Effect of Sampling Clock Offset

Sampling clock errors introduce the clock phase error and the clock frequency error. Clock phase error effects are similar to symbol timing errors and can be treated in the same way. The constant fractional error can be compensated by a simple rotation or interpolation techniques. However, the time varying offset results in phase changes and ICI, because the sub-carriers are not orthogonal any more.

If we define the sampling clock frequency offset as

s

where Ts and Ts` are the transmitter sampling period and the receiver sampling period respectively. The received signal can be expressed as [12,13]

( )

n k

15

is the noise caused by the clock frequency offset with variance [13]

[ ] ^{2 ( )2}

) 3 , (

Var π β

β n k k

N ≈ (2.19)

The degradation grows at a rate proportional to the square of the product of the clock offset β and the subcarrier index k. The phase rotation increases with symbol index n. The clock offset β is small in most practical case, sinc(πβk)≈1. Thus, the effect of sampling clock offset can be approximated as an additional phase rotation. Under wireless communication conditions Nβ(n,k) can be neglected (βk << 1), but the phase rotation increases with symbol index and cannot be neglected.

Table 2.2 lists the parameters of several wireless communication standards about the effect of sampling clock offset. In DAB system, the number of symbols in a frame is fixed as 76 and the modulation scheme is DQPSK. Therefore, the sampling clock offset is not a serious problem in this system. However, when the frame size is not fixed or the number of subcarriers is large, we suggest that the sampling clock synchronization is needed, especially for 8K-mode DVB-T.

16

Table 2.2 Parameter comparison among various OFDM standards.

Fs : the sampling frequency. Nsubcarrier : the number of subcarriers.

Fs N subcarrier Modulation

802.11n 20MHz 64

128

BQPSK QPSK 16QAM 64QAM

DAB 2.048MHz

2048 512 256 1024

DQPSK

DVB

9.14MHz 8MHz 6.8MHz

2048 8192

QPSK 16QAM 64QAM

802.16a 22.857MHz 2048

QPSK 16QAM 64QAM

17

Chapter 3

Introduction to IEEE 802.11n

3.1 Overview of IEEE 802.11 Standard

The original version of the standard IEEE 802.11 [5] released in 1997 specifies two raw data rates of 1 and 2 megabits per second (Mbps) to be transmitted via infrared (IR) signals or in the Industrial Scientific Medical frequency band at 2.4 GHz. IR remains a part of the standard but has no actual implementations.

In the IEEE 802.11 family, the most popular techniques are those defined by the a, b, and g amendments to the original standard; security was originally included, and was later enhanced via the 802.11i amendment. Other standards in the family (c–f, h–j, n)

18

are service enhancement and extensions, or corrections to previous specifications.

802.11b [15] was the first widely accepted wireless networking standard, followed by 802.11a [6] and 802.11g [16].

802.11a standard uses the 5 GHz band, while 802.11b and 802.11g standards use the unlicensed 2.4 GHz band. Operating in an unregulated frequency band, 802.11b and 802.11g equipments will result in interference from microwave ovens, cordless phones, and other appliances using the same 2.4 GHz band.

The IEEE 802.11 standard was adopted in 1997. Since then, several extensions to the standard have been developed, and more are emerging. The complete family of the current and emerging 802.11 standards are listed in Table 3.1.

3.2 History and Current Status of IEEE 802.11n

The 802.11n is the next generation extension of the physical layer. It is expected that 802.11n will support throughput rates (useful data rates) of over 100 Mbps. The standard is still in the earlier development phase. Among the proposed approaches to provide such high data rates are smart antenna technology, enhanced modulation, and increased channel bandwidth (using both 2.4 and 5GHz bands).

IEEE 802.11n standard process has three stages: the stage 1 is the preparation stage from Jan. 2002 to Sep. 2002; the stage 2 is the IEEE 802.11 High Throughput Study Group (HTSG) from Sep. 2002 to Sep. 2003; the stage 3 is the IEEE 802.11n Task Group from Sep. 2003 to Sep. 2005 (expected).

19

Table 3.1 Summary of IEEE 802.11 standards.

