數位電視廣播接收機設計：演算法及基頻架構

國 立 交 通 大 學

電信工程學系碩士班

碩士論文

數位電視廣播接收機設計：演算法及基頻架構

DVB-T Receiver Design: Algorithms and

Baseband Architecture

研 究 生：黃俊傑 Student: Jun-Jue Huang

指導教授：蘇育德 博士 Advisor:

Dr. Yu Ted Su

數位電視廣播接收機設計： 演算法及基頻架構

DVB-T Receiver Design:

Algorithms and Baseband Architecture

研 究 生：黃俊傑

Student : Jun-Jue Huang

指導教授：蘇育德 博士

Advisor

:

Dr.

Yu

T.

Su

國 立 交 通 大 學

電信工程學系碩士班

碩 士 論 文

A Thesis Submitted to

The Institute of Communication Engineering

College of Electrical Engineering and Computer Science

National Chiao Tung University

In Partial Fulfillment of the Requirements

For the Degree of Master of Science

In

Communication Engineering

June 2004

Hsinchu, Taiwan, Repubic of China

數位電視廣播接收機設計： 演算法及基頻架構

研究生：黃俊傑

指導教授：蘇育德 博士

國立交通大學電信工程學系碩士班

摘要

歐規的數位影像廣播(DVB-T)系統使用了正交分頻多工(OFDM)的技術，在 無線傳輸的通道下能提供高速率傳輸、高效率的頻譜使用率的多媒體服務及對抗 頻率選擇的通道衰減。 本篇論文提出了一個可以工作在單頻網路(SFN)的數位影像廣播接收機 (DVB-T receiver)的基頻架構。我們將會討論基頻信號處理單元的演算法。這些 演算法包含時間與頻率同步、通道估計/等化器以及突波雜訊抑制(Impulse noise suppression)。此外我們還提出了利用決策重建及遞迴通道估計之抑制突波方 法，通道估計的演算法能完全利用到時域及頻域的資訊。 我們透過電腦模擬來評估每個子系統的性能以及整體效能還有相對參數的 最佳化。

DVB-T Receiver Design: Algorithms and Baseband

Architecture

Student : Jun-Jue Huang Advisor : Dr. Yu T. Su

Institute of Communication Engineering National Chiao Tung University

Abstract

To offer high-bit-rate high performance, bandwidth-efficient multimedia services and combat the inevitable frequency-selective fading, the European standard for terrestrial digital video broadcasting (DVB-T) has adopted the orthogonal frequency-division mul-tiplexing (OFDM) technique for broadcasting over wideband wireless channels.

This thesis presents a baseband architecture and develop algorithms for various cor-responding signal processing units for a single frequency network (SFN) DVB-T receiver. These algorithms serve the functionalities of time and frequency synchronization, chan-nel estimation/equalization and impulse noise suppression. Among others, we propose a fast frequency synchronizer and a decision-aided algorithm for joint channel estimation and impulse noise suppression. The channel estimation part makes full use of the time and frequency correlation information. The performance of each subsystems and the overall system is evaluated through computer simulations and related parameters are optimized accordingly.

誌 謝

本論文得以順利完成，首先要感謝我的指導教授蘇育德教授，在

這兩年的研究生生活中，無論在電信領域的專業或生活上的待人處

世，都使我有很大的收穫。也要感謝蒞臨的口試委員，他們提供的意

見和補充資料使本文得以更加完整。此外，我要感謝聯發科技對本計

畫的贊助，尤其李宗霖學長不時的提供寶貴意見與幫助。另外，實驗

室學長陳彥志的鼎力相助、還有同學及學弟的幫忙勉勵，讓我在學業

及研究上獲益匪淺

最後，要感謝的就是一直關心我鼓勵我的家人，他們使我在求學

的過程中無後顧之憂，得以追求自己的目標，願他們永遠平安、幸福！

Contents

Chinese Abstract i Abstract ii Acknowledgements iii Contents iv List of Figures vi List of Tables x 1 Introduction 1 1.1 DVB-T systems . . . 3

2 Frequency and Timing Synchronization Subsystems 10 2.1 Joint coarse timing and fractional frequency offset estimation . . . 10

2.1.1 Coarse timing recovery in multipath fading channels . . . 14

2.2 Coarse frequency synchronization . . . 15

2.2.1 Improved coarse frequency synchronization . . . 18

2.3 Timing tracking . . . 19

2.4 Computational complexity . . . 22

3 Channel Estimation 26

3.1 Fundamental of OFDM Channel Estimate . . . 26

3.2 DVB-T channel model . . . 29

3.2.1 Jakes model . . . 30

3.3 Phase compensation . . . 30

3.4 Transform-domain channel estimation algorithm . . . 32

3.4.1 Cutoff frequency . . . 33

3.5 Model-based channel estimation . . . 35

3.6 2-D model-based channel estimate with transform-domain processing . . 38

3.7 Computational complexity . . . 39

3.8 Numerical examples . . . 40

4 Impulse Noise Suppression 44 4.1 Background . . . 44

4.2 Impulse noise model . . . 44

4.3 Impulse noise detection . . . 46

4.4 Blanking method . . . 46

4.5 Decision-aided reconstruction for IN suppression (DARINS) . . . 47

4.6 Iterative channel estimation using DARINS . . . 50

4.7 Viterbi approach for impulse noise suppression . . . 52

4.8 Computational complexity . . . 53

4.9 Simulation and numerical examples . . . 54

5 Baseband Architecture 56

6 Conclusion 63

List of Figures

1.1 The mother convolutional code of rate 1/2. . . 3

1.2 Puncturing pattern and transmitted sequence. . . 4

1.3 Inner coding and interleaving. . . 4

1.4 Mapping of input bits onto modulation symbols. . . 5

1.5 Symbol interleaver address generation scheme for the 2K mode. . . 6

1.6 DVB-T scatter pilot structure. . . 7

1.7 Carrier indices for continual pilot carriers. . . 7

1.8 Basic block diagram of a DVB-T system. . . 8

1.9 Outer interleaver and deinterleaver. . . 9

2.1 _{Structure of OFDM signal with cyclicly extended symbol s(n) in} non-dispersive channel. . . 12

2.2 MMSE synchronization. Symbol start position at the 500th sample. . . . 13

2.3 MC synchronization. Symbol start position at the 500th sample. . . 14

2.4 The MSE performance of coarse two timing synchronizers. . . 15

2.5 The MSE performance of two fractional frequency offset synchronizers. . 16

2.6 Structure of an extended OFDM frame showing the relation of the channel impulse response duration and the legitimate starting position of the FFT window. . . 17

2.7 The Lock-in probability of coarse timing synchronizer in AWGN and (DVB-T defined) Rayleigh fading channels. . . 18

2.9 Block diagram of a coarse frequency synchronization algorithm. . . 20

2.10 Frequency domain correlation when the true carrier frequency offset is 2/T . 21 2.11 Compensation characteristic of coarse frequency synchronizers with the carrier frequency offset ranges from 1.5 to 2.5 subcarrier spacings (6.696KHz to 11.16KHz in 2K mode of DVB-T system). . . 22

2.12 Determination of the thresholds used in (2.17) by examining the behavior of the averaged ratio between the peak correlation and second largest correlation, E[c] = E{max(φM−1/φM, φM +1/φM)}, as a function of the normalized carrier frequency offset. . . 23

2.13 The MSE performance of the coarse frequency synchronizer where χ ranges from 1.5 to 2.5 (6.696KHz to 11.16KHz in 2K mode). . . . 24

