Additive White Gaussian Noise

The AWGN is established by the random generator (

randn). The output

random signal is normally distributed with zero mean and variance equal to 1. The AWGN noise can be modeled as

10 10

[ (1, ) (1, )] 2

P SNRS

w randn n j randn n



    (2.15)

Where ^P_S is signal power, SNR is signal-to-noise ratio (dB), and n is length of data signal.

28

Chapter 3.

Design of Dual-Mode Channel Equalizer

In this chapter, a low complexity and high performance dual-mode channel equalizer is proposed. It includes channel estimator, equalizer, phase error tracker and modified normalized least-mean-square (NLMS) channel tracker. Data distortion caused by multi-path fading, AWGN, residual CFO and SCO can be eliminated by these four parts. Following is the block diagram of the proposed channel equalizer. After passing through the FFT, channel estimator uses received preambles to estimate the channel frequency response (CFR). The estimated CFR will be sent to the equalizer. Then, equalizer uses the estimated CFR to equalize the distorted data sub-carriers. After doing the equalization, equalized data sub-carriers will be sent to the phase error tracker and compensator. The tracked phase error combined with unequalized data, equalized data and estimated CFR are then sent to modified NLMS channel tracker to calculate the updated CFR. Finally, compensated data sub-carriers are sent to De-Mapper.

Fig. 3.1 Block Diagram of Proposed Channel Equalizer

29

3.1. Dual-Mode Design of Channel Estimation

The signal is transmitted over frequency-selective fading channel. After removing the cyclic prefix and guard interval, the post-FFT signal of the l-th OFDM symbol can be expressed by: post-FFT signal can be simplified as an equivalent model [7]:

e p f caused by AWGN, symbol timing offset, ICI, and other non-ideal parameters. With the assumption that the timing synchronization is perfect, there is no timing offset.

The equivalent model can be simplified as:

a f

p f ⁺

=

^{[ 2 ( )/ ]}

+

_,

( ) ( ) ( )

^{j l k T Tu g Tu}

l k l k l k

Y k X k H e W

(3.3)

Where the attenuation factor ( )

a f is very close to 1 and therefore can be neglected.

k

30

3.1.1. Channel Estimation for UWB

In UWB system, use zero-forcing (ZF) methodology with received two preambles to estimate the fading channel. Using the average value, the estimation error can be reduced and the performance will be improved. Simulation result shows that it will contribute 1~2dB gain in SNR. Considering that the pre-defined signal

L( )

X k in preamble, the estimated of the k-th sub-channel is given by:



1 2



( ) ( ) ( ) / 2 ( )

E L L L

H k



Y k



Y k X k

(3.4)

Where

Y

_L1( )

k

_,

Y

_L2

( ) k

are the first and second received preamble.

In channel estimation, these two received preambles are also used to estimate the noise power which can be described as follows:

1 2 1 2 2

Based on the correlative property between adjacent sub-channels, the estimation of sub-channels can be further improved by delivering them into the 3-taps smoothing filter. The smoothing filter is a finite impulse response filter [8], which can be described as:

31

After doing channel estimation, the estimated sub-channel

H k will be

_E( ) convoluted by the smoothing filter. The equation is given by:

=-= å

¹

- ×

( )

1

( ) ( )

S E

H k

m

H k m S m

(3.7)

After smoothing, each sub-channel will be a weighted summation of itself and nearby sub-channels. Simulation reveals that the system performance on PER will improve about 1dB for different transmission modes.

3.1.2. Channel Estimation for WIMAX

In WIMAX system, long preamble is used to estimate the fading channel. In standard of 802.16-2004, only even sub-carriers are utilized in long preamble. DC sub-carrier and odd sub-carriers are transmitted with zero value. Consequently, the ZF methodology is used to estimate the CFR of even sub-carriers at first, and then use 6-tap raised-cosine interpolator to get CFR of DC sub-carrier and odd sub-carriers. Following is the description of channel estimation for WIMAX system.

Considering that the pre-defined signal

X k in preamble, the estimated CFR

_L( ) of the k-th even sub-carrier is given by:

,

( ) ( ) / ( )

32

Where D is the spacing of even sub-carriers, and β is the roll-off factor. And, let k equal to -5, -3, -1, 1, 3, 5, the coefficient of six taps can be generated.