Standard Description Status

802.11 The original 1 Mbps and 2 Mbps 2.4 GHz RF and IR standard

Released in 1997

802.11a 54Mbps,5GHz Ratified in1999, shipping products in 2001

802.11b Enhancements to 802.11 to support 5.5 and 11 Mbps, 2.4GHz

Ratified in1999

802.11c Access point bridging Completed

802.11d Regulatory extensions Completed

802.11e Quality of Service Completed 802.11f Inter Access Point roaming Completed

802.11g 54Mbps,2.4GHz

(backwards compatible with b)

Completed in 2003

802.11h Transmit power control, Dynamic frequency selection

Completed

802.11i Enhanced security Completed

802.11j Japanese regulatory extensions Completed 802.11k Radio resource measurement Ongoing

802.11m Maintenance Ongoing

802.11n Higher throughput improvements (100+ Mbps)

Expected completion in 2006-2007

20

In January 2004, IEEE announced that it had formed a new 802.11 Task Group (TGn) to develop a new amendment to the 802.11 standard for local-area wireless networks. The real data throughput rate will be at least 100 Mbps (which may require an even higher raw data rate at the physical layer), and should be up to 4–5 times faster than 802.11a or 802.11g, and perhaps 20 times faster than 802.11b. It is projected that 802.11n will also offer a better operating distance than current networks. There are two competing variants of the 802.11n standard: WWiSE (backed by companies including Broadcom) and TGn Sync (backed by Intel, Philips and others). The standardization process is expected to be completed by the end of 2006.

802.11n builds upon previous 802.11 standards by adding MIMO (multiple-input multiple-output). The additional transmitter and receiver antennas allow for increased data throughput through spatial multiplexing and increased range by exploiting the spatial diversity, perhaps through coding schemes like Alamouti coding.

TGnSync [4] and WWiSE [3] are the two major proposals for IEEE 802.11n Task Group.Both proposals emphasize compatibility with existing installed base, building on experience with interoperability in 802.11a/g and previous 802.11 amendments.

Therefore, in the next section, we review the physical layer of wireless LAN 802.11a systems based on OFDM technology.

3.3 Physical Layer of IEEE 802.11a

The 802.11a standard, introduced at the same time as 802.11b, is intended for the 5 GHz license-free UNII band and provides data rates up to 54 Mbps. The 5 GHz band has an advantage of large bandwidth allocated for the unlicensed operations. There are

21

455 MHz available (5.15 – 5.35 MHz and 5.470 – 5.725 MHz) for use by WLAN systems in Europe. This allows 19 non-overlapping channels in the 5 GHz band versus 3 non-overlapping channels in the 2.4 GHz band.

802.11a is based on Orthogonal Frequency Division Multiplexing (OFDM) modulation, and allows to achieve higher data rates within about the same channel bandwidth as 802.11b.

The IEEE 802.11a operates at a sampling rate of 20M Hz and uses 64-point FFT.

The OFDM frame duration is 80 samples where 64 is for data while 16 is cyclic prefix.

Since the symbol rate on each subcarrier is slower than the original data rate, the OFDM technique is particularly efficient in time dispersive environments. The 802.11a OFDM signal consists of 52 carriers. Data are sent on 48 carriers simultaneously, with 4 carriers used as pilots to aid in channel estimation at the receiver. The main system parameters of IEEE 802.11a Wireless LAN standard are listed in Table 3.2.

Using different modulation QAM combined with punctures of convolutional encoder, variable data rate can be achieved with a minimum 6Mbps and maximum 54 Mbps. Table 3.3 shows supported data rates. Various data rates are provided by changing the redundancy in the error correction coding and by changing modulation scheme.

Adopted in 2003, the 802.11g extension enables 54 Mbps data rates, the same data rate as provided by the 802.11a standard, but now in the 2.4 GHz band. This is achieved by using the same data rates and modulation formats as used in the 802.11a standard.

Additionally, the 802.11g standard is backward compatible with the 802.11b standard, i.e. the 802.11b modulation formats and data rates are supported.

22

Table 3.2 The parameters of IEEE 802.11a system.

