 2.11. This situation is obvious in SCO effect in mobile environment. In order to simulate the influence of SCO in carrier phase mismatch, we plus one term to modify the equation and is expressed as
2 ( ) / 2 /
ˆ ( ) ( ) i k cur pre N ( ) i k N
H k =H k e π ε −ε −εΔδ =H k e π εΔ (2-11)
N-5
Cyclic prefix
Root mean square delay spread
Fig 2.11 Relative channel impulse response with multi-path
Summary of this section, we understand the carrier phase mismatch in time axis is happened in a specific situation. It is in mobile environment with SCO effect and 2-D CE must be used in receiver platform. However, 2-D CE is the most common architecture in state-of-the-art and SCO effect in mobile environment is the significant issue for synchronization in DVB-H system. Thus, the problem of carrier phase mismatch has to be solved.
2.2 Carrier Phase Alignment
Phase alignment locates after fine symbol synchronization scheme and passes information to channel estimator and equalizer, as shown in Fig 2.12. In resent research, carrier phase rotation problem caused by residual symbol timing offset is brought up to discuss. Large phase rotation will produce significant errors in linear channel interpolation, as mentioned in Section 2.1.4. To solve this problem, in [5], it provides a phase compensation method. It can deal with the interpolation error by compensating the phase rotation of pilots and symbols. And the compensating equation is expressed as
ˆ ( )p p( ) j kˆp
H k =H k e⋅ θ (2-12)
Fig 2.12 Location of phase alignment in receiver platform
where θˆp is detected out from channel frequency response of post-FFT symbols. Note that it doesn’t move the symbol boundary and it uses phase compensator to replace fine symbol scheme. It will cause a problem in fast frequency selective channel when the system is without fine symbol synchronization, the samples drift. Also, we show the comparison of performance between 2-D CE and 1-D CE in Fig 2.13.
Fig 2.13 Comparison of performance between 2-D CE and 1-D CE
However, two problems remain in [5]. The system of [5] is not scattered pilot based. 2-D CE is not discussed in [5] but the carrier phase mismatch is happened with 2-D CE. Moreover, in [5], the influence of SCO with Doppler effects is not considered. However, these two conditions are significant issues for synchronization in DVB-H system.
The proposed carrier phase alignment in time axis is to align the phase rotation of previous post-FFT symbols in 2-D interpolator buffers. The block diagram is shown in Fig 2.14.
Fig 2.14 the phase rotation of pilots’ CFR caused by different symbol timing offset
Frequency axis
Time ax is
Stored in Memory
Fig 2.15 2-D channel interpolation
In Fig 2.15, it shows 2-D CE. Interpolation in time axis acts before in frequency axis. The proposed phase alignment in time axis is to align the phase rotation of previous post-FFT symbols in 2-D interpolator buffers.
First step of carrier phase alignment, we take out the CFR of post-FFT symbol pilots by interpolation in time axis. Then, CFR is passed through fine symbol synchronization and we get the updating symbol bound. When the symbol boundary updated, the current symbol is passed to frequency domain and cause the phase mismatch to previous symbols in buffers.
axis will multiply the alignment factor in 3 parts, one is pilots before 3 previous symbols and the other parts are the estimated pilots and the symbol data before divider. Here the equations are expressed as at resampler out. After aligning the pilots in time axis, we interpolate the CFR of pilots in every 3 subcarriers in time axis, it can be expressed as
, , , Then interpolating the frequency axis subcarrier CFR to get total CFR in each subcarrier, it is expressed as Before subcarrier data are sent into divider, we align the phase as CFR of carriers. And the equations are expressed as
2 / 2 /
Architecture of the proposed phase alignment in time axis is shown in Fig 2.16.
S-1(20K Bytes)
Fig 2.16 Proposed time axis phase alignment architecture
After multiplying phase alignment factor e-i2πΔε⁄N, the CFR of pilots and symbol data are both on the same phase criterion. And the phase alignment is completed.
2.3 Fast Synchronization System
For the reason of power saving, Time-Slicing methodology in DVB-H system is used.