But, using 6-tap raised-cosine interpolator to get CFR of sub-carrier number -99, -97, 97, 99 will result in large error [9]. For example, to get CFR of sub-carrier number -99, it needs CFR of sub-carrier number -104, -102, -100, -98, -96, -94. But, sub-carriers are transmitted with zero value at number -104, -102. Receiver doesn’t have any information at these two places. If zero value is applied to substitute the CFR of these two places, it will result in large error. So, the linear interpolation is used to get the CFR of sub-carrier number -99, -97, 97, 99.

Otherwise, DC sub-carrier (number 0) is transmitted with zero value. In order to get CFR of sub-carrier number -5, -3, -1, 1, 3, 5, CFR of DC sub-carrier is needed.

To interpolate the DC value, CFR of sub-carrier number -10, -6, -2, 2, 6, 10 are used to get the CFR of DC sub-carrier [9]. Next, DC value is used to get the CFR of sub-carrier number -5, -3, -1, 1, 3, 5. For example, to interpolate the CFR of sub-carrier number 5, CFR of sub-carrier number DC, 2, 4, 6, 8, 10 are used as inputs to the interpolator. Following the same rule, CFR of sub-carrier number -5, -3, -1, 1, 3 can be generated.

According to the above statement, 6-tap raised-cosine interpolator is needed.

Using 6-tap raised-cosine interpolator to get CFR of odd sub-carrier can be described as follows:

33 (MMSE) methodology is very suitable to equalize the distorted signal. Traditional zero-forcing equalization will increase the noise and degrade the system’s performance. Consequently, MMSE equalization is used to suppress the interference and noise effects in UWB system. The compensating value of the MMSE

channel estimation part, X k_L( )²is transmitted preamble power, which can be fixed as 1 in UWB system. Finally, the signal is equalized as:

ˆ ( )

_{l l}

( )

_MMSE

( )

X k = Y k C × k

(3.12)

For WIMAX system, there are four different modulation types, such as BPSK, QPSK, 16-QAM, 64-QAM. For 16-QAM, 64-QAM conditions, using MMSE

34

methodology to do equalization will suppress the signal and noise simultaneously.

The attenuation signal will cross the decision boundary, and result in decision error.

Consequently, MMSE methodology is not suitable for WIMAX system. In this place, ZF methodology is used to equalize the distorted signal. Following is the compensating value of the ZF equalization:

( ) 1/ ( )

ZF E

C k  H k

(3.13)

Next, the signal is equalized as:

ˆ ( )

_{l l}

( )

_ZF

( )

X k = Y k C × k

(3.14)

3.3. Dual-Mode Design of Phase Error Tracking and compensation

CFO and SCO are the other two data distortion sources for OFDM systems, which are caused mainly by a crystal oscillator frequency mismatch between transceiver and DAC/ADC mismatch. Generally, timing synchronization is applied to compensate these two effects. Nevertheless, other impairments will make the synchronization imperfect. The residual CFO and SCO will cause the data phase rotation in frequency domain and result in inter-carrier interference (ICI). In case of a coherent demodulation scheme, the error due to the rotation of a signal constellation will be fatal for transmission bursts, because the accumulated phase rotation will shift the constellation point to cross the decision boundary. It will cause high error rates and therefore the phase error tracking (PET) is applied in OFDM systems for phase rotation tracking and compensation.

Following the eq. 3.3, after doing the equalization, the equalized data can be

35 effect. The phase rotation of the l-th symbol and k-th sub-carrier can be derived as:

p pz

æ + ö

The first term is caused by CFO effect. This phase rotation is constant for all data sub-carriers in an OFDM symbol and increases with symbol index. The second term is caused by SCO effect, which is a linear phase rotation with sub-carrier index.

This also increases with symbol index. So, the PET is used to track the mean phase error caused and phase error slope caused by these two effects.

The PET is designed based on the known pilot sub-carriers. In order to achieve correct tracking of phase error exceeding ±

p

, the pre-compensation [10] is added in the PET. Before PET, the pilot sub-carriers will first be compensated with the phase error tracked in the previous OFDM symbols. Therefore, only the difference of the phase error between previous and preset OFDM symbols needs to be tracked with pilot sub-carriers. This will enhance the PET accuracy. The PET algorithm with pre-compensation is given as:

36

K=K

WIMAX ,

l=1 means the first received OFDM symbol, 

,lK is the detected phase

error of l-th OFDM symbol, 



_,lK is defined as the pilot phase after pre-compensation with the previous tracked phase error _l1  K _l1.

