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CHAPTER 2. SYSTEM PLATFORM

2.3.4 AWGN Model

The AWGN channel model is established by the random generator in Matlab. The output random signal is normally distributed with zero mean and variance equal to 1. The complex AWGN noise can be modeled as

2 1 10

1 20

SNR PS

l randn j

l randn t

w

⋅ +

=[ ( , ) ( , )]

)

( (2.12)

Where PS is the data signal power, SNR is the signal to noise power ratio, and l is the data signal length.

Chapter 3.

A Frequency Synchronizer Design for OFDM WLAN Systems

As for the complement to periodic and non-constant-power preamble in IEEE 802.11a, low-complexity frequency estimators are of interest. Such estimator is relied on the phase information of auto correlations. In this chapter, we chose fewer samples for auto correlation based on the average power of preamble before FFT process. We also derive the performance and show how the correlation samples should be properly chosen with acceptable SNR loss.

3.1 Carrier Frequency Offset Synchronization

For packet-based OFDM wireless systems, the burst synchronization is needed. We generally used data-aided methods which inserted the special synchronization information to estimate the CFO. The data-aided CFO estimation can achieve the system requirement in a very short time period.

3.1.1 The algorithms of CFO estimation and compensation

In the 1994, Paul H. Moose [14] proposed a method to estimate frequency offset from the demodulated data signals in the receiver. This method involves repetition of a data symbol and compares the phases of each of the carriers between the successive symbols. Since the modulation phase values are not changed, the phase shift of each of the carriers between successive repeated symbols is due to the frequency offset.

received training symbol r that interfered by CFO n ∈ is shown in (3.11), and –K…K are

The kth elements of the N point DFT of the first and second N points of (3.11) are shown in (3.12) and (3.13) respectively.

1

Including the AWGN as below,

1

Both the ICI and the signal of the first and second observations are altered in exactly the same way, by a phase shift proportional to frequency offset. Therefore, the offset ∈ will be estimated using observations (3.15) is shown in (3.16).

⎭⎬

This algorithm, however, can only correctly distinguish the phase rotation in the range [-π, π], the estimation limitation is shown in equation (3.17). In (3.17) and (3.18), the NTs

means the time interval between the two repeat symbols. Minimizing the interval time to the OFDM symbol time can make the maximum CFO estimation range to be half of the subchannel bandwidth. According to the (3.18), the method to get a larger CFO estimation range is to shorten the training symbol time. The idea is also suggested in the [14].

π π

π∈= 2 NTsf

2 (3.17)

NTs

f 2

1

(3.18)

After finishing the acquisition of CFO, we counteract the frequency offset that we estimated to compensate the following complex data signal as equation (3.19).

,...

, , ˆ );

ˆ = r ⋅exp(− j2kT k = 0 1 2

rk k π (3.19)

Where r are the received complex signals that influenced by CFO k ∈ and k are the indexes of data signal.

3.1.2 The structure of CFO estimation and compensation

The training symbols are provided for burst synchronization in the packet-based transmission system. As previous discussion in section 3.2.1, the repeated OFDM symbols can be used to perform the CFO synchronization. One reason we using time domain estimation and compensation is that the frame detector can get a less distortion training pattern to judge the frame boundary more accurately. The other one is that the compensated training data can be used to estimate the channel response directly by the channel equalizer after FFT process.

In order to cover a larger CFO estimation range, we need two stages CFO estimation as Figure 3.1 by means of short and long symbols in the preamble. According to the properties of short and long training symbols, coarse CFO estimation gets a rougher estimate under a wider frequency offset range while fine CFO estimation gets narrower but more accurate results.

Taking advantages of both estimation results in a more precise estimate for CFO under a wider CFO range. Basing on the IEEE 802.11a specification, the maximum tolerance center frequency offset of the transmitter and the receiver shall be within ±40ppm of 5.3 GHz RF frequency; that is equal to ±212 KHz; and further, due to the 0.8µs short and 3.2µs long training preamble provided for coarse and fine CFO estimation, the enduring estimation range

are about -118ppm ~ 118ppm (-625KHz ~ 625KHz) and -30ppm ~ 30ppm (-156.25KHz ~

Figure 3.1 The structure of two stages CFO synchronization

In the acquisition scheme, coarse and fine CFO estimations and compensations are performed by using the same algorithms. The coarse CFO estimation is available from equation (3.20). short training symbol. Before fine CFO estimation, the long training symbols shall be compensated with the frequency estimated as equation (3.21).