The saving of power consumption is in (1-6), where Bd means burst duration, St means synchronization time, Dj means delta-t jitter Cb means constant bandwidth, Bs means burst size and Ps means power saving. In this equation, Bd, Cb and Bs are defined in the DVB-H data, [4]. Hence, note that the synchronization time dominates the saving of power consumption in fixed mode. In Fig 2.17, it shows the composition of completed synchronization time. According to Fig 2.17, we can get the information as
St = max{(Ta + Ttps + Trs); (Ta + Tt)} (2-18) where St means synchronization time, Ta means acquisition time, Ttps means transimission parameter signaling (TPS) decode time, Trs is Reed-Solomon (RS) packet synchronization time and Tt means the SCO/CFO tracking time.
Burst Duration Off-time
Synchronization Time
RS packet sync.
Acquisition Time
TPS decode
SCO/CFO tracking
Fig 2.17 composition of completed synchronization time
The determination of synchronization time depends on SCO/CFO tracking is longer or the summation of TPS decoded time and RS packet synchronization time is longer. SCO/CFO tracking time depends on channel effects. However, the TPS decoder and RS packet synchronization needs a fixed time to receive enough symbols. Hence, in this section, we discuss the TPS decoded and RS packet synchronization. In Fig 2.18, it shows the location of these two designs in the receiver platform.
Fig 2.18 Location of fast synchronization in receiver platform
Acquisition time is about 10 symbols, TPS decoded time is about 2 frames (136 symbols), RS sync. Time is about 4/2/1 frames (272/136/68 symbols) and the total synchronization time in costs 417/281/213 symbols in 8k/4k/2k mode in conventional method.
And we can see the symbol duration time in this equation:
symbol duration=N T (1+GI) × × (2-19) where N is 2k/4k/8k, T is elementary period 7/64, 1/8, 7/84 and 7/40 μs in 8MHz, 7MHz, 6MHz and 5MHz channel and GI is 1/4, 1/8, 1/16 and 1/32.
2.3.1 TPS Decode
The structure of TPS listed in DVB-T/H standard [3] is composite of 68-bit word (one frame) and concludes 16-bit synchronization word and 1 initialization bit. The transmission parameter information shall be transmitted as shown in table 2-1. Here, one symbol includes one bit TPS and one frame includes 68 bits TPS information.
The mapping of each of the transmission parameters: constellation characteristics, α value, code rate(s), super-frame indicator and guard interval onto the bit combinations is performed according to clauses appendix A. The left most bit is sent first.
Table 2-1 TPS signaling information and content Bit number Purpose/Content
s0 Initialization
s1 to s16 Synchronization word
s17 to s22 Length indicator
s23, s24 Frame number
s25, s26 Constellation
s27, s28, s29 Hierarchy information
s30, s31, s32 Code rate, HP stream
s33, s34, s35 Code rate, LP stream
s36, s37 Guard interval
s38, s39 Transmission mode
s40 to s47 Cell identifier
s48, s49 DVB-H signaling
s50 to s53 Reserved for future use
s54 to s67 Error protection
The first bit, s0, is an initialization bit for the differential 2-PSK modulation. The modulation of the TPS initialization bit is derived from the PRBS sequence defined in [3]. Bit 1 to 16 of the TPS is a synchronization word. The first and third TPS block in each super-frame haves the following synchronization word:
s1 - s16 = 0011010111101110.
The second and fourth TPS blocks have the following synchronization word:
s1 - s16 = 1100101000010001.
The conventional design [1] of TPS decoded costs 135 (68 + 67) symbols time in the worst situation to receive the completed TPS word and then synchronizes the header. This is the primitive method, that it uses more than one frame to find the synchronization word and initialization bit and then decodes TPS. The conventional operation of TPS word distributes in Fig 2.19.
Fig 2.19 the operation of conventional TPS word
The proposed method can decode out TPS faster than conventional method. The proposed method is to buffer the previous 68-bit TPS word. When finding the 16-bit synchronization word and initialization bit, we read the previous 51 words information as TPS decoded word.
Hence, we can advance the time of 51 symbols. The worst case of the decoded time is 84 (67+17) symbols. We can see the operation of proposed TPS word distribution in Fig 2.20.
16 51
16 51
Worse case searching time
Worse case searching time