Next, use the pre-compensation pilot phase to calculate the mean phase error

l, which can be shown in eq. 3.18 and phase error slope

g

l, which can be shown in eq. 3.19, and the related parameters for UWB and WIMAX systems are shown in eq. 3.20.

37

where

g

_l-1is the previous, Wg , C are constant terms, K⁺ is index list of positive

pilot sub-carriers , K^- is index list of negative pilot sub-carriers.

{ } { }

To consider the hardware complexity, the proposed phase error tracker has the advantage of reducing the multiplicative computation. In the pilot phase pre-compensation part, it only needs one multiplier. Using mean-average method, it only needs to do constant multiplication of two times in each OFDM symbol.

After PET, the data sub-carriers are compensated according to the tracked phase error, which can be indicated as:

( ) ˆ ( ) exp( ( ))

Consequently, interpolator is used to get the CFR of odd sub-carriers. Because the ideal interpolator is not practical, there is some aliasing effect occurred in interpolation. Aliasing effect will increase the channel estimation error, and degrade

38

the performance of equalizer. Otherwise, noise, interference and time-variant characteristic will also increase the channel estimation error. Consequently, channel tracker is applied to mitigate the above non-ideal effects and enhance the accuracy of channel estimation.

Standard LMS methodology suffers from a gradient noise amplification problem. To overcome this difficulty, NLMS methodology normalizes the adjustment of tap-weight vector. But, in OFDM system, residual CFO and SCO will result in phase rotation in frequency domain. The traditional NLMS methodology can not be directly used. So, the modified-NLMS methodology is proposed with consideration the phase rotation. Following is the detail algorithm of proposed modified-NLMS channel tracking.

The equalized signal after compensating with tracked phase error is sent into slicer (map the signal to nearest constellation point according to modulation type) to compute the decision signalX k_l( ). For each sub-carrier

k, a single tap frequency

domain NLMS filter is used. The modified-NLMS error

E k is as follows:

_l( )

( ) ( ) exp( ( ) ( )

_l 1

( )

l l l l l

E k  Y k   j   k   X k H 

_

k

(3.22)

Where Y k_l( ) is unequalized signal of

l-th OFDM symbol, 

_l

 k 

_l is the compensated phase error com from PET, H_l1( )k is the previous estimated CFR.

The gradient at sub-carrier

k (

H k_l( )) of

l-th symbol is given by:

39

* 2

( ) ( ) ( )

( )

l l l

l

H k E k X k

  

X k

(3.23)

Finally, using the gradient and previous estimated CFR, the update eq is given as:

( )

1

( ) ( )

l l l

H k  H

_

k     H k

(3.24)

Where  is the constant gain.

Then, the updated CFR H k_l( )can be used for next OFDM symbol.

40

Chapter 4.

Simulation Result and Performance Analysis

In order to verify the proposed design, complete system platforms are established according to the UWB standard (802.15.3a) and the fixed WIMAX standard (802.16d) on Matlab. The platform has been introduced in chapter 1.

Channel estimation accuracy, PET performance, and system performance will be simulated and compare to system constraint of two standards.

4.1. Performance Analysis of the Proposed Dual-Mode Channel Equalizer for UWB system

To analyze the performance of a proposed scheme, we simulate the PER (%) for different SNR and different CFO, SCO value with CFO and SCO variation being considered. The simulation is processed with multi-paths CM2 channel with data rate 480 (Mb/s). The simulation result is shown in Fig. 4.1. The cross-section view for PER (%) with different CFO, SCO values is shown in Fig. 4.2. From the simulation result, it shows that the proposed PET can track the phase error correctly and compensate the phase error under 60 ppm of CFO, SCO value. Above 60 ppm of CFO, SCO value, resulted ICI and phase error will increase grossly to degrade the system performance. Under IEEE 802.15.3a demanded [2], the CFO, SCO value should be less than total 40 ppm (±20 ppm), and the proposed PET can track the phase error accurately.

41

Fig. 4.1 PER (%) simulation for different SNR and CFO, SCO value under CM2, data rate 480Mb/s

Fig. 4.2 PER (%) simulation result with different CFO, SCO value in CM2

In most WLAN and WPAN systems, a PER less than 8% is required. Therefore, PER 8% can be the indication of system performance. The PER (%) with different transmission mode and different channel model are shown in Fig. 4.3. and Fig. 4.4.