127

Where k is index of long training symbol, and T is sample period that equal to 1/20MHz.

Therefore the fine CFO estimation is represented as equation (3.22).

⎥⎥ long training symbol.

After finishing the acquisition of CFO, both coarse and fine estimation is available. The

following complex data signals including of long symbols, header and payload shall be compensated by estimated coarse and fine CFO as equation (3.23) and rk is the complex signal beginning from long symbols.

,...

, , ];

ˆ ) (ˆ

ˆ = r ⋅exp[− j2 k ∈ +∈ T k = 01 2

rk k π coarse fine (3.23)

3.2 The Proposed CFO Estimation Scheme

In a real system, several synchronization issues must be taken care including frame detection, multipath cancellation and other channel effects. The only purpose that we considered in low-complexity method is trying to reduce the number of correlations as far as we keep the performance of CFO estimation. We analyze the average-power distribution of preamble in IEEE 802.11a, and decided which points of preamble we used for complex multiplier to estimate the CFO.

3.2.1 Property of Preamble

According to the specification of IEEE 802.11a, besides the format of preamble, the signals which carried by the preamble are non-constant power. In other words, the power distribution of each sample in the short and long training symbols is different; it also affects the accuracy of the following frequency synchronization. Therefore, we analyze the power distribution of the time-domain preamble under both AWGN and multipath fading channel as Figure 3.2. Because AGC and packet detection need to take several short training symbols before coarse CFO estimation, we use four short symbols and two long symbols for power analysis. We separate the index of samples of short and long training symbols into two parts;

one is even index of samples, the other is odd one; and sum their power respectively. From Figure 3.2(a) and (b), the z-axis represents the probability that the odd-index power larger even-index one, and we can obviously see that the results from short and long training

symbols are opposite and they also be influenced graver by multipath effect.

3.2.2 Samples Power Detection

For low complexity method, we can reduce the half samples of short and long training symbols for correlations according to the information of even or odd index from power distribution of samples. In the realistic system, we need the packet detection before the CFO acquisition. Nevertheless, even if we have packet detection, we can not ensure how accurate is;

furthermore, because of the multipath effect, the power distribution of samples in the short and long training symbols could be changed probably in the same time. For these reasons, we take one more short-symbol to detect the next coming short symbols which samples have stronger power. Due to one short symbol includes 16 samples, and we sum each sample power of even and odd index respectively. And then we can determine that even or odd index samples have stronger power for coarse CFO estimation. Certainly, the opposite result of the detection can be used for following fine CFO estimation. Therefore, the algorithms of the coarse and fine CFO estimation can be modified as equation (3.24) and (3.25) respectively;

and λ is decided by sample power detector. Consider about limited short training symbols and the performance trade off, we used twice correlations that total three short symbols needed.

Figure 3.3 shows the synchronization flow with the sample power detection and the interactive between the packet detection and CFO compensation before FFT demodulation.

)

SNR [dB] RMS [ns]

Probability [%]

Pr( odd-index power > even-index power)

*Simula

ted packets per SNR : 100000

(a)

SNR [dB] RMS [ns]

Probability [%]

Pr( odd-index power > even-index power)

*Simulated packets per SNR : 100000

(b)

Figure 3.2 Power distribution of (a) Short training symbols (b) Long training symbols

Received data Received data

Short training Symbol start?

Short training Symbol start?

Coarse CFO estimation and compensation Coarse CFO estimation

and compensation

Detect long training symbol and fine CFO estimation Detect long training symbol

and fine CFO estimation

Long training Symbol start?

Long training Symbol start?

Fine CFO compensation Fine CFO compensation

FFTFFT

Sample power detection Sample power detection Yes

No

Even/Odd Odd/Even

Yes No

Figure 3.3 The synchronization flowchart with sample power detection

Chapter 4.

A High Speed and Low Complexity Frequency Synchronizer for OFDM-based UWB System

For general OFDM-based wireless access systems, we proposed a frequency synchronizer in chapter 3. Based on this design, the modifications can be made when dealing with different applications with particular requirements and specifications. In this chapter, a high-speed and low complexity frequency synchronizer is proposed for 528MHz OFDM-based UWB system.

4.1 Motivation

To speed up the implementation and power-reduction of 528MHz UWB frequency synchronizer, a novel low-power scheme combining data-partition-based, power-aware CFO estimation and approximate phasor compensation is proposed. It can reduce redundant computation of synchronization algorithm according to performance requirement. Following the algorithm improvement, the needed memory and clock speed of frequency synchronizer can be both decreased. In the further, we can reduce more power consumption in the better channel condition by power-aware concept. Simulation results show the power elimination efficiency is 69.4 ~ 75.6% and the paid performance loss can be limited to 0.04 ~ 0.6dB for typical 8% packet-error-rate (PER) for UWB.

4.2 Effect of Carrier Frequency Offset

receiver. So the required CFO estimation range must be ±40ppm (TX+RX) in frequency synchronizer. Besides, in order to enhance system performance, an accurate CFO estimation is generally requested in frequency synchronizer. However as system migrates from WLAN to UWB, the performance degradation caused by CFO becomes different. According to [14], the average power of frequency-domain signal without inter-carrier interference (ICI) can be derived as equation (4.1).

[ ]

Y 2 X 2H 2

{

[sin ] [Nsin( N)]

}

2

E K = π∈ π∈ (4.1)

Where YK is the received signal, |X|2 is the average transmitted signal power, |H|2 is the average channel response power, ∈ is the relative CFO of the channel (the ratio of actual CFO to the subcarrier spacing), and N is the point number of the DFT used for OFDM. In the (4.1), it can be found that the signal power is degraded by relative CFO ∈. The CFO also causes ICI which is added to the received signal. According to [14], the average power of ICI can be derived as equation (4.2).

[ ] { }

{ }

=

∈ +

= K k

p K k p

K X H N p N

I E

0

2 2 2

2

2 sinπ 1 sin[π( ) ] (4.2)

Where IK is the ICI of the OFDM system, which using 2K+1 subcarriers. From (4.1) and (4.2), the signal-to-ICI ratio (SIR) of UWB and WLAN system can be calculated and then drawn in Figure 4.1. Since the specifications containing subcarrier spacing, RF frequency, and subcarrier number of UWB and WLAN system are different, the SIR of UWB is ~18dB higher than that of WLAN. The main cause is that the subcarrier spacing of UWB (4.125MHz) is 13.2 times wider than that of WLAN (312.5 KHz). Therefore the relative CFO ∈ of UWB becomes lower. The lower relative CFO leads to less performance degradation.

To understand the required CFO-estimation accuracy from a system-level view, we simulated baseband PER with different CFO-estimation error. The simulated SNR loss for 8%

PER caused by CFO-estimation error is shown in Figure 4.2.From Figure 4.2, it is found the

tolerant CFO-estimation error of UWB can be higher than of WLAN in the same SNR-loss constraint. For example, in 1dB SNR-loss constraint, the estimation error of UWB can be tolerated to 5ppm, but the estimation error of WLAN must be lower than 0.4ppm. Based on the performance comparison, the required accuracy and design complexity of CFO estimation in UWB can be less than that in WLAN. And a low-power scheme with algorithm reduction can be exploited in frequency synchronizer.

2 4 6 8 10

10 15 20 25 30 35 40 45 50

IEEE 802.11a system in 5.8GHz RF band UWB system in 10.6GHz RF band

CFO estimation error [ppm]

Signal-to-ICI ratio [dB]

Figure 4.1 Signal-to-ICI ratio under CFO effect

*Simulated packets per SNR: 1500, Data bytes per packet: 1024

0 2 4 6 8 10

0 1 2 3 4 5 6 7 8

CFO [ppm]

SNR Loss for 8% PER [dB] 480Mb/s UWB system @ 10.6GHz RF 54Mb/s IEEE 802.11a system @ 5GHz RF

Figure 4.2 SNR loss caused by CFO estimation error

4.3 The Proposed CFO Estimation and Compensation Scheme

The Figure 4.3 shows the block diagram of the proposed frequency synchronizer. In the beginning, the received preamble is sent to CFO estimator. Then the estimated result is sent to CFO compensator. And the late preamble and data signal are compensated and sent out. The compensated output signal can be used for timing synchronization and data demodulation.

Besides, the proposed design is developed based on a data partition scheme in CFO estimator and an approximate phasor compensation scheme in CFO compensator to reduce design complexity. The proposed low-complexity algorithms will be described below.

CFO Compensator CFO

Estimator

Preamble

From

ADC To FFT

To Symbol-timing

detector

Preamble and data

Estimated result

Figure 4.3 Block diagram of frequency synchronizer

4.3.1 Data-partition-based CFO Estimation

The conventional CFO estimator algorithm which uses full repeated symbols for auto-correlation is derived as equation (4.3).

⎪⎪

Where ∈ˆ is the estimated CFO, rn is the n-th received sample, and N is the total sample amount of one symbol. So r0 ~ rN-1 are the samples of one symbol duration. In UWB system, N is equal to 165 for repeated OFDM symbols [8]. And in CFO estimator, the first symbol with N samples needs to be stored in memory or delay-line [9]. To reduce the required memory access, a low-power algorithm based on data partition is proposed. It can be derived as equation (4.4).

⎣ ⎦ used sample amount is reduced from N toN λ⎦, which shown in Figure 4.4. Therefore, the design complexity of auto-correlation containing the memory size to store the used samples and the multiplication of used samples can be efficiently reduced.

Besides, the different correlation distance will affect the estimation accuracy and range.

The signal power of image part will be increased because of long correlation distance, and then the estimation accuracy will be improved. However, the long correlation distance also decreased the estimation range. For the estimation accuracy and range trade off, the correlation distance is limited to 3NT, that equal to 0.9375µs. So the estimation range can achieve ±0.5/0.9375µs = ±533KHz [14], that is ±50.3ppm of the highest RF frequency (10.6GHz) of UWB system. Thus the proposed algorithm can meet the requested ±40ppm CFO estimation range. Coincident, the 3NT correlation distance also can be applied in the

multi-band UWB system [4], for example, used time-frequency code 1 for band group 1, where the first OFDM symbol is transmitted on sub-band 1, the second OFDM symbol is transmitted on sub-band 2, the third OFDM symbol is transmitted on sub-band 3, the fourth OFDM symbol is transmitted on sub-band 1, and so on. This concept of the correlation distance also shown in Figure 4.4(b).

(a)

(b)

r0 r1 r2 r3 rN-2 rN-1 rN rN+1 rN+2 rN+3 r2N-2r2N-1

Received signal:

* * * * * *

Required ??

Tan-1

r0 r1 r2 r3 rN-1 r3N r3N+1r3N+2r3N+3 r4N-1

Received signal:

* * * * *

Tan-1 Multiplication: λ 1

Figure 4.4 (a) The conventional CFO estimation (b) The proposed data-partition-based CFO estimation

In order to reduce complexity and keep performance simultaneously, we have to find a good λ value. As Figure 4.5 shown, if high λ value is chosen, the complexity will be lower, but the CFO estimation error will be increased. In the section 4.3.3, we will choose a good λ value according to the performance loss.

0 5 10 15

Proposed: lamda = 4 lamda = 8

Figure 4.5 CFO estimation error with different complexity

4.3.2 Approximate phasor Compensation

In compensation part, the ideal method is to directly compensate the received signal with the phasor. It can be derived as equation (4.5).

ˆ ) system, the sample period (T=1/bandwidth=1/528MHz) is shorter than 1.9ns. So the compensating phasors for neighboring samples are approximate to each other. Hence the proposed approximate compensation scheme is derived as equation (4.6).

) proposed algorithm where λ = 4. So each phasor can be used to compensate λ samples. And the phasor computations of (4.6) can be reduced to ~ 1/λ of that of (4.5). Figure 4.7 shows the

∈ˆ= 424 KHz (40pm of 10.6GHz). And the x-axis is the receiving time (kT). As shown in Figure 4.7, the difference between the real parts of compensating phasor can be less than 2%.

The difference is small so the approximate phasor compensation can be used to reduce the phasor computations.

r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 θ0 θ1 θ2 θ3 θ4 θ5 θ6 θ7 θ8 θ9 θ10 θ11

0 1 2 3 4 5 6 7 8 9 10 11

Received data:

Required ??

r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11

θ0 θ4 θ8

0 1 2 3 4 5 6 7 8 9 10 11

Received data:

LUT complexity

λ 1

(a)

(b)

Figure 4.6 CFO compensation scheme (a) Conventional approach (b) Proposed approach

600 610 620 630 640 650 660

<2%

Figure 4.7 Real parts of compensating phasor

4.3.3 Reduced parameter search

In order to find a good λ for data-partition CFO estimation and approximate CFO compensation scheme, we simulated the PER curves with different design complexity.

PER Analysis with Different Design Complexity

Figure 4.8 shows the PER curves with different λ values which control required memory size and design complexity. The required SNR of different design complexity and its SNR loss are listed in Table 4.1. The SNR loss of the proposed design (λ=4) compared with perfect synchronization (CFO-estimation error = 0.0ppm) is only 0.07dB for 8%

PER. PER of the proposed design is close to the design with λ = 2. That means the design complexity can be reduced from 50% to 25% with very little SNR loss. As λ is increased from 4 to 8, only 25%-12.5% = 12.5% design complexity are reduced further.

But the SNR loss will be increased to 0.21dB equal to three times of the proposed design.

Hence the design with λ = 4 is proposed to achieve low design complexity with an acceptable performance loss.

λ= 1, (100% memory) λ= 2, (50% memory)

Proposed:λ= 4, (25% memory) λ= 8, (12.5% memory) λ= 16, (6.25% memory) λ= 32, (3.125% memory)

Perfect synchronization PER = 8%

*Data rate: 240Mb/s, Simulated packets per SNR: 1500, Data bytes per packet: 1024, Channel CFO: 40ppm

Figure 4.8 PER with different design complexity

Table 4.1 The required SNR for 8% PER of the different design complexity Design

Parameter (λ) Design SNR (dB) SNR Loss compared with perfect synchronization (dB)

1 5.31 0

2 5.34 0.03

4 5.38 0.07

8 5.52 0.21

16 5.67 0.36

32 6.02 0.71

4.3.4 Power Aware CFO estimation

After introduction of the approximate CFO compensation, we focus on data-partition CFO estimation again. We’ll try to reduce more complexity of data-partition estimation by power-aware concept. In the previous design, we used higher accuracy estimation which means higher complexity to estimate the CFO at every packet; we define it as fine estimation.

However, in the better CFO environment, we can reduce the turn on probability of fine estimation at every packet. First, we used a lower accuracy estimation which means lower complexity to estimate the CFO at every packet; we define it as coarse estimation. The coarse estimation is used to decide whether the fine estimation turn on or not according to CFO environment. So we will not use any estimated result from coarse estimation. If coarse-estimation detect the worst CFO environment (fast variation), then fine-estimation will turn on; otherwise, we will use the previous result of fine estimation. For this reason, the complexity will be reduced greatly in the better CFO environment. Figure 4.9 shows the concept of power aware.

F F F F F F F F F Fine Estimation (Est.)

P0 P1 P2 P3 P4 P5 P6 P7 P8 P9

C+F C C C C C+F C C C Coarse Estimation (Est.)

P0 P1 P2 P3 P4 P5 P6 P7 P8 P9

Conventional:

Proposed: Lower-complexity coarse est. is added

Figure 4.9 Power aware concept

In the further, we have to decide when the fine estimation turns on. We have a decision methodology as Figure 4.10. First, we will choose a threshold. If the difference of estimated results between coarse estimation and previous fine estimation is greater than threshold, then the fine estimation will be turned on. Therefore, the current estimated result is from new fine estimation. Otherwise, the fine estimation is turned off; the current estimated result is from

In the further, we have to decide when the fine estimation turns on. We have a decision methodology as Figure 4.10. First, we will choose a threshold. If the difference of estimated results between coarse estimation and previous fine estimation is greater than threshold, then the fine estimation will be turned on. Therefore, the current estimated result is from new fine estimation. Otherwise, the fine estimation is turned off; the current estimated result is from

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