Sampling rate 20MHz

Number of FFT points 64

Number of data subcarriers 48 Number of pilot subcarriers 4

Subcarrier spacing 0.3125 MHz (=20MHz/64)

OFDM symbol period 4μs (80 samples)

Cyclic prefix period 0.8μs (16 samples)

FFT symbol period 6.2μs (64 samples)

Modulation scheme BPSK,QPSK,16QAM,64QAM

Coding 1/2 convolutional, constraint length 7,

optional puncturing

Data rate 6, 9, 12, 18, 24, 36, 48, 54 Mbps

Short training sequence duration 8μs Long training sequence duration 8μs Long training symbol GI duration 1.6μs

23

Table 3.3 Data rates and rate-dependent parameters of 802.11a standard.

In IEEE 802.11a standard, a frame is composed of three fields. Figure 3.1 shows the frame format of IEEE 802.11a. The preamble field is modulated with QPSK, and no interleaving and scrambling. Figure 3.2 shows the preamble format and the possible arrangement of the synchronization and channel estimation for the receiver.

In the preamble field, the preambles are composed of ten repeated short symbols and two repeated long symbols. Both the total durations of short training symbols and long training symbols are 8 µs. The SIGNAL field is modulated with BPSK, interleaving, but no scrambling. Because the SIGNAL contains the most important information of the packet, every synchronization and channel estimation must be done before decoding of the SIGNAL. In the DATA field, modulation and coding rate depend on the information carried by SIGNAL field, interleaving and scrambling are executed.

24

Figure 3.1 The frame format of IEEE 802.11a standard.

Short Training Symbol Field

•Frame Timing Sync.

•Coarse CFO Sync.

•Symbol Timing Sync.

Long Training Symbol Field

•Fine CFO Sync.

•Channel Estimation.

Figure 3.2 The training symbol structure of 802.11a.

Pad One OFDM Symbol

DATA

Variable Number of OFDM Sy mbols

Pad One OFDM Symbol

DATA

Variable Number of OFDM Sy mbols PLCP Preamble

12 Symbols

SIG NAL One OFDM Symbol

DATA

Variable Number of OFDM Sy mbols

25

3.4 Preamble Format of IEEE 802.11n

For the purpose of compatibility with the 802.11 legacy devices, the legacy part of preamble format in WWiSE and TGnSync proposals is the same as in 802.11a. If the legacy preambles are transmitted from multiple antennas, the mapping of this single spatial stream to multiple antennas has to be done such that beamforming in far-field is mitigated. One method for achieving this is to use a cyclical delay diversity (CDD) mapping. The cyclical delay is used by both WWiSE and TGnSync proposals. In WWiSE proposal, the CDD format of each spatial data stream is disclosed clearly in the documents. For the reason given above, we will use WWiSE cyclical delay format for simulation.

Green-field preambles and mixed-mode preambles are the two preamble types in WWiSE proposal. Green-field preambles operate with only 11n devices, but mixed-mode preambles are capable of operation in presence of legacy 11a/g device.

Green-field preambles have greater efficiency than mixed-mode preambles. Figure 3.3 shows the two preamble types of WWiSE proposal. Since the synchronization procedures have to be operated before the SIGNAL field, we must use the preambles in front of the SIGNAL field to correct the timing and frequency offsets.

26

(b) Mixed-mode preamble format.

(a) Green-field preamble format.

STRN LTRN

GI2₅ SIGNAL

100 ns cs

GI2₅ SIGNAL

100 ns cs

−

Figure 3.3 The preamble formats in WWiSE 802.11n proposal.

Note: STRN: the short training sequence. LTRN: the long training symbol. GI2: the guard interval of the successive long training symbol. SIGNAL: the signal field

capable of 11a. SIGNAL-N: the new signal field in 11n.

27

Chapter 4

Synchronization Techniques for MIMO OFDM Systems

Synchronization plays an important role in the receiver design of MIMO-OFDM systems. The tasks of synchronization include frame detection, symbol timing synchronization, carrier frequency offset synchronization, and sampling clock offset synchronization. The methods for synchronizations in MIMO-OFDM systems are similar to SISO-OFDM systems. However, we can combine more estimated parameter samples from multiple receiver antennas than SISO cases and obtain more accurate synchronization.

First, we have to detect the frame start, then estimate the coarse symbol timing, and the coarse frequency offset. Finally, we estimate the fine frequency offset, the fine

28

symbol timing, and the sampling clock offset. Figure 4.1 shows the flow of synchronization scheme.

Step 1: Detect the beginning of frame.

Step 2: Use the short training sequence to estimate the coarse CFO, average the coarse CFOs estimated by multiple receiver antennas to obtain the more accurate estimation, and compensate the coarse CFO.

Step 3: Use the short training sequence to estimate the coarse symbol timing.

Step 4: Use the long training sequence to estimate the fine CFO, average the fine CFOs estimated by multiple receiver antennas to obtain the more accurate estimation, and compensate the fine CFO.

Step 5: Use the pilots in data symbol to estimate the clock offset, average the clock offsets estimated by multiple receiver antennas to obtain more accurate estimations, and compensate the clock offsets.

We will discuss those schemes further in the following sections.

29

Channel Estimation & S-T decoding

MIMO Combing of Coarse CFO

MIMO Combing of Fine CFO

MIMO Combing of COE Frame Timing Estimation

Coarse CFO Estimation

Compensate the Clock Offset Clock Offset Estimation Fine Symbol Timing Estimation

Compensate the Fine CFO Fine CFO Estimation Compensate the Coarse CFO

Coarse Symbol Timing Estimation

Figure 4.1 The flow chart of the synchronization scheme.

30

4.1 Frame synchronization [44]

The short training sequence is used to detect the frame start by defining a signal power threshold. The power threshold is obtained by the moving-average of signal power of the following equation:

∑

= − ⋅ −

where j is the receiver antenna index, n is the sample index, Nw is the moving average window length, and c is the selected power level. Then the moving average of auto-correlation output defined in (4.2) for STRN is compared with the calculated power threshold. If the auto–correlation values exceed the threshold consecutively, frame detection is declared.

15 2

In Figure 4.2, the solid line indicates the absolute values of the auto–correlation outputs (4.2), the doted line indicates the threshold (4.1). Figure 4.3 shows the block diagram of frame detection.

31

Figure 4.2 The power threshold values and the auto-correlation outputs vs. sample index for STRN in the frame detection [44].

Sampled signal

Auto-Correlator

Moving Average

( . )²

Moving Average

Threshold mapping

Compare

Frame Detection Sampled

signal

Moving Average

( . )²

Moving Average

Threshold mapping

Compare

Frame Detection

Figure 4.3 The functional block diagram of the frame detection [44].

32

4.2 Carrier Frequency Synchronization

4.2.1 Conventional Methods for Carrier Frequency Synchronization [17,18,19,20,21]

The short training sequence is used to estimate the coarse carrier frequency offset.

Since the format of short preamble, r_j,n−k and r_j,n−k−16 are repeated data which have

the same phase; the phase of φ_j,n is affected by the carrier frequency offset so that the coarse frequency can be estimated. Furthermore, the frequency offset estimation of up to +/- 2 subcarrier spacings can be obtained base on the phase of the auto-correlation function in Equation (4.3).

The angle can be detected in three different ways, the conventional method is to detect the peak location or a fixed location of the auto-correlation outputs [17,18,19,20,21]. Equations (4.5) and (4.6) indicate the two methods respectively.

∑= − ⋅ − − proper fixed index.

33

After compensating the coarse frequency offset, one can use the long training sequence, which is formed by two repeated 64-point long training symbols and a 32-point guard interval, for fine carrier frequency offset.

∑= − ⋅ − −

Like the method of the coarse frequency offset estimation, there are two conventional ways to detect the angles of the auto-correlation outputs. We describe the two ways in Equations (4.9) and (4.10) respectively.

}

4.2.2 The Proposed Smoothed Method for Carrier Frequency Synchronization

Since the short training sequence is composed of ten repeated short training symbols and the long training sequence is formed by two repeated 64-point long training symbols and a 32-point guard interval, we can average some selected points of the auto-correlation output to decrease the noise effect.

)}

coarse N avg

f T φ

π ^(4.11)

34

)}

( )

/ 1

* {(

64

* 2

1

1 2 ,

∑ ∑

= ∈

∠

=

∆ ^NRX

j n win n j

RX S

fine N avg

f T ψ

π ^(4.12)

where win1 and win2 are the selected ranges for the auto-correlation outputs. We will compare the performance of the three methods in the next chapter.

Figure 4.4 shows the ranges we selected for the averaging window. The solid line indicates the absolute value of the auto-correlation outputs for the short training sequence (4.3), and the doted line indicates the absolute value of the auto-correlation outputs for the long training sequence (4.7).

Figure 4.4 The selected ranges of the coarse (win1) and fine (win2) frequency estimation.

35

4.3 Symbol Timing Synchronization

4.3.1 Coarse Symbol Timing Synchronization

As the number of spatial data stream increases, the matched filtering method [22,23,24] used in 802.11a fails. Figure 2.4 shows the phenomenon clearly. The dotted line indicates the absolute value of the auto-correlation outputs (4.13), and the solid line indicates the absolute value of the matched-filter outputs (4.14). We assume that there is only one receiver antenna in Figure 4.5.

∑

= − ⋅ − −

As the number of the spatial data stream increases, the matched-filter outputs will decrease accordingly. For the reason given above, one can’t use the matched filter output values to estimate symbol timing reliably. The double-sliding-window method [45] can be used to overcome this problem. These two consecutive sliding windows accumulate the absolute values of the short training sequence auto-correlation outputs defined in Equation (4.13).

∑= − −

where A and B are the two sliding window values. In the sliding process, B window

36

will slide in the long training field, while A window still in the short training field; the ratioj,n reaches its maximal value. One can use the location of peak value to indicate the coarse symbol timing.

37

Figure 4.5 Auto-correlation outputs and matched filter outputs, using the conventional symbol synchronization technique. (a) NT=1. (b) NT=2. (c) NT=3. (d)

NT=4.

38

4.3.2 Fine Symbol Timing Synchronization

4.3.2.1 Conventional Method for Fine Symbol Timing Synchronization [25, 26]

After the stage of coarse symbol timing estimation, it is assumed that the estimation error is within +/- 5 samples. As the number of transmitter antennas is more than three, the accuracy is not enough for the equalizer. For the reason mentioned above, one has to further increase symbol timing accuracy.

In the literature [25,26], detecting the first path of the channel impulse response is the major method to estimate the fine symbol timing. The conventional method [25, 26]

uses IFFT operation to transfer the estimated channel frequency response to time domain, then detect the first path whose magnitude is larger than a proper threshold as follows.

where n is the frame index, k is the subcarrier index, Rn,k is the received data after FFT, m is the sample time index, Xn,k is the all-pilot preamble in the long training field,

2 ,k

Xn =1 k=1,2,…,N in 802.11n, η is the threshold, δ is the estimated fine symbol

39

timing, α is 0.5 in our simulation. We define this conventional method as conventional frequency-domain fine symbol timing synchronization (CFDFS) method in the following.

4.3.2.2 The Proposed Method for Fine Symbol Timing Synchronization

The CFDFS method with IFFT should introduce serious round-off errors, this phenomenon can be analyzed further in the future. For the reason, without resorting to frequency-domain operations we propose the direct time-domain fine symbol timing synchronization (DTDFS) method based on circular convolution to estimate the channel impulse response.

*

Since the estimation error is less than +/- 5 samples after the coarse symbol timing estimation, we can reduce the computation complexity by directly calculating time-domain circular convolution outputs in the range of the +/- 5 points as shown by Equation (4.24) and adjust the fine symbol timing. This simplified method is defined as simplified direct time-domain fine symbol timing synchronization (STDFS) method.

( )

m r

( )

m x

( )

m m N N N

hˆ_n = _n ⊗ _n^* − =1,2,..,5 & −4, −3,.., (4.24) Table 4.1 shows the computation complexity of the three methods, we can find that the computation complexity of the proposed STDFS method is almost the same as the conventional IFFT method or even less, when the number of subcarriers is large and

40

the range for adjustment is small. Furthermore, the proposed method based on simplified circular convolution uses the received signal for computation directly. For the reason, the proposed SFDFS method should reduce the round-off errors in practice.

Table 4.1 The computational complexity comparison of fine symbol timing estimation.

Methods No. of multiplications No. of additions CFDFS [25, 26] (Radix-2) ^N×log₂ ^{N+N 2N×log}₂ ^N

Proposed DTDFS N ² N

(

N−1

)

Proposed STDFS L×N L

(

N −1

)

N: FFT length L: the range for fine search and adjustment

4.4 Sampling Clock Offset Synchronization

4.4 Sampling Clock Offset Synchronization

在文檔中 多重輸入輸出正交分頻多工系統之同步設計研究 (頁 28-0)