Simulation results show that for channel model CM4, data rate 110Mbit/s, with the requirement of 8% PER, the proposed design can achieve this demand at SNR 6.98dB. For transmission in AWGN, the proposed scheme can get this demand at

42

SNR 2.82dB. The comparison of simulation results with system constraint and references is shown in Table 4.1. It shows that the proposed design can achieve 1.36dB to 7.25dB gain in SNR for different simulation conditions.

0 2 4 6 8 10 12

43

Table 4.1 –Performance Result for UWB system

Entry Proposed [11] [12] System

Constraint AWGN

Data rate=200Mbits/s 3.8 dB 3.8 dB 4.11 dB 5.16 dB AWGN

Data rate=480Mbits/s 6.65 dB 7.2 dB 5.03 dB 9.66 dB CM4 Channel &AWGN

Data rate=200Mbits/s 9.91 dB 14.2 dB 14.18 dB 15.1 dB CM2 Channel &AWGN

Data rate=480Mbits/s 13.85 dB 18.5 dB 15.01 dB 21.1 dB

It should be noted that under the worst environment, CM4, the proposed dual-mode channel equalizer will have 5.19dB gain. In the case of receiving data rate of 480Mbit/s, it will have 7.25dB gain. Hence, the proposed joint scheme makes the receiver more robust to CFO and SCO effects and could suppress the error rate at low SNR with high data rate receiving.

44

4.2. Performance Analysis of the Proposed Dual-Mode Channel Equalizer for WIMAX system

In WIMAX system, the accuracy of channel estimation is a key factor for system performance. To analyze the accuracy of channel estimation, mean-square-error (MSE) between estimated CFR and real CFR is measured.

Performance of proposed modified-NLMS channel tracker is simulated with condition under SUI-3 channel, 64-QAM modulation. Following is the comparison of MSE between using modified-NLMS channel tracker and without modified-NLMS channel tracker.

Fig. 4.5 MSE analysis of Modified-NLMS channel tracker

The proposed modified-NLMS channel tracker contributes 3~18dB gain in MSE compared with only ZF channel estimation. Fig. 4.6 shows the channel estimation error from sub-carrier number 70 to sub-carrier number 110, between ideal CFR, using modified-NLMS channel tracker and without modified-NLMS channel tracker.

45

Fig. 4.6 Channel Estimation Error from sub-carrier number 70 to 110

The rate of convergence of modified-NLMS channel tracker depends on the step size. Smaller step size will converge much slower than larger step size. But, smaller step size will contribute smaller MSE than larger step size. Following is the learning curve of proposed modified-NLMS channel tracker with 300 iterations. In this simulation, we select step size with the value equal to 0.0085.

Fig. 4.7 Learning Curve for modified-NLMS channel tracker

46

Fig. 4.8 shows the bit error rate (BER) with modified-NLMS channel tracker and without modified-NLMS channel tracker under SUI-3 channel, 64-QAM modulation, CFO=0.1 ppm, SCO=16 ppm.

Fig. 4.8 BER Comparison

As it can be seen from Fig. 4.8, design with proposed modified-NLMS channel tracker can contribute 1 dB SNR gain than design without modified-NLMS channel tracker. And, by using modified-NLMS channel tracker, it only result 1 dB SNR loss comparing to use ideal channel. Under different simulation conditions, modified-NLMS channel tracker can contribute different SNR gain. From simulation results, modified-NLMS channel tracker can contribute 1~1.5 dB SNR gain with different simulation conditions.

In 802.16d standard, CFO, SCO value should less than ±8 ppm. With the aid of synchronization, we assume the residual CFO is 0.1 ppm. The BER curves of different transmission mode under SUI-1 to SUI-3 channel, system bandwidth=20MHz, CFO=0.1 ppm, SCO=16 ppm are shown in Fig. 4.9, Fig. 4.10, and Fig. 4.11. Table 4.2 shows the required SNR to attain 10^^-6 BER under SUI-3 channel, and also shows the comparison with reference and system constraint.

47

Fig. 4.9 BER performance under Bandwidth=20 MHz, CFO=0.1 ppm, SCO=16 ppm, SUI-1 channel

Fig. 4.10 BER performance under Bandwidth=20 MHz, CFO=0.1 ppm, SCO=16 ppm, SUI-2 channel

48

Fig. 4.11 BER performance under Bandwidth=20 MHz, CFO=0.1 ppm, SCO=16 ppm, SUI-3 channel

Table 4.2 –Performance Result for WIMAX system

Entry Proposed [13] System Constraint

BPSK, Code Rate=1/2 10 dB None 11.4 dB

QPSK, Code Rate=1/2 13.7 dB 13.8 dB 14.4 dB QPSK, Code Rate=3/4 15.7 dB 19.6 dB 16.2 dB

16-QAM, Code Rate=1/2 20 dB 18.8 dB 21.4 dB

16-QAM, Code Rate=3/4 22 dB 25.6 dB 23.2 dB

64-QAM, Code Rate=2/3 23.8 dB 29.2 dB 27.7 dB 64-QAM, Code Rate=3/4 27.9 dB 31.5 dB 29.4 dB

From Table 4.2, it can be shown that the proposed dual-mode channel equalizer for WIMAX application can contribute 0.5~3.9dB SNR gain in different simulation conditions.

49

Chapter 5.

Hardware Implementation

5.1. Signal Flow of Dual-Mode Channel Equalizer

The signal flow of proposed dual-mode channel equalizer for UWB system is shown in Fig. 5.1. In the beginning of receiving, it estimates the CFR

H

E (k) by two preambles YL1 (k) and YL2 (k). With the knowledge of these known preambles, the noise power

σ

E2

can be estimated. Then the estimated CFR will be passed through the smoothing filter to reduce the noise effect in channel estimation. After that, the CFR is stored in ram for the following equalization. In the equalization part, it uses the estimated noise power (

σ

E2) and the estimated CFR (HS

(k)) to equalize received

data

Y

l

(k) under MMSE methodology. After doing equalization, the data phase will

be extracted and sent to PET. In PET part, the phase error will be estimated by pilot sub-carriers. After that, the data sub-carriers are compensated according to these estimated phase errors. Finally, the compensated data sub-carriers are sent to De-Mapper.

For WIMAX system, signal flow is shown in Fig. 5.2. Except for the raised-cosine interpolator, modified-NLMS channel tracker, the signal flow compared to UWB is almost the same. Consequently, most functional blocks, such as divider, smoothing filter, PET, tan^-1 ...etc, can be reused to save hardware resource.

2-parallelism architecture is used to meet high sample rate up to 528 MHz for UWB. The architecture of each functional block is introduced as following sections.

50

Fig. 5.1 Signal Flow of Proposed Channel Equalizer for UWB

L

Fig. 5.2 Signal Flow of Proposed Channel Equalizer for WIMAX

51

5.2. Architecture of Dual-Mode Channel Estimator

Fig 5.3 shows the architecture of dual-mode channel estimator. In UWB mode, dual-mode channel estimator will turn on two parallel data paths. According to pre-defined UWB preamble, look-up table (LUT) combined with following adder and multiplier performs the ZF channel estimation. In this mode, control circuit selects C1 constant ( 2 ) as an input to the multiplier. Once ZF channel estimation has been done, the estimated CFR will be stored in UWB ram. In WIMAX mode, maximum sample rate is only 32MHz. In order to save power consumption, only parallel 1st data path is turned on. In this mode, control circuit selects C2 constant (1/ 2 ) as an input to the multiplier. After doing ZF channel estimation, the signal will be sent into 6-taps raised-cosine interpolator to interpolate the CFR of odd data sub-carriers. After doing interpolation, CFR of all data sub-carriers are stored in WIMAX ram.

Fig. 5.3 Architecture of proposed dual-mode channel estimator

52

For UWB mode, MMSE equalizer is used to equalize the distorted signal. To use MMSE methodology, information of noise power is needed. So, two received preambles of UWB are used to estimate the noise power in proposed dual-mode channel estimator. Fig. 5.4 shows the architecture of noise power estimator. When first received preamble is coming, it will be stored in UWB ram. When second received preamble is coming, first preamble will be read out. And, these two preambles are sent to subtractor. These subtracted values are then sent to the square

For UWB mode, MMSE equalizer is used to equalize the distorted signal. To use MMSE methodology, information of noise power is needed. So, two received preambles of UWB are used to estimate the noise power in proposed dual-mode channel estimator. Fig. 5.4 shows the architecture of noise power estimator. When first received preamble is coming, it will be stored in UWB ram. When second received preamble is coming, first preamble will be read out. And, these two preambles are sent to subtractor. These subtracted values are then sent to the square

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