2.14 Learning curves of the conventional carrier frequency synchronizer. . . 25

2.15 Learning curves of modified fast carrier frequency synchronizer. . . 25

3.1 Generation of PRBS sequence. . . 27

3.2 A typical DVB-T channel’s impulse response with a duration of 12 taps. 29 3.3 The DVB-T single frequency network (SFN) concept. . . 30

3.4 Combined impulse response of a DVB-T single frequency network with two stations. . . 31

3.5 _{LS channel estimation, m ∈pilot and k = 0, ..., N − 1. . . .} 32

3.6 A typical transform domain response ˆ_Gp(p) when (a) AWGN and Doppler shift are absent (i.e., noiseless static channel) and (b) SNR = 5 dB, Doppler frequency = 90 Hz. . . 34

3.7 Block diagram of a channel estimation algorithm based on transform-domain processing; m ∈pilots and k = 0, ..., N − 1 and p = 0, ..., Np− 1. . 35

3.8 Complete channel estimation process incorporating transform domain fil-tering; m ∈ pilot set and k = 0, ..., N − 1. . . . 35

3.10 DVB-T pilot symbol distribution in time-frequency. In the button of this figure, regres.(3,4) means that use 3 pilots in time domain and 4 pilots in

frequency domain to make regression model. . . 38

3.11 Block diagram of a two-stage channel estimator that consists of a TDP unit and a model-based channel estimation unit. . . 39

3.12 BER performance comparison of various channel estimates; zero Doppler shift, r.m.s. delay spread = 1.36 µs. . . . 41

3.13 BER performance comparison of various channel estimates; Doppler fre-quency = 88 Hz, r.m.s. delay spread = 5.13µs. . . . 42

3.14 The effect of the 2D model size on the BER performance; Doppler shift = 88 Hz, r.m.s. delay spread = 9.1245µs. . . . 42

3.15 The effect of the FFT window size on the BER performance; Doppler frequency = 88 Hz, r.m.s. delay spread = 1.36µs. . . . 43

4.1 The Cook pulse (An impulse noise model). . . 45

4.2 Impulse noise and blanking noise . . . 47

4.3 Modeling Impulse noise as clipping noise. . . 48

4.4 Decision-aided reconstruction for impulse noise suppression (DARINS) operation flow. . . 49

4.5 Initial channel estimation for DARINS (a) FSA (b) OSA. . . 50

4.6 The operation flow of propose algorithm. (DARINS with ICE). . . 52

4.7 QPSK modulation, code rate is 1 2 in DVB-T Rayleigh fading channel with impulse noise (Cook pulse). Iteration 3 times. regres. (3,3). Doppler frequency 0Hz. r.m.s. delay spread 1.36µs (12.5 OFDM sample). . . . . 55

4.8 QPSK modulation, code rate is 1₂ in DVB-T Rayleigh fading channel with impulse noise (Cook pulse). Doppler frequency from 44Hz. r.m.s. delay spread 5.13µs (48 OFDM sample). . . . 55

5.1 Proposed DVB-T baseband receiver architecture. . . 59 5.2 The architecture of the coarse timing and fine frequency offset

synchro-nization unit. . . 60 5.3 The architecture of the coarse frequency offset synchronization unit. . . . 60 5.4 The architecture of the 2D model-based channel estimator with

transform-domain processing. . . 61 5.5 Architecture of the timing tracking unit. . . 61 5.6 Block diagram showing the architecture for the DARINS with ICE

algo-rithm. . . 62 5.7 An estimation of the overall system execution time, symbol 0 to symbol

2 is in the regular mode while symbol 9 to 10 is in the IN (impulse noise) mode. . . 62

List of Tables

3.1 Path gains and phase rotations associated with the DVB-T channel im-pulse response of Fig. 3.2. . . 32

Chapter 1

Introduction

A wideband communication channel is usually characterized by both time-selective and frequency-selective fading. The Orthogonal frequency division modulation (OFDM) technique converts a wideband signal into an array of narrowband signals for parallel transmission so that each narrow band signal suffers from frequency-nonselective fading. If the symbol time is less than the coherent time and a cyclic prefix longer than the maximum delay of the channel is inserted in every symbol, the receiver needs only a one-tap equalizer to compensate for the corresponding complex multiplicative channel distortion.

Because of its anti-fading capability and high spectral efficiency and, equally im-portantly, since the corresponding hardware realization technology has become feasible and affordable, OFDM has arisen intensive interest in the worldwide telecommunication community in the past decade and has been adopted as the radio transmission technique for European digital video terrestrial broadcasting (DVB-T) standard [1] and wireless local area network (LAN) standards like IEEE 802.11a and 802.11g physical layer (PHY) [2].

DVB-T, the Terrestrial Digital TV system, is now widely deployed around the world, using its more natural modes to deliver a maximum of programmes to fix, portable and even mobile receivers. The spectrum and economical efficiencies of the DVB-T standard are derived from its hierarchical modulation modes which offer a way to deploy two

independent services using only one radio frequency channel and only one transmitter. As will be shown in Chapter 3, the Single Frequency Networks (SFN) mode of operation further improves the spectrum efficiency of DVB-T.

Two major synchronization issues arise in the design of an OFDM receiver. The first one is the detection and estimation of the OFDM symbol arrival time. Sensitivity to a time offset is higher in multicarrier systems than in single-carrier systems. The second issue of concern has to do with the frequency offset. Frequency offset is due both to the Doppler effect in the mobile communication environments and to the instabilities of and mismatch between the transmitter and the receiver oscillators. The demodulation of an OFDM signal with a nonzero frequency offset cause inter-carrier interference (ICI) and results in higher bit error rates. ICI also affects the performance of other synchroniza-tion subsystems and might incur inter-symbol interference (ISI) that is supposed to be eliminated by inserting guard intervals between successive OFDM symbols.

A radio communication system may experience several kinds of impairments. The combination of thermal, atmospheric, or galactic noise can be represented by a sta-tionary Gaussian random processes. However, man-made noise that appears in urban environments created by the electrical self-starter of cars, power lines, heavy current switches, arc welders, fluorescent lights, etc., cannot be assumed to be Gaussian nor are they stationary. As it has a relatively shot duration, it is more appropriately rep-resented by an impulse noise (IN) model. Besides presenting synchronization, channel estimation and IN suppression (INS) algorithms, the other main theme of this thesis is to propose a baseband architecture that can operate in a normal mode when no impulse noise is present and is capable of switching to the impulse-noise-suppression (INS) mode automatically when impulse noise is present.

The rest of this thesis is organized as follows. The ensuing section introduces the basic DVB-T system structure. Chapter 2 then presents algorithms for timing and frequency synchronization. An effective channel estimator is proposed in Chapter 3. In Chapter

4, we present an algorithm for impulse noise suppression and its extended version that perform both INS and channel estimation. Chapter 5 outlines a baseband architecture and finally, Chapter 6 summarizes our main contributions and draws concluding remarks.

1.1

DVB-T systems

Fig. 1.8 illustrates the European standard (ETSI) of terrestrial system for digital video broadcasting (DVB-T) whose specifications are described in the followings. The source bits unit transmits data stream in the format of MPEG-2 transport layer defined by the ISO/IEC 13818-1 standard. The outer code is the shortened (204,188,t=8) Reed-Solomon (RS) code that derived from the original systematic (255, 239, t = 8) RS code. Fig. 1.9 illustrates the convolutional byte-wise (outer) interlaever with depth I = 12 that is applied to the RS-encoded packet. The outer-interleaved bytes, after a byte-to-bit conversion, are then send to the convolutional inner encoder. The system allows for a range of punctured convolutional codes, based on a mother convolutional code of rate 1/2 with 64 states; see Fig. 1.1.

Figure 1.1: The mother convolutional code of rate 1/2.

shown in Fig. 1.3.

Figure 1.2: Puncturing pattern and transmitted sequence.

Figure 1.3: Inner coding and interleaving.

The inner interleaving consists of bit-wise interleaving (Fig. 1.4) followed by symbol interleaving (Fig. 1.5). Both bit-wise interleaving and the symbol interleaving processes are block-based.

As mentioned before, the system uses OFDM transmission. All data carriers in one OFDM frame are modulated by either QPSK, 16-QAM, 64-QAM, non-uniform 16-QAM or non-uniform 64-QAM constellations. The exact values of the constellation point are

z ∈ {u + jv} with values of u, v given below for the various constellations:

QPSK u ∈ −1, 1, v ∈ −1, 1 16-QAM u ∈ −3, −1, 1, 3, v ∈ −3, −1, 1, 3 Non-uniform 16-QAM u ∈ −4, −1, 1, 4, v ∈ −4, −1, 1, 4

Figure 1.4: Mapping of input bits onto modulation symbols.

64-QAM

u ∈ −7, −5, −3, −1, 1, 3, 5, 7, v ∈ −7, −5, −3, −1, 1, 3, 5, 7

Non-uniform 64-QAM

u ∈ −8, −6, −4, −2, 2, 4, 6, 8, v ∈ −8, −6, −4, −2, 2, 4, 6, 8.

The transmitted signal is organized in frames. Each frame has a duration of T_F and consists of 68 OFDM symbols. Four frames form a super-frame. Each symbol is consti-tuted by a set of K = 6817 carriers in 8K mode and K = 1705 carriers in 2K mode and is transmitted with a duration of T_S. It is composed two parts: a useful (information) part with duration T_Uand a guard interval (cyclic prefix) with duration ∆. The symbols in an OFDM frame are numbered from 0 to 67. All symbols contain data and reference information. In addition to the transmitted data an OFDM frame contains scatter pi-lot, continual pilot and TPS (transmission parameter signalling) carriers. Location of scatter pilot is shown in Fig. 1.6. There are 177 continual pilots in the 8K mode and

Figure 1.5: Symbol interleaver address generation scheme for the 2K mode.

45 in 2K mode; they are inserted according to Fig. 1.7. The TPS carriers are used for the purpose of signalling parameters related to the transmission scheme that includes channel coding and modulation. The TPS is transmitted in parallel on 17 TPS carriers for 2K mode and on 68 carriers for the 8K mode.

For the receiver performs reverse operations of transmitter properly, it needs a syn-chronizer to supply correct estimates for extracting the timing, carrier and frequency offset information and an channel equalizer to compensate for the frequency domain distortion incurred by the transmission channel. The following chapter presents some feasible solutions to the synchronization subsystem design.

˃ ˇ ˋ ˄˅ ˄ˇ ˄ˉ ˅˃ ˃ ˆ ˉ ˌ ˄˅ ˄ˈ ˄ˋ ˅˄ ˅ˇ ˅ˊ ˆ˃ ˆˆ ˆˉ ˆˌ ˇ˅ ˇˈ ˇˋ ˢ˙˗ˠʳ ̆̌̀˵̂˿ʳ ́̈̀˵˸̅ ˢ˙˗ˠʳ˶˴̅̅˼˸̅ʳ˼́˷˸̋ ˣ˼˿̂̇ ˗˴̇˴

Figure 1.6: DVB-T scatter pilot structure.

˦̂̈̅˶˸ʳ˵˼̇̆ ˢ̈̇˸̅ʳ˸́˶̂˷˸̅ ˢ̈̇˸̅ʳ ˼́̇˸̅˿˸˴̉˸̅ ˜́́˸̅ʳ˸́˶̂˷˸̅ ˜́́˸̅ʳ ˼́̇˸̅˿˸˴̉˸̅ ˠ˴̃̃˸̅ ˙̅˴̀˸ʳ ˴˷˴̃̇˴̇˼̂́ ˣ˼˿̂̇ʳʹʳ˧ˣ˦ʳ ̆˼˺́˴˿ ˦˸̅˼˴˿ʳ̇̂ʳ̃˴̅˴˿˿˸˿ ˜˙˙˧ ˣ˴̅˴˿˿˸˿ʳ̇̂ʳ̆˸̅˼˴˿ ˚̈˴̅˷ʳ˼́̇˸̅̉˴˿ʳ ˼́̆˸̅̇˼̂́ ˗˂˔ ˟ˣ˙ ˖˻˴́́˸˿ ˢ̈̇˸̅ʳ˷˸˶̂˷˸̅ ˢ̈̇˸̅ʳ˷˸ˀ˼́̇˸̅˿˸˴̉˸̅ ˜́́˸̅ʳ˷˸˶̂˷˸̅ ˜́́˸̅ʳ˷˸ˀ˼́̇˸̅˿˸˴̉˸̅ ˗˸ˀ̀˴̃̃˸̅ ˖˻˴́́˸˿ʳ˸̆̇˼̀˴̇˼̂́ʳ ʹʳ˸̄̈˴˿˼̍˴̇˼̂́ʳʹʳ ˹̅˸̄̈˸́˶̌ʳ ̆̌́˶˻̅̂́˼̍˴̇˼̂́ ˙˙˧ ˦˸̅˼˴˿ʳ̇̂ʳ̃˴̅˴˿˿˸˿ ˥˸̀̂̉˸ʳ˺̈˴̅˷ʳ ˼́̇˸̅̉˴˿ ˔˂˗ ˟ˣ˙ ˣ˴̅˴˿˿˸˿ʳ̇̂ʳ̆˸̅˼˴˿ ˧˼̀˼́˺ʳ ̆̌́˶˻̅̂́˼̍˴̇˼̂́ ˧̅˴́̆̀˼̇̇˸̅ ˥˸˶˸˼̉˸̅

Chapter 2

Frequency and Timing

Synchronization Subsystems

Synchronization is an essential part for any digital communication system. Without accurate synchronization, it is impossible to reliably recover the transmitted data. In this chapter we address both timing and frequency synchronization issues associated with a DVB-T receiver.

2.1

Joint coarse timing and fractional frequency

off-set estimation

The estimation of the symbol starting position determines the alignment of the fast Fourier transform (FFT) window in the receiver with the useful portion of the desired OFDM symbol. A false estimate leads to inter symbol interference (ISI) and is likely to destroy the orthogonality of the received signal and the resulting inter channel inter-ference (ICI) causes severe performance degradation. Timing estimation consists of two main tasks–signal (presence) detection and symbol synchronization. In a broadcast sys-tem, however, a receiver does not need to detect the presence of a transmitted waveform, because it is always there. Although in deriving our synchronizer we assume that the channel is non-dispersive and the only perturbation source is additive white Gaussian noise (AWGN) w(n), our simulation indicates that the algorithm works for both AWGN and time dispersive channels.

The time-frequency uncertainty in the received OFDM waveform consists of the uncertainty about the signal arrival time and that about the carrier frequency. The time uncertainty manifests itself in the delay associated with the channel impulse response

δ(n − θ), where θ is assumed to be a multiple of the sampling interval. The frequency

uncertainty results in an additional multiplicative term ej2πχn/N _{on the received signal,}

where χ = Ω + ε = ∆f /T , ∆f being the frequency offset in Hz, T the OFDM frame interval, Ω an integer, and 0 ≤ ε < 1. Hence χ denotes the normalized frequency offset as a multiple of the subcarrier space 1/T , Ω is the integer part of ζ while ε is the fractional part. The frequency synchronization process is often divided into two stage, one for compensating for the integer part, Ω, and is referred to as coarse synchronization, and the other is responsible for estimating the fractional part ε. It is assumed that all subcarriers experience the same frequency shift ζ. When dealing with estimating the fractional part only, we can, without loss of generality, assume that

r(n) = s(n − θ)ej2πεn/N + w(n), 0 < ε < 1. (2.1)

In what follows, we show that both the frequency and time synchronization can be derived from the received signal samples’ cyclic prefix. Several coarse symbol synchro-nization algorithms utilizing the cyclic prefix have been investigated for OFDM sys-tems adopting the maximum correlation (MC) [4], or the minimum mean-squared error (MMSE) [5] criterion.

