Chapter 3 Introduction to IEEE 802.11n
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.
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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].
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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, rj,n−k and rj,n−k−16 are repeated data which have
the same phase; the phase of φj,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.
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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.
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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 Nhˆn = 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×log2 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
4.4.1 Sampling Clock Offset Estimation
4.4.1.1 Conventional Methods for Sampling Clock Offset Estimation [27,28]
Sampling clock offset results in a slow shift of sampling instants, and rotating the phase of data carried by subcarriers. For analyzing the sample clock offset, we define the normalized sampling clock offset as β in (4.25). The n-th received symbol with clock offset β can be expressed as (4.26)
s s s
T T T −
= '
β (4.25)
41
where Ts and Ts` are the transmitter sampling period and the receiver sampling period respectively. where N is the number of subcarriers, and Ng is the length of guard interval.
The method for sampling clock synchronization adopted here for acquisition uses the phase difference between two consecutive training symbols [27] as shown in Equation (4.28).
)
In the equation, by conjugating the (n-1)-th symbol and multiply it with the n-th symbol, the channel phase will be eliminated and the phase difference can be calculated. With the information of the phase difference, the sampling clock offset can be estimated using the information with various feasible ways. (4.29), (4.30), and (4.31) show three possible estimation schemes.
Method 1 [27]: carryingk pilot tones
k k k right averagek Z Y left averagek Z Y
⊂
=
42
) 1(
) (
2 Yright Yleft
C Ng N
N × ∠ −∠
= +
β) π (4.30)
Method 1 directly averages the overall phase-difference cases between any two pilot subcarriers and estimate the clock offset. Method 2 first separates the pilot carriers in two groups, then finds the difference of their averaged phase values, and finally estimates the clock offset.
4.4.1.2 The Proposed Method for Sampling Clock Offset Estimation
Method 1 treats the all phase-difference cases between any two pilot subcarriers equally and estimate the sampling clock offset by averaging all the offset estimate samples. In Equation (4.29), we can find the phase differences of various pilot pairs are divided by different constants. Since the constant is the distance the pilot carriers, the ability of eliminating noise effect increases with the distance between the pilot carriers.
Owing to that the ability of eliminating noise effect increases with the distance between the pilot carriers, we propose the method (4.31) by only using the most separated pilot carriers to estimate the sampling clock offset and simultaneously reduce the computational complexity.
Proposed Method :
43
⎥⎦
⎢ ⎤
⎣
⎡ ∠ − + − ∠ − +
+
= − (( − ) ( − ))
) )(
(
2 max min Zn,kmax n,kmax n 1,kmax Zn,kmin n,kmin n 1,kmin Ng
N k k
N φ φ φ φ
β) π
(4.31) When the number of receiver antennas is more than one, each receiver antenna performs the sampling clock offset estimation independently first. Since all the reception data streams use the same sampling clock oscillator, one can average all the estimated clock offset samples and obtain a low-noise clock offset estimation, then finally performs the clock offset compensation for all the reception data streams with the same clock offset.
4.4.2 Sampling Clock Offset Compensation
As soon as the sampling clock offset has been estimated, there are various feasible schemes to compensate the offset, such as adjusting the sampling frequency of ADC in the continuous-time domain, or rotating the FFT outputs in frequency domain, or correcting the timing by using a resampling interpolator in discrete-time domain.
The VCXO (Voltage-controlled crystal oscillator) is used to control the sampling frequency of ADC. However, a VCXO usually has higher cost and higher noise jitter than a XO (Crystal oscillator). For these reasons, the scheme is not suitable for 802.11n.
When the sampling clock offset compensation is performed by rotating the FFT outputs in frequency domain, no over-sampling is needed and the timing error correction can be done by a single complex multiplication. However, this method works well only when a small frequency offset is guaranteed. Accurate and expensive
44
XOs are required at both transmitter and receiver sides. Furthermore, the cost of updating the rotor coefficients is quite high. If a look-up table is used for coefficient updating, it will require a large memory.
Various interpolators [29,30,31,32,33] have been proposed to usually perform the compensation by time-domain resampling and applied to the compensation structure, shown in Figure 4.6. With a free-running oscillator, timing correction can be done by some discrete-time signal processing techniques on sample sequence. A simple interpolator may be a finite impulse response filter (FIR) that produces a fractional delay. The interpolator coefficients are time-varying, because they depend on the timing error to correct. Due to the time-varying filtering, the FFT output data suffers a time-varying phase rotation and attenuation. Such distortion introduces additional noises, especially on high frequency subcarriers that are close to the Nyquist frequency.
The noise can be reduced by over-sampling the received signal or by using a high-order interpolator. However, due to the high sampling rate and high computation complexity, those schemes might not be suitable for very high-rate systems.
ADC FFT
Phase Error Detector
to next stage Interpolator
Timing
&
Carrier Frequency Synchronization
Figure 4.6 Structure of discrete-time resampling timing correction.
In the following subsections, we will find suitable interpolators with low complexity and high performance.
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4.4.2.1 Designs of Digital Resampling [43]
Figure 4.7 shows an ideal fractional delay (FD) block, which can be viewed as a digital version of a continuous- time delay line. Therefore, the impulse response of an LSE (least square error) fractional delay filter is a shifted and sampled sinc function.
) ( sin )
(n c n D
h = − (4.32)
where n is the sample index and D is the delay with a fractional part d = D-floor(D) and an integral part floor(D).
S(n) h(n) S(n-D)
Figure 4.7 The discrete- time delay block.
- 4 - 3 - 2 - 1 0 1 2 3 4
- 0 .4 - 0 .2 0 0 . 2 0 . 4 0 . 6 0 . 8 1
S a m p le I n d e x (n )
Impulse response h(n)
(a)
46
- 4 - 3 - 2 - 1 0 1 2 3 4
- 0 .2 0 0 . 2 0 . 4 0 . 6 0 . 8
S a m p le I n d e x ( n )
Impulse Response h(n)
(b)
Figure 4.8 The impulse response of the sinc interpolator with the delay (a) d=0.0, (b) d=0.3
Figure 4.8 shows the LSE sinc impulse response when d=0 and d=0.3. Since the impulse response of sinc fraction delay filter is infinite-length, it should be truncated for practical applications. Since its impulse response is not absolutely summable and suffers from the well-known Gibbs phenomenum, the sinc FD filter is impractical with poor performance.
To design an efficient FD filter, finite-length, truncated and properly windowed sinc functions with small Gibbs phenomenon are desired. Signal interpolation is conceptually equal to a resampling operation on reconstructed signals in continuous-time domain. In order to obtain the reconstructed continuous-time signals, least-square interpolation, equirriple interpolation, windowed-sinc interpolation and polynomial-based interpolation are frequently used. In this work, we use various interpolators to perform the compensations, and assess theier performances when applied to IEE802.11n standard.
Since a resampling interpolator’s coefficients are time-varying, the introduced
47
time-varying phase rotation and attenuation are difficult to be equalized. Before simulating these interpolators, let’s check the frequency responses of some popular interpolators [43].
Figure 4.9 (a) (b) (c) (d) shows the responses of 4-tap fractional-delay FIR filters, which are obtained from several major windowed sinc functions. Figure 4.10 (a), (b), (c) , and (d) shows the responses of various 4-tap fractional-delay FIR filters, which are designed by general least-squares approximation, equirriple approximation, Lagrange interpolation and Cubic B-spline interpolation, respectively. Since the received data will be demodulated and decoded in frequency domain, frequency responses of those interpolators are important. Due to time-varying coefficients, a fractional delay FIR has different frequency responses with respect to the fractional part d of input delay D.
The magnitude response error and phase delay error will introduce additional noise. Therefore, an interpolator with small phase error and small magnitude response error is desired. In Figure 4.9 and 4.10, we can find that the magnitude distortion of the Cubic B-spline interpolation is serious at the high frequency band especially. For the reason, the performance of the Cubic B-spline interpolation is poor in its application to IEEE 802.11n. We will simulate these interpolation designs in the next chapter and find suitable designs for IEEE 802.11n.
48
NORMALI ZED FREQUENCY
MAGNITUDE
NORMALI ZED FREQUENCY
PHASE DELAY
NORMALI ZED FREQUENCY
MAGNITUDE
NORMALI ZED FREQUENCY
PHASE DELAY
NORMALI ZED FREQUENCY
MAGNITUDE
Windowed Sinc [Kaiser] L=4beta=3.3 wp= 1
0 0.2 0. 4 0.6 0.8 1
NORMALI ZED FREQUENCY
PHASE DELAY
NORMALI ZED FREQUENCY
MAGNITUDE
Windowed Sinc [Chebyshev] L=4 alpha= 40 wp=1)
0 0.2 0. 4 0.6 0.8 1
NORMALI ZED FREQUENCY
PHASE DELAY
(c) (d)
Figure 4.9 Frequency responses of windowed Sinc FIR FD filters: (a) Rectangular window; (b) Hamming window; (c) Kaiser window; (d) Chebyshev window.
d=0
49
NORMALI ZED FREQUENCY
MAGNITUDE
NORMALI ZED FREQUENCY
PHASE DELAY
NORMALI ZED FREQUENCY
MAGNITUDE
NORMALI ZED FREQUENCY
PHASE DELAY
NORMALI ZED FREQUENCY
MAGNITUDE
NORMALI ZED FREQUENCY
PHASE DELAY
(c) (d)
Figure 4.10 Frequency responses of various FIR FD filters: (a) General least-squares approximation; (b) Equirriple approximation; (c) Lagrange interpolation; (d) Cubic
d=0 d=0
50
B-spline interpolation
4.4.2.2 Discrete-time Over-resampling Techniques [34,35,36]
The windowed-sinc and some other FD interpolators obtained from other key design techniques, discussed in the previous section are realized by resampling the reconstructed analog functions from the original discrete samples. Intuitively, pure digital signal interpolation is a fundamental approach for FD interpolation. One can perform digital “over-sampling” operations [35,36] to achieve high-resolution FD.
With N-times oversampling, one can split a unit delay into N divisions, as shown in Figure 4.11. In the figure, H(z) is an Nth-band low-pass filter. Note that the proto-type filter H(z) can be obtained by various optimization techniques, such as least-square and equirriple approximations.
↑N H(z)
Figure 4.11 Block diagram of a digital N-times over-sampling LTI interpolator.
An N-branch polyphase interpolator can be formed by polyphase decomposition
An N-branch polyphase interpolator can be formed by polyphase decomposition