兩徑通道引起之深衰落正交分頻多工系統影響研究

國 立 交 通 大 學

資訊科學與工程研究所

碩 士 論 文

兩徑通道引起之深衰落

正交分頻多工系統影響研究

Compensation for

Deep Fading Effect of Two-Ray Channel

in OFDM System

研 究 生：葉邵穎

指導教授：許騰尹 教授

ii

ii

兩徑通道引起之深衰落正交分頻多工系統影響研究

Compensation for Deep Fading Effect of Two-Ray Channel

in OFDM System

研 究 生：葉邵穎 Student：Shao-Ying Yeh

指導教授：許騰尹 Advisor：Terng-Yin Hsu

國 立 交 通 大 學

資 訊 科 學 與 工 程 研 究 所

碩 士 論 文

Submitted to Institute of Computer Science and Engineering College of Computer Science

National Chiao Tung University in partial Fulfillment of the Requirements

for the Degree of Master

in

Computer Science

August 2009

Hsinchu, Taiwan, Republic of China

iii iii

摘要

iv

iv

Abstract

This paper proposes a method in Rx for deep-fading channel with no variation Tx.

Because of OFDM system is multicarrier modulation. Therefore, the performance is

affected by selective fading. When the transmitted signal through pass the deep fading

channel. The deep fading data will lose after FFT.

This paper of contribution is resolved the deep-fading channel in Rx with no variation

v

v

Acknowledgement

I would like to thank my advisors, Dr. Terng-Yin Hsu, for advice, guidance and constant

care. To my dear isIP Lab. members, this work would not have been possible without your

support. You make me feel free and comfortable. Always be grateful to my family, your

unconditional love encourages me all the time.

Sincerely, Shao-Ying Yeh

vi vi

Table of Contents

CHAPTER 1 INTRODUCTION... 1

-1.1TWO-RAY CHANNEL...-1

-1.2DEEP FADING EFFECT...-2

1.2.1 OFDM System... 3

CHAPTER 2 SYSTEM PLATFORM... 5

-2.1IEEE802.11A PHYSPECIFICATION...-5

2.1.1 Transmitter... 5

2.1.2 Receiver ... 6

2.1.3 Packet Format... 7

-2.2TWO-RAY CHANNEL MODEL...-7

CHAPTER 3 THE PROPOSED ALGORITHM ... 9

-3.1PSEUDO CHANNEL BLOCK DIAGRAM...-9

-3.2PSEUDO CHANNEL ALGORITHM PROCESS...-10

3.2.1 Removed Redundant AWGN... 11

3.2.2 Convolute Pseudo Channel... 12

-vii

vii

3.2.4 Noise Enhance ... 14

CHAPTER 4 SIMULATION RESULTS ... 15

CHAPTER 5 CONCLUSION AND FUTURE WORK ... 19

5.1.1 Conclusion ... 19

5.1.2 Future Work ... 20

-viii

viii

List of Figures

Figure 1-1 Two-ray channel... - 2 -

Figure 1-2 Two-ray channel impulse response... - 2 -

Figure 1-3 Two-ray channel frequency response,H k ... - 3 - [ ]

Figure 1-4 Transmitted Data,S k ... - 4 - [ ]

Figure 1-5 Received Signal,Y k ... - 4 - [ ]

Figure 1-6 Received Data,S k ... - 4 - '[ ]

Figure 2-1 IEEE 802.11a transmitter... - 6 -

Figure 2-2 IEEE 802.11a receiver ... - 6 -

Figure 2-3 IEEE 802.11a packet format ... - 7 -

Figure 2-5 Two-ray channel model... - 8 -

Figure 2-6 Carrier error rate ... - 8 -

Figure 3-1 Block Diagram... - 9 -

Figure 3-2 A sample of transmitted signal and index 16 of signal ... - 10 -

Figure 3-3 A sample of received signal on index 16,y₁₆( )t ... - 11 -

Figure 3-4 Removed redundant AWGN after 2 unit time... - 12 -

Figure 3-5 Pseudo channel impulse response... - 12 -

Figure 3-6 Convolute two-ray channel and pseudo channel ... - 13 -

Figure 3-7 Convolute the receiver signal and pseudo channel... - 13 -

Figure 3-8 Compare no removed and removed AWGN ... - 14 -

Figure 4-2 BER vs. SNR ... - 16 -

Figure 4-3 PER vs. SNR... - 17 -

Figure 4-4 SNR vs. CER by pseudo channel algorithm with removed redundant AWGN ... - 17 -

Figure 4-5 SNR vs. CER on 36dB by pseudo channel algorithm with removed redundant AWGN ... - 18 -

ix

ix

List of Tables

- 1 -

1

-Chapter 1

Introduction

As the wireless communication is widely applied, serious effect occur in some environment. A special channel called two-ray channel reveals when transmit signals by two paths between transmitter and receiver occurs to.

There is a simple idea in [1]. The idea is precoding OFDM system. In Tx, the signal is precoded before transmitted. And [2] enhance [1]’s method, the ideal is zero-padding in Tx. Insert zero-value in GI(Guard Interval) for equalizer in time-domain. The two methods are result of good performance. But IEEE 802.1 series are not used.

In this paper of contribution is only resolved two-ray channel in Rx by the specification of IEEE, the Tx is not varied. The occasion two-ray channel is introduced in section 1.1. And section 1.2 describes the deep fading effect induced by two-ray channel. Finally, section 1.3 show how OFDM system is crashed by two-ray channel

1.1 Two-ray Channel

In wireless communication, the signal in TX transmitted through channel and received

in RX. If RX receives the two signals which delay n apart and have the same attenuation, ₀

2

2

-Figure 1-1 Two-ray channel

1.2 Deep Fading Effect

In this paper, we define the deep fading effect which is some approximating zero or

zero values on channel frequency response. And the approximating zero or zero values on

channel frequency response are defined deep fading points.

Figure 1-2 Two-ray channel impulse response

The two-ray channel of CIR (channel impulse response) is shown in Figure 1-2, and the

mathematic is expressed as:

0

[ ] [ ] [ ] (1.1)

- 3 -

3

-Now, we transfer the CIR to CFR (channel frequency response) by FFT, shown as

Figure 1-3. Observation, there is some deep fading points over spectrum.

Figure 1-3 Two-ray channel frequency response,H k [ ]

1.2.1 OFDM System

The OFDM systems may be severely distortion by two-ray channel. Because of the

OFDM (Orthogonal Frequency-Division Multiplexing) is one of multicarrier modulation

and equalization in frequency domain.

In general, the bit-stream data is modulated to tones, transmitted data [ ]S k . In Rx, the

transmitted signal through pass to channel,H K , and add AWGN,[ ] N k , the received [ ] signal is Y k . Because of attenuation of the channel on every tone should be compensated. [ ] Therefore, the equalizer compensate for the attenuation to the estimated data '[ ]S k . Above

description is in frequency domain, and express as:

[ ] [ ] [ ] [ ] [ ] '[ ] (1.2) [ ] [ ] [ ] [ ] Y k H k S k N k Y k S k H k N k S k H k = + ⇒ = = +

For example, Figure 1-4 show the Tx which transmitted data are all ones tones in

frequency, and this signals which through pass to two-ray channel, Figure 1-3 , is received

in Rx, shown in Figure 1-5. And then we equalize the received signal, shown in Figure 1-6.

4

4

-deteriorated on deep fading points.

Figure 1-4 Transmitted Data, [ ]S k

Figure 1-5 Received Signal, [ ]Y k

- 5 -

5

-Chapter 2

System platform

2.1 IEEE 802.11a PHY Specification

Orthogonal Frequency Division Multiplexing (OFDM) is a multi-carrier modulation

that achieves high data rate and combat multi-path fading in wireless networks. The main

concept of OFDM is to divide available channel into several orthogonal sub-channels. All of

the sub-channels are transmitted simultaneously, thus achieve a high spectral efficiency.

Furthermore, individual data is carried on each sub-carrier, and this is the reason the

equalizer can be implemented with low complexity in frequency domain.

2.1.1 Transmitter

The transmitter block diagram of OFDM specified in IEEE 802.11a proposal is shown

as Figure 2-1. The source data is first scrambled to prevent a succession of zeros or ones,

and then it is encoded by convolutional encoder, which is used as Forward Error Correction

(FEC). The FEC-encoded bit stream is punctured in order to support four coding rates, 1/2,

2/3, 3/4 and 5/6.

The interleaver changes the order of bits to prevent burst error. Then the interleaved

6

6

-modulations, BPSK, QPSK, 16-QAM and 64-QAM.

There are 64 frequency entries for each IFFT, or 64 sub-carriers in each OFDM symbol.

52 of them are data carriers, 4 of them are pilot carriers and the rest 8 are null carriers.

Finally, the time domain signals appended to the Guard Interval (GI) of 1/4 symbol length,

are transmitted by RF modules.

Figure 2-1 IEEE 802.11a transmitter

2.1.2 Receiver

The receiver block diagram is shown as Figure 2-2. Signals received from the RF

modules are first synchronized to recognize each OFDM symbol. Each OFDM symbol is

transformed to frequency domain by the Fast Fourier Transform (FFT). If the OFDM

symbol belongs to long preamble (described in section 2.1.3), then it is used for channel

estimation. Otherwise, it belongs to payload and is decoded by equalizer, which needs the

CFR information estimated by the channel estimation block.

After separated by equalizer, the data carriers are demodulated to bit-level stream.

Then these bit-level data stream is de-interleaved. Finally, the data stream is decoded by

FEC which includes de-puncturing, Viterbi decoder and de-scrambler.

Analog

RF Sync FFT Equalizer Channel Estimation

- 7 -

7

-2.1.3 Packet Format

The packet format fields are shown as Figure 2-3. The OFDM training structure (PLCP

preamble), wheret to₁ t denote short training symbols, and each of transmitted time ₁₀

is0.8 sμ .Thet₁tot₇are used to signal detection, AGC(Automatic Gain Control) and, diversity selection. The other, t to₇ t , are used to timing synchronize and coarse frequency offset ₁₀

estimation.

The T and ₁ T denote long training symbols, and each of transmitted time is ₂

3.2 sμ .The long training symbols are used to Channel estimation and fine frequency offset estimation. The total training length is 16 sμ . In this paper, the key points are the format of long training symbol.

The PLCP preamble is followed by SIGNAL field and DATA, which data rate (RATE)

and PSDU length (LENGTH) of information in SIGNAL field.

Figure 2-3 IEEE 802.11a packet format

2.2 Two-ray Channel Model

In this section, our two-ray channel model of CIR and CFR is shown in Figure 2-4. It

is two comparable pulses which are delayed 2 units apart in CIR, and there is two deep

fading points on index 16 and 48 in CFR. It is the simplest two-ray channel model, but it

8

8

-Figure 2-5 Two-ray channel model

Figure 2-5 show carrier error rate in two-ray channel model. We can observe although

SNR approximate 60dB, there is two errors, highlight in figure, on spectrum,

- 9 -

9

-Chapter 3

The proposed algorithm

3.1 Pseudo Channel Block Diagram

The pseudo channel block diagram show in Figure 3-1.

Figure 3-1 Block Diagram

10

10

-is non-deep-fading tones. After the “Sync.”(synchronize), if received signal -is preamble,

then input the data to “Channel Estimator” for estimating CFR, and then feed CFR into

“Pseudo Channel Block”. In this paper, the channel model is fixed, and we assume the

channel estimation is accuracy.

Else if the signal is payload, then we resolve the non-deep-fading tones at first by

equalizer, ”QAM Decision Unit”, and feedback resolved data to “Pseudo Channel Block”.

The remainder, deep-fading tones, is resolved by “Pseudo Channel Block”.

3.2 Pseudo Channel Algorithm Process

In Figure 3-1 below, pseudo channel process have three steps. The first step is removed

redundant AWGN. The second step is convolute pseudo channel. Final step is decision.

Before discuss the process, we have use a simple example for understanding the

algorithm easily. In Figure 3-2, we transmit p t and follow ( )( ) d t in Tx. Because of we

focus the deep-fading tones, so the index 16, 48 are discussed in the example. Therefore, we

only descript the process by index 16. Figure 3-2 below, X₁₆( )t is the 16th carrier in

OFDM system and P ,₁₆ D are the transmitted data. ₁₆

Figure 3-2 A sample of transmitted signal and index 16 of signal

Figure 2-5 show the two-ray channel we focus in this paper. When the 16th carrier

- 11 -

11

-and is added AWGN (Additive White Gaussian Noise). Figure 3-3 show effected signal by

two-ray channel. In Rx, the received signal is shown in Figure 3-3 below, r t . Formal ₁₆( ) expression is shown as:

[ ] [ ]* [ ] [ ] (3.1)

y n =h n s n +w n

[ ]

s n is the transmitted signal. y n is the received signal. The two-ray channel, [ ][ ] h n ,

we defined in section 2.2. w n is AWGN. And the notation ‘*’ means convolution. [ ]

Figure 3-3 A sample of received signal on index 16,y₁₆( )t

Observation, there is no signal power about transmitted data after 2 unit time and it is

only AWGN. By the general OFDM system, we get a interval signal after GI (Guard

Interval) which is only AWGN in the 16th carrier. Therefore, there is noise enhance on index

16 in two-ray channel.

3.2.1 Removed Redundant AWGN

In Figure 3-3 below, the redundant AWGN of the received signal is replaced by zeros,

shown in Figure 3-4. But the previous signal should leave the deep-fading data by feedback

12 12 -0 ''[ ] [ ] ( [ 80 ] [ 1 80 ] [ 2 80 ]) (3.2) '[ ] [ ]* [ ] ''[ ] k j w n w n n j n j n j y n h n s n w n δ δ δ = = × − + − − + − − = +

∑

Figure 3-4 Removed redundant AWGN after 2 unit time

3.2.2 Convolute Pseudo Channel

Figure 3-5 Pseudo channel impulse response

At the first, we define pseudo channel for the two-ray channel. Figure 3-5 show the

pseudo channel and express as:

39 0 [ ] ( 1) [i 2 ] (3.3) i hps n δ n i = =

∑

If we convolute two-ray channel and pseudo channel, we can find the result which is

13 13 -39 0 [ ]* [ ] ( ( 1) [ 2 ]) * ( [ ] [ 2]) (3.4) [ ] [ 80] i i hps n h n n i n n n n δ δ δ δ δ = = − − + − = − −

∑

Figure 3-6 Convolute two-ray channel and pseudo channel

Now, convolute the receiver signal and pseudo channel, shown in Figure 3-7. And the

expression is followed as:

0 0 0 ''[ ] '[ ]* [ ] [ ]* ( [ ]* [ ]) [ ] (3.5) [ ] [ 80] [ ] [ ] [ ] [ ] y n y n hps n s n h n hps n w n s n s n w n s n p n w n = = + = − − + = − +

14

14

-3.2.3 Decision

In Figure 3-7, the rectangle show reconstruction of signal which is deep-fading by

two-ray channel. Therefore, we can decision the deep-fading signal after convolution

pseudo channel. The first, we transfer y n by FFT and express as: ''[ ]

0

''[ ] [ ] [ ] [ ] (3.6)

Y k =S k −P k +W k

Then, estimate the data we resolve by previous data, P k . Express as: [ ]

0

'[ ] ''[ ] [ ] [ ] [ ] (3.7)

S k =Y k +P k =S k +W k

3.2.4 Noise Enhance

Observation, if we don’t execute the first step, removed redundant AWGN. The result

is also Equation 3.7. But Figure 3-8 show the noise enhance on deep-fading point, 16 and

48.

15

15

-Chapter 4

Simulation results

In this chapter, to evaluate the pseudo channel algorithm, a typical OFDM system

based on IEEE802.11a Wireless LANs, TGn Sync Proposal Technical Specification is used

as the reference design platform. The performance of proposed algorithm is simulated under

two-ray channel which we defined in section 2.2 with Additive White Gaussian Noise

(AWGN).

In the simulations, the source data of transmitted length is 1024 Bytes and use the

coding rate of 3/4 and modulation of 64-QAM. Follow as Table 4-1

Parameter Value

System Platform IEEE 802.11a

Modulation 64-QAM Coding rate 3/4

PSDU length 1024 Bytes Carrier frequency 2.4 GHz

Bandwidth 20 MHz

Symbol rate 250 KHz IFFT/FFT period 3.2 sμ

GI duration 0.8 sμ

Approx. packet duration 200 sμ

16

16

-In Figure 4-1, the no algorithm method is divergence, and only the pseudo channel

algorithm is convergence on 51dB. Additional removed redundant AWGN is convergence

on 36dB, it gain 15dB. Figure 4-2 shows the SNR vs. BER. Figure 4-3 shows the SNR vs.

PER.

Figure 4-2 BER vs. SNR

And the SNR vs. CER by pseudo channel algorithm with removed redundant AWGN

on every carrier is shown in Figure 4-5. The influenced carrier decrease on about 30dB, and

it convergent on 36dB. In Figure 4-6, CER which no algorithm is 0.98 on 36dB. And the

pseudo channel with removed redundant AWGN of CER is 0.68. To observe, the expected

17

17

-Figure 4-3 PER vs. SNR

Figure 4-4 SNR vs. CER by pseudo channel algorithm

18

18

-Figure 4-5 SNR vs. CER on 36dB by pseudo channel algorithm

19

19

-Chapter 5

Conclusion and Future Work

5.1.1 Conclusion

This thesis proposes a pseudo channel method. The deep fading carrier is fading by

resonance phenomenon in two-ray channel. It is all zero value by sum of peak and trough.

And then, the ADC in receiver sample zeros on deep fading carriers.

Therefore, find the remaining energy of deep fading carriers is main ideal of the

algorithm. And we find the GI have the remaining energy, but complex with previous data.

The feedback mechanism should be used for cancelling previous data.

Although, it works to reconstruct the deep fading carriers, but the noise enhance is a

big problem. Because of total energy in GI is less than one FFT length. The SNR loss

occurs.

The removed redundant AWGN is proposed for gain SNR. And the performance gain

15dB against no removing. But there is still 23dB gap.

A common sense is up sample in ADC, and it get more non-zero values in GI on deep

20

20

-5.1.2 Future Work

The next study is enhancing performance by MIMO-OFDM system. It is simple idea

that the number of received antenna will gain the same number time of performance. But

the preliminary studying find it is better than the idea. Because of the STBC is a diversity

which changes the channel type. Therefore, the deep fading effect in two-ray channel is

21

21

-Bibliography

[1] Xiang-Gen Xia, “A New Channel Independent Precoded OFDM Systems Robust to Spectral Null Channels”, 2000 IEEE.

[2] Jian Wang, Jian Song, Zhi-Xing Yang, Lin Yang, and Jun Wang, “Frames Theoretic Analysis of Zero-Padding OFDM Over Deep Fading Wireless Channels”, 2006 IEEE.

[3] John Terry and Juha Heiskala, “OFDM Wireless LANs: A Theoretical and Practical Gide” [4] Simon R. Saunders, “Antennas and Propagation for Wireless Communication System” [5] Kaveh Pahlavan and Allen H. Levesque, “Wireless Information Networks”

[6] Tzi-Dar Chiueh and Pei-Yun Tsai, “OFDM Baseband Receiver Design for Wireless Communications”

[7] Simon Haykin and Barry Van Veen, “Signals and Systems” [8] Andrea Goldsmith, “Wireless communications”