Suppose, as shown in Fig. 2.1, we have collected 2N +Ng consecutive samples of r(n)

during the observation interval and the samples contain (N + Ng) consecutive samples

associated with one complete OFDM symbol. Because the channel delay θ is not known, we have find out which sample represents the starting position of that complete symbol. Define the index sets

N_g N s(n) n 1 T 2N+N_g Observation interval 9 9'

Figure 2.1: Structure of OFDM signal with cyclicly extended symbol s(n) in non-dispersive channel.

and

ζ
≡ {θ + N, . . . , θ + N + Ng− 1} (2.3)

and denote the (2N +Ng) samples by the vector r = [r(1) · · · r(2N +Ng)]T. As the cyclic

prefix is copied from{r(n), n ∈ ζ
} = rζ
, both are highly correlated while the remaining

samples {r(n), n ∈ ζ ∪ ζ
} are independent from them. Many algorithms have exploited this property for timing offset estimation. Speth, Classen, and Meyr [5] suggested that by minimizing the metric

Λ(θ) =

N
g−1

n=0

|r(θ + n + N) − r(θ + n)|2 _(2.4)

where N is the FFT window size, one can jointly estimate the coarse symbol start position and the frequency offset by the following algorithm

ˆ θM M SE = arg min θ {Φ(θ) − |γ(θ)|} = arg maxθ {|γ(θ)| − Φ(θ)} ˆ εM M SE = − 1 2π∠γ(ˆθM M SE) (2.5) where γ(θ) = θ+N
g−1 n=θ r(n)r∗(n + N), Φ(θ) = 1 2 θ+N
g−1 n=θ |r(n)|2_{+|r(n + N)|}2 _(2.6)

0 200 400 600 800 1000 1200 1400 1600 1800 2000 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 Sample index Λ ( θMMSE )

Figure 2.2: MMSE synchronization. Symbol start position at the 500th sample.

The term Φ(θ) is an energy term, its contribution depends on the SNR= σ2

s/σn2;

further-more, the magnitude of the correlation coefficient between r(n) and r(n + N) is given by ρ =    E{r(n)r∗(n + N)}  E{|r(n)|2}E{|r(n + N)|2}   = σ2 s σ2 s + σn2 = SNR SNR + 1. (2.7) Keller and Hanzo proposed the MC algorithm [4], which is perhaps the simplest joint timing and frequency offset estimate

ˆ θM C = arg max θ {|γ(θ)|} (2.8) ˆ εM C = − 1 2π∠γ(ˆθM C). (2.9)

Obviously, the complexity of MMSE algorithm is higher than that of the MC algorithm whilst its performance is improved with the increasing complexity. Fig. 2.4 plots the MSE performance of coarse timing estimate and Fig. 2.5 plots the MSE performance of fractional frequency offset tracking.

0 200 400 600 800 1000 1200 1400 1600 1800 2000 0 0.05 0.1 0.15 0.2 0.25 Λ ( θMC ) Sample index

Figure 2.3: MC synchronization. Symbol start position at the 500th sample.

2.1.1

Coarse timing recovery in multipath fading channels

The above coarse timing synchronization algorithms are derived under the assumption that the only noise source is AWGN. They yield satisfactory performance in a multipath channel in which the leading arrival path is the strongest. If this is not the case, as shown in Fig.2.6 where the presence of multipath propagation makes a part of the guard interval be interfered by the preceding symbol, these algorithms are likely to give wrong timing estimation and will result in ISI. No ISI occurs if the starting position of the FFT window is within region A. The only effect on the subcarriers is a phase rotation that increases with the subcarrier index. On the other hand, if the starting position of the FFT window is within region B, the subcarriers will suffer from ISI in addition to the phase rotation, and the orthogonality amongst subcarriers is destroyed. The received signal can then be expressed as

r(n) = (s(n)  h(n))ej2πεn/N + w(n). (2.10)

where h(n) is the impulse response of channel and w(n) is the AWGN. Lee and Cheun (LS) [3] modified the MMSE and MC synchronization algorithms mentioned before to

0 5 10 15 20 10−2 10−1 100 101 102 103 SNR Mean−squared error MC, AWGN MMSE, AWGN

MC, Rayleigh fading channel MMSE, Rayleigh fading channel

Figure 2.4: The MSE performance of coarse two timing synchronizers.

design coarse timing synchronization algorithms for OFDM systems in multipath chan-nels in which the leading path is not the strongest one. The modification made in [3] is simple and straightforward, it only uses an extended sample interval. The LS algorithm extends the sample interval used by Φ(θ) and γ(θ) from [θ, (θ+Ng−1)] to [θ, (θ+Ns1−1)]

or [θ, (θ + Ns2− 1)], where Ns1 = Ng + Nm and Ns2 = 2Ng − 1, Nm being maximum

delay spread. Hence Φ(θ) and γ(θ) are modified according to

γ(θ) = θ+N
s1−1 n=θ r(n)r∗(n + N) or γ(θ) = θ+N
s2−1 n=θ r(n)r∗(n + N), (2.11) Φ(θ) = 1 2 θ+N
s1−1 n=θ |r(n)|2_{+|r(n + N)|}2 _{or Φ(θ) =} 1 2 θ+N
s2−1 n=θ |r(n)|2_{+|r(n + N)|}2_(2.12)

A block diagram of this modified coarse timing synchronizer is given in Fig. 2.8.

2.2

Coarse frequency synchronization

0 5 10 15 20 10−7 10−6 10−5 10−4 10−3 SNR Mean−squared error

MMSE, Rayleigh fading channel MC, Rayleigh fading channel MMSE, AWGN

MC, AWGN

Figure 2.5: The MSE performance of two fractional frequency offset synchronizers.

gorithms for OFDM signals is to detect the location of guard bands (virtual carriers) which are supposed to be located at both edges of the OFDM spectrum to avoid adjacent channel interference. We can use this algorithm to estimate coarse frequency offset of a DVB-T signal. Han [7] proposed a two-stage frequency domain algorithm for coarse frequency synchronization. As shown in Fig. 2.9, it first calculates the correlation of two frequency domain pilots associated with the same subcarrier for two successive symbols at candidate frequency-shifted pilot positions. In other words, if Ri(k) represents the

ith symbol of the kth subcarrier, Pm = [p1 + m, p2 + m, ..., pL+ m] is the set of the

subcarriers to be correlated and m denotes the subcarrier offset from P0, then the coarse

frequency estimate is given by ˆ Ωo= arg max m (φm), where φm =   
k∈Pm Ri(k)R∗_i+1(k)   . (2.13) Fig. 2.10 illustrates the correlation process when the received frequency domain signal has a normalized carrier frequency offset of two. We use the continual pilots for coarse frequency synchronization in our DVB-T system, the positions of the continual pilot [1]

N_g N A B B Channel Im pulse Response ˆ g N

T

 FFT W indow

Figure 2.6: Structure of an extended OFDM frame showing the relation of the channel impulse response duration and the legitimate starting position of the FFT window.

indices are 0, 48, 54, 87, · · · . If the maximum value φM is obtained from correlating with

subcarriers 2, 50, 56, 89, · · · , the estimated integer frequency offset is two because the position of the maximum correlation is obtained at two subcarrier spacings away from the original continual pilots. The second stage is needed to improve the performance of the first stage when the fractional carrier offset is around +0.5 or −0.5. We then use the ratio of the maximum value φM and one of its adjacent values φM +1 or φM−1 to reduce

the carrier frequency uncertainty.

ˆ Ω = ⎧ ⎪ ⎨ ⎪ ⎩ ˆ Ωo− 0.5, if φM−1 > φM +1 and φ_M−1 φM > µ1, ˆ Ω_{0+ 0.5,} if _φM−1 < φM +1 and φ_M+1 φM > µ2 ˆ Ωo, elsewhere, (2.14)

0 5 10 15 20 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 SNR Lock−in Probability

MMSE max. delay speard known MC max. delay speard known MC conventional method MMSE conventional method

Figure 2.7: The Lock-in probability of coarse timing synchronizer in AWGN and (DVB-T defined) Rayleigh fading channels.

2.2.1

Improved coarse frequency synchronization

Based on Han’s idea, we propose the following extended version of (2.14) for fine frequency synchronization ˆ χ = ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ ˆ Ωo− 0.1, if φM−1 > φM +1 and φ_M−1 φM > µ−1, ˆ Ωo− 0.2, if φM−1 > φM +1 and φM−1φM > µ−2, ˆ Ωo− 0.3, if φM−1 > φM +1 and φ_M−1 φM > µ−3, ˆ Ωo− 0.4, if φM−1 > φM +1 and φ_M−1 φM > µ−4, ˆ Ωo− 0.5, if φM−1 > φM +1 and φM−1φM > µ−5, ˆ Ωo+ 0.1, if φM−1 < φM +1 and φ_M+1 φM > µ+1 ˆ Ωo+ 0.2, if φM−1 < φM +1 and φM+1φM > µ+2 ˆ Ωo+ 0.3, if φM−1 < φM +1 and φM+1φM > µ+3 ˆ Ωo+ 0.4, if φM−1 < φM +1 and φ_M+1 φM > µ+4 ˆ Ωo+ 0.5, if φM−1 < φM +1 and φM+1φM > µ+5 ˆ Ωo, elsewhere, (2.15)

where µ−5∼ µ+5 are thresholds to be optimized.

synchro-̍ˡ ̅ʻ́ʼ 2 1 2 ˜ 2 1 2 ˜ ˠ̂̉˼́˺ʳ̆̈̀ ʻˁʼʽ ˜ ‘ ˀ (.) ) (.) J ˴̅˺ʳ̀˴̋ 1 2S  Hˆ ˆ T ˠˠ˦˘ ˠ˖ ˠˠ˦˘ ˠ˖ ˠ̂̉˼́˺ʳ̆̈̀

Figure 2.8: Block diagram of the LS coarse timing synchronization algorithm.

nizer from±0.25 to ±0.1. With such an enhanced resolution, the residual frequency error can easily be compensated for by any correlation-based fine frequency synchronizer and the acquisition time can be reduced significantly.

2.3

Timing tracking

After establishing the coarse frame timing, one still has to fine-tune the timing clock to improve the performance when the receiver is operating in a mobile environ-ment. This is because the drifting of the clock will make the system lose lock and its performance deteriorate as ISI arises if the clock is left without tracking. Furthermore, a residual timing error also induces phase rotations after de-multiplexing in the frequency domain. The residual timing error is often corrected after channel equalization has been accomplished. The channel estimation/equalization procedure is presented in Chapter 3. For the moment, let us assume that the channel impulse response is perfectly known

˙̅˸̄ˁʳ̂˹˹̆˸̇ʳ ˶̂̀̃˸́̆˴̇˼̂́ ˙˙˧ ˄ʳ̆̌̀˵̂˿ʳ ˷˸˿˴̌ ˖̂̅̅˸˿˴̇˼̂́ ˘̋̇̅˴˶̇˼̂́ʳ̂˹ʳ ̃˼˿̂̇ʳ̃̂̆˼̇˼̂́ ˜

¦

˙̅˸̄ˁʳ̂˹˹̆˸̇ʳ ˸̆̇˼̀˴̇˼̂́ ˦˼˺́˴˿ʳ̂̈̇̃̈̇ ˦˼˺́˴˿ʳ ˼́̃̈̇ m I

Figure 2.9: Block diagram of a coarse frequency synchronization algorithm.

and denote the frequency domain samples with perfect timing recovery by

R(k; 0) =

N
₋₁ n=0

x(n)e−j2πkn/N + W (k), k = 0, ..., N − 1, (2.16)

so that that corresponding to a timing error of θe is given by

R(k; θe) = N
−1 n=0 x(n − θe)e−j2πkn/N + W (k) = R(k; 0)e−j2πkθe/N , k = 0, ..., N − 1 (2.17)

where θe is the residual timing error and x(n) = s(n) ⊗ h(n), ⊗ being the convolution

operation. The estimated channel responses at pilot carriers when a group delay in time domain is present can be represented by

ˆ

Hp(m) = Hp(m) · e−jmθe + ∆Hp(m), m ∈ pilot tones (2.18)

where Hp(m) is true channel transfer function and ∆Hp(m) is the estimation error.

We notice that to estimate the timing error θe is equivalent to estimating the unknown

˹ ˹ ˼ˀ̇˻ʳ ̆̌̀˵̂˿ ˖̂́˽̈˺˴̇˸ʳ̂˹ʳ ʻ˼ʾ˄ʼˀ̇˻ʳ ̆̌̀˵̂˿ 1 I 0 I I2 ˖̂́̇˼́̈˴˿ʳ̃˼˿̂̇ʳ̃̂̆˼̇˼̂́ʳ ˣ_˃ː̎˃ʿʳˇˋʿʳˈˇʿʳˋˊʿˁˁˁ̐ ʳʳʳʳʳ˖̂́̇˼́̈˴˿ʳˣ˼˿̂̇ ʳʳʳʳʳ˗˴̇˴ ˇˋ ˇˌ ˈ˃ ˈˇ ˈˈ ˈˉ ˋˊ ˋˋ ˋˌ ˖̂̅̅˸˿˴̇˼̂́ ˹ ˇˋ ˇˌ ˈ˃ ˈˇ ˈˈ ˈˉ ˋˊ ˋˋ ˋˌ ˼ˀ̇˻ʳ ̆̌̀˵̂˿ ʻ˴ʼ ʻ˵ʼ

Figure 2.10: Frequency domain correlation when the true carrier frequency offset is 2/T .

presented in [8] can be applied to estimate θe. The estimator in [8] that provides the

best overall performance is given by ˆ

θe =

N
p−2

m=0

w(m)∠ ˆHp∗(m) ˆHp(m + 1) (2.19)

where Np is the number of pilot subcarriers and

wm = 3 2Np N2 p − 1 ⎧ ⎨ ⎩1−  m − (N₂p − 1) Np 2 ₂⎫_⎬ ⎭ (2.20)

A simpler but inferior estimator is [8]e phase estimator is ˆ θe = 1 N − 1 N
p−2 ∠ ˆHp∗(m) ˆHp(m + 1) (2.21)

1.5 2 2.5 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 SNR 10 dB, AWGN channel

Normailzed Frequency Offset

Estimated Frequency Offset

Perfect frequency estimation Han’s coarse frequency estimation Modified Han’s coarse frequency estimation

Figure 2.11: Compensation characteristic of coarse frequency synchronizers with the carrier frequency offset ranges from 1.5 to 2.5 subcarrier spacings (6.696KHz to 11.16KHz in 2K mode of DVB-T system).

2.4

Computational complexity

It has been found that between the two coarse timing synchronizers, the MMSE and MC algorithms, the former has a better performance but needs more computational complexity. The MC algorithm needs Ng additions and Ng complex multiplications

while the MMSE algorithm needs extra 2Ng additions and 4Ng real multiplications.

The modified coarse timing synchronizers for multipath channels necessitate even higher complexity–Ng is increased to Ns1 or Ns2.

The coarse frequency offset synchronizer calls for Ncp additions and Ncp

multiplica-tions in computing φm and N-symbol memory to stored the last symbol samples, where

Ncp is the number of continual pilot. The total complexity depends on the maximum

frequency offset that we assumed. Without regard to the channel estimation, the timing tracking subsystem requires Np− 1 additions and Np− 1 complex multiplications when

1.5 2 2.5 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Norimalized frequency offset

c

Figure 2.12: Determination of the thresholds used in (2.17) by examining the behavior of the averaged ratio between the peak correlation and second largest correlation, E[c] =

E{max(φM−1/φM, φM +1/φM)}, as a function of the normalized carrier frequency offset.

2.5

Numerical Behavior

The lock-in probability performance shown in Fig. 2.7 indicates conventional timing recovery algorithm can not overcome the multipath effect, where we have defined the lock-in probability as the probability that the FFT window starts at the legitimate region (see Fig. 2.6). One candidate solution is to extended correlation length and another one is to modify our coarse timing estimate by simply advancing a few samples ahead to avoid locking to the wrong path. We find through extensive simulation that by using that timing estimate whose value is 10-sample earlier than the original coarse timing estimate is enough to overcome the multipath effect. The lock-in probability (no ISI) then becomes very high. After finishing the coarse timing synchronization and meantime fractional frequency offset synchronization, one needs to evaluate the angle of γ(ˆθ). Figs.

2.14 and 2.15 show respectively the learning curves of of the conventional and modified coarse frequency synchronizers. Our modified fast coarse frequency synchronizer renders

1.5 2 2.5 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 Mean−squared error

Normalized frequency offset SNR 10dB, AWGN channel Han’s algorithm

Modified Han’s algorithm

Figure 2.13: The MSE performance of the coarse frequency synchronizer where χ ranges from 1.5 to 2.5 (6.696KHz to 11.16KHz in 2K mode).

0 2 4 6 8 10 −0.5 0 0.5 1 1.5 2 Symbol index

Estimated frequency offset

Normialized frequency offset is 1.6. SNR 10dB Rayleigh fading channel Coarse frequency offset estimation Fine frequency offset estimation

Figure 2.14: Learning curves of the conventional carrier frequency synchronizer.

0 2 4 6 8 10 −0.5 0 0.5 1 1.5 2

Normialize frequency offset is 1.6. SNR 10dB Rayleigh fading channel

Symbol index

Estimated frequency offset

Coarse frequency offset estimation Fine frequency offset estimation

Chapter 3

Channel Estimation

3.1

Fundamental of OFDM Channel Estimate

In this chapter we study methods that use the scatter pilot to estimate the channel frequency response. Most channel estimation methods for OFDM transmission systems have been developed under the assumption of a static or slow fading channel, where the channel transfer function remains stationary within at least one OFDM data frame. In practice, the channel transfer function of wideband radio channel might have significant changes even within one OFDM data frame. Therefore, it is preferable to estimate channel characteristic based on the pilots in each individual OFDM data frame instead of many adjacent frames.

Fig 1.8 shows that the modulated data{S(k)} are transformed and multiplexed into the time-domain sequence {s(n)} by inverse DFT

s(n) =

N
−1 k=0

S(k)ej2πkn/N, n = 0, ..., N − 1 (3.1)

where N is the number of subcarriers. The received signal can be represented by

r(n) = s(n) ⊗ h(n) + w(n). (3.2)

where h(n) is the impulse response of channel and w(n) is the AWGN. The channel impulse response can be expressed as

h(n) =

M
−1 i=0

where M is the total number of propagation paths, hi, fDi and τi are the complex

weight, Doppler shift and normalized relative delay of the ith path (i.e., the true delay minus the shortest path delay then divided by T ). The received pilot signals {Rp(k)} are extracted from {R(k)} and the channel transfer function {H(k)} can be obtained from the information carried by {Hp(k)}. With the knowledge of the channel response

{H(k)}, the transmitted data samples {S(k)} can be detected by simply dividing the

received frequency domain sample by the estimated channel response ˆ

S(k) = R(k)_ˆ

H(k), k = 0, 1, ..., N − 1 (3.4)

where ˆ_{H(k) is an estimate of H(k). After signal de-mapping and decoding, the source} binary information sequence is reconstructed at the receiver. The DVB-T standard assigns pilots in the frequency domain and their arrangement is suitable for aiding syn-chronization and channel estimation in fading channel. The pilot signals{Sp(m)} is ±4₃

generated using the pseudo random binary sequence (PRBS) whose generator polyno-mial is given by X11_{+ X}2_{+ 1; see Fig. 3.1. Let H}

p = [Hp(0) Hp(1) . . . Hp(Np− 1)]T be

Figure 3.1: Generation of PRBS sequence.

the channel response of at pilot subcarrier and Rp = [Rp(0) Rp(1) . . . Rp(Np − 1)]T be

the corresponding received vector. The received pilot signal vector can be expressed as

where Sp = ⎡ ⎢ ⎣ Sp(0) 0 . .. 0 _Sp(Np − 1) ⎤ ⎥ ⎦ (3.6)

Ip and Wp are the inter-carrier interference (ICI) and the AWGN components in pilot

locations. The conventional least squares (LS) channel estimate is given by ˆ Hp,ls = S−1p Rp =  Rp(0) Sp(0) Rp(1) Sp(1) · · · Rp(Np− 1) Sp(Np − 1) T (3.7)

The LS estimate on data positions are obtained through interpolating ˆHp,ls and is very

sensitive to Gaussian noise and ICI. The piecewise-linear interpolation method has been studied in [9]. In the linear interpolation algorithm, two successive pilot subcarriers are used to determine the channel response for data subcarriers that are located in between the pilots. For data subcarrier k, mL ≤ k ≤ (m + 1)L, L is the distance between two pilots. The estimated channel response using linear interpolation method is given by

ˆ H(k) = H(mL + l) = (1 −ˆ l L) ˆHp(m) + l LHˆp(m + l) = _Hˆp(m) + l L( ˆHp(m + l) − ˆHp(m)), 0≤ l ≤ L (3.8)

Theoretically, using higher-order polynomial interpolation will fit the channel response better than the linear interpolation but the computational complexity grows as well. Using the second-order polynomial interpolation yields

ˆ H(k) = H(mL + l) = Cˆ 1Hˆp(m − 1) + C0Hˆp(m) + C−1Hˆp(m + 1), (3.9) where ⎧ ⎨ ⎩ C1 = α(α+1)₂ C0 = −(α − 1)(α + 1) C−1 = α(α−1)₂ (3.10) and α = l/N.

3.2

DVB-T channel model

Fig. 3.2 plots a static version of DVB-T channel impulse response whose path gains and phases are given in Table 3.1. In simulation, we have used Rayleigh fading channel. DVB-T can operates at a single frequency networks (SFN) in which the same program is broadcasted simultaneously at two or more sites using the same frequency. The SFN architecture fills gaps within or extend the service provided by a single transmitter. This technique is applicable for a DVB-T system due to its resilience to multiple signals. The use of a single channel from multiple transmitters to serve an area allows the efficient use of spectrum. In analogue, multiple channels were required to serve an area and hence reduced the number of services possible. The use of SFN allows more services to be introduced. The maximum delay of SFN is assumed to be smaller than guard interval. In our simulation, we used two identical channel profiles to model a SFN channel, see Fig. 3.4. 0 5 10 15 20 25 30 35 40 45 50 −0.5 −0.4 −0.3 −0.2 −0.1 0 0.1 0.2 0.3 0.4 0.5

Channel Tap Index n

Magnitude Response

˦̇˴̇˼̂́ʳ˄ ˦̇˴̇˼̂́ʳ˅

Figure 3.3: The DVB-T single frequency network (SFN) concept.

3.2.1

Jakes model

Jakes model [10] is a very popular channel model for mobile multipath channels that takes into account the Doppler effect and is based on the assumptions that the receiver is moving at speed v while the arrival angles of multipath components are uniformly distributed. The time correlation of the channel is then given by

R(∆t) = J0(2π · ∆t · fd) (3.11)

where Doppler frequency fd = v · fc/c, fc is the carrier frequency and c is the speed of

light. J0(x) is the zero-th order Bessel function of the first kind.

3.3

Phase compensation

In Chapter 2, we mentioned that the residual timing error tends to introduce phase rotation that leads to model mismatch errors for interpolation-based channel estimation.

˦̇˴̇˼̂́ʳ˄ ˖˻˴́́˸˿ʳ˼̀̃̈˿̆˸ʳ̅˸̆̃̂́̆˸ ˦̇˴̇˼̂́ʳ˅ ˖˻˴́́˸˿ʳ˼̀̃̈˿̆˸ʳ̅˸̆̃̂́̆˸ ̇ ˧̂̇˴˿ʳ˶˻˴́́˸˿ʳ˼̀̃̈˿̆˸ʳ̅˸̆̃̂́̆˸

Figure 3.4: Combined impulse response of a DVB-T single frequency network with two stations.

This model mismatch error is an increasing function of the timing error ˆ

θe =

N
p−2

m=0

w(m)∠ ˆHp∗(m) ˆHp(m + 1) (3.12)

where Np is the number of pilot subcarrier and

wm = 3 2Np N2 p − 1 ⎧ ⎨ ⎩1−  m − (N₂p − 1) Np 2 ₂⎫_⎬ ⎭ (3.13)

Recall that the simple estimator of [8] based on the phase estimates are ˆ θe = 1 N − 1 N
p−2 m=0 ∠ ˆHp∗(m) ˆHp(m + 1). (3.14)

Given ˆ_θe, the channel responses at pilot locations are updated via

˜

Hp(m) = Hˆp(m) · ej ˆθem

≈ Hp(m) + EH
p(m) (3.15)

After this phase compensation, the channel responses at data carriers are interpolated by using linear or higher-order polynomial interpolation and the resulting estimates ˜_Hd(k)

is refined as

ˆ

Hd(k) = H˜d(k) · e−jk

θe

L_{. (3.16)}

Table 3.1: Path gains and phase rotations associated with the DVB-T channel impulse response of Fig. 3.2. Least-Square Channel Estimation Interpolation Pre-Phase Compensate (Timing Tracking) Post-Phase Compensate 2 ˆ ( ) j Nem LS H k e ST ˆ ( )_LS H m 2 ˆ ( ) j Nek LS H k e ST ( ) R m ˆ ( )_LS H k

Figure 3.5: LS channel estimation, m ∈pilot and k = 0, ..., N − 1.

3.4

Transform-domain channel estimation algorithm

A channel estimation based on transform-domain processing was proposed in [11]. This method employs lowpass filtering in the transform domain so that intercarrier interference and additive white Gaussian noise components in the received pilots are significantly reduced. Rewriting (3.7) as ˆ Hp,ls(m) = Hp(m) +[I(m) + W (m)] Xp(m) , m = 0, . . . , N p− 1 (3.17)

component [I(m)+W (m)]_X

p(m) in (3.17) is a zero mean Gaussian random process as well.

Vari-ation of the true frequency transfer function Hp(m) within one or a few OFDM frames

is usually very slow with respect to the pilot subcarrier index m but that of the noise component [I(m)+W (m)]_X

p(m) is fast and large. We can use this property to separate the two

components by employing a transform-domain lowpass filter where the transform domain refers to the “frequency domain” in DFT-IDFT transformations. Therefore, a sequence in the frequency domain is the spectral sequence of its counterpart in the frequency. The argument p of the transform domain can be viewed as the ”frequency” which reflects the variation rate of a frequency domain function. The transform domain representation of

ˆ Hp,ls(m) becomes ˆ Gp(p) = N
p−1 m=0 ˆ Hp,ls(m)e−j2πmp/Np, (3.18)

where p ∈ [0, Np − 1] is the transform domain index. Fig. 3.6 plots the frequency

responses of two channel conditions, one with noise and Doppler shift ((b)) and another one without ((a)) As expected, the signal component in ˆ_Gp(p) is located at the lower

”frequency” (around p = 0 and p = Np− 1) region, while the noise component is spread

over the full band (p = 0, . . . , Np− 1).

The lowpass filtering can be realized by simply setting the samples in the “high frequency” band to zero, that is

˜

Gp(p) =

 _ˆ

Gp(p), 0≤ p ≤ pc, Np− pc ≤ p ≤ Np − 1,

0, otherwise (3.19)

where pc is the cutoff frequency of the filter in the transform domain. Such a low-pass

filtering reduces the noise component by an order 2pc/Np.

3.4.1

Cutoff frequency

The cutoff frequency pc of the transform domain lowpass filter is an important

fre-0 50 100 150 −100 −50 0 50 100

(a) Transform domain index p

Amplitude 0 50 100 150 −60 −40 −20 0 20 40

(b) Transform domain index p

Amplitude

Figure 3.6: A typical transform domain response ˆ_Gp(p) when (a) AWGN and Doppler

shift are absent (i.e., noiseless static channel) and (b) SNR = 5 dB, Doppler frequency = 90 Hz.

pc dynamically by tracking the channel variation. Comparing parts (a) and (b) of Fig.

3.6, we find that most of the energy concentrates at the lower frequency region where the desired components dominate. It is thus suggested that pc be determined from the

following relation pc p=0| ¯Gp(p)|2+ Np−1 p=Np−pc| ¯Gp(p)|2  Np−1 p=0 | ¯Gp(p)|2 = Λ (3.20)

where the numerator is the energy in the passband, the denominator represents the total energy, Λ ∈ [0.9, 0.95], and ¯_Gp(p) is the average value of ˆGp(p) of the present data

˟˦ʳ˖˻˴́́˸˿ʳ ˘̆̇˼̀˴̇˼̂́ ˡ_̃ˀ̃̂˼́̇ʳ ˜˗˙˧ ˟̂̊̃˴̆̆ʳ ˙˼˿̇˸̅ ˦˸˿˸˶̇˼̂́ʳ̂˹ʳ ˖̈̇̂˹˹ʳ ˙̅˸̄̈˸́˶̌ʳ ˡ_̃ˀ̃̂˼́̇ʳ ˜˗˙˧ ˥ʻ˾ʼ ,

ˆ

_{( )}

p ls

H

m

ˆ ( )_p G p ( ) p G p ˆ _{( )} TD H m

Figure 3.7: Block diagram of a channel estimation algorithm based on transform-domain processing; m ∈pilots and k = 0, ..., N − 1 and p = 0, ..., Np− 1.

Least-Square Channel Estimation Interpolation Transform-Domain Processing Pre-Processing Phase Compensation (Timing Tracking) Post Processing Phase Compensation 2 ˆ _{( )} e m j N LS H k e ST ˆ _{( )} LS H m HˆTD( )m 2 ˆ _{( )} j Nek TD H k e ST ( ) R m ˆ _{( )} TD H k

Figure 3.8: Complete channel estimation process incorporating transform domain filter-ing; m ∈ pilot set and k = 0, ..., N − 1.

3.5

Model-based channel estimation

We now examine the effectiveness of the novel model-based estimation method of [12] for estimating DVB-T channels. The LS channel estimation is given by

ˆ Hp,ls(m, n) = R p(m, n) Xp(m, n) = H p(m, n) + W (m, n) + I(m, n) Xp(m, n) , (3.21)

where p indicate the pilot positions. H(m, n), Xp(m, n) and Rp(m, n) denote the channel

response, transmitted signal and received samples at the mth subcarrier during the nth symbol interval. The channel responses H(m, n) can be viewed as a sampled version of the two-dimension continuous complex fading process H(f, t). We choose a operating

region in the time-frequency plane and approximate the sampled fading process H(m, n) in this region by the quadrature surface

f (x, y) = ax2+ bxy + cy2 + dx + ey + f, (3.22)

where the coefficients (a, b, c, d, e, f ) are determined such that
(m,n)∈pilot tones   ˆHp,ls(m, n) − f (m, n) 2 (3.23)

is minimized. Rewriting (3.25) in more compact form
(m,n)∈pilot tones   ˆHp,ls(m, n) − qTmnc 2 (3.24)

where cH _{= (a, b, c, d, e, f ) is the coefficient vector and q}T

mn = (m2, mn, n2, ., m, 1) is the

pilot location vector. We shall only consider the case of one-dimensional (1-D) regression model.

ˆ

Hmodel(m) = c0+ c1m + c2m2, 0≤ m < L, (3.25)

where L is the block length. ˆ c = arg min c L−1
m=0   ˆHp,ls(m) − qTmc 2 (3.26)

where cH _{= (a, b, c) is the coefficient vector and q}T

m = (m2, m, 1) is the pilot location

vector. Fig. 3.9 indicates the fitting processing. We can write (3.26) more concisely by

ˆ c = arg min c   ˆHp,ls− Qc 2 (3.27) where ˆHp,ls= ( ˆHp,ls(0), ˆHp,ls(1), ..., ˆHp,ls(L − 1))T and Q = ⎛ ⎜ ⎜ ⎜ ⎝ qT 0 qT 1 .. . qT L−1 ⎞ ⎟ ⎟ ⎟ ⎠= ⎛ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ 1 0 0 · · · 0 1 1 1 · · · 1 1 2 22 _{· · · 2}d .. . ... ... . .. ... 1 (L − 1) (L − 1)2 · · · (L − 1)d ⎞ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠. (3.28)

Note that from (3.25) Qc = ( ˆ_Hmodel(0), ˆHmodel(1), ..., ˆHmodel(L − 1))T = ˆHmodel is the

new estimate of channel impulse response. By solving (3.27), the coefficients of the regression polynomial is

ˆ

c = (QTQ)−1QTHˆp,ls, (3.29)

and we obtain the new estimates ˆ H_{model(m) = q}T_mˆ_c. (3.30) ˆ H_model = Qˆc = Q(QTQ)−1QTHˆp,ls= V ˆHp,ls, (3.31) where V = Q(QTQ)−1QT_. (3.32) , ( ) ˆ _{( )} ( ) p p ls p R m H m X m model ˆ ( ) ( ) f m H m

Figure 3.9: Indication of the least-squared-fitting processing.

According to [12], we know that the model-based channel estimation gives better performance when uniform pilot structure is in place. However, as shown in Fig. 1.6,

˃ ˇ ˋ ˄˅ ˄ˇ ˄ˉ ˅˃ ˃ ˆ ˉ ˌ ˄˅ ˄ˈ ˄ˋ ˅˄ ˅ˇ ˅ˊ ˆ˃ ˆˆ ˆˉ ˆˌ ˇ˅ ˇˈ ˇˋ

ˢ

˙

˗ˠʳ̆̌̀

˵̂˿ʳ́̈̀

˵˸̅

ˢ˙˗ˠʳ˶˴̅̅˼˸̅ʳ˼́˷˸̋

ˣ˼˿̂̇ ˗˴̇˴

̅˸˺̅˸̆ˁʳʻˆʿˇʼ

Figure 3.10: DVB-T pilot symbol distribution in time-frequency. In the button of this figure, regres.(3,4) means that use 3 pilots in time domain and 4 pilots in frequency domain to make regression model.

the pilot distribution in DVB-T is not uniform, we modify the model-based approach by first estimate the channel responses at selected subcarriers using a 1D model. Regarding the recovered channel responses as pilots, we then apply the 2D model-based procedure for solving the remaining data locations; see Fig. 3.10).

3.6

2-D model-based channel estimate with

transform-domain processing

Shown in Fig. 3.11 is a block diagram that represents an improved channel estimator, concatenating the transform-domain processing algorithm with the 2-D model-based channel estimator. As the transform-domain processing (TDP) unit suppresses the ICI and AWGN effects, the following 2-D model-based channel estimation unit stands a much better chance to find a curve that comes very close to real channel response.

We therefore expect this two-stage algorithm to give enhanced performance for DVB-T systems. Ntis the transform size (FFT size), we can change Ntto reduce the complexity

Least-Square channel estimation Model-based channel estimation ˆ ( )_LS H k _Hˆ_TD( )_m ( ) R m ˆ _{( )} Model H k Transform-domain processing N_t

Figure 3.11: Block diagram of a two-stage channel estimator that consists of a TDP unit and a model-based channel estimation unit.

of our proposed algorithm. In our simulation, we select 3 different number for Nt, thus,

Np, 128 and 64, see Fig. 3.15, where Np is the number of pilot tones in a OFDM symbol.

If Nt= Np means all pilots will input to TDP for suppress all kinds of interference.

3.7

Computational complexity

LS channel estimation needs Np complex division or 5Np multiplication in a symbol.

Two addition and two real multiplication are needed per subcarrier in the linear inter-polation.Thus, use LS with linear interpolation needs 5Np+ 2N real multiplications in a

OFDM symbol. In 2K mode DVB-T system, it requires about 2 complex multiplication per subcarrier.

The channel estimation based on transform-domain processing uses two FFTs to estimate the channel response. the both of size is Np (if we used FFT interpolation the

size of FFT is Np and N). By using the decimation-in-frequency radix-2 implementation

of FFT, the total number complex multiplications required is roughly 2Nplog₂Np. By

using the parameters in 2K mode DVB-T system, the transform-size is replaced by 256. It requires at least 2N complex multiplication and 2N real multiplications in an OFDM symbol, TDP (by using linear interpolation) requires about 4 complex multiplication

per subcarrier.

It is preferred to use (3.29) and (3.30) in calculation for complexity consideration of regression model. The computational algorithm is

ˆ

c = P ˆHp,ls, (3.33)

ˆ

H_{model(m) = q}T_mˆ_c, (3.34)

where P = (QTQ)−1QT _{is a constant matrix. The dimension of P is (d + 1) × L, so to}

obtain c we need 2(d + 1)L real multiplication since P is real. Calculating each channel response at the data tone using (3.34) needs 2(d + 1) real multiplication. Since there are L(r − 1) data tones, where r is the subcarrier spacing of pilot tone, we need totally 5L + 2L(r − 1)(d + 1) + 2(d + 1)L real multiplications. Average over L(r − 1) data locations, we need less than 4(d + 1) real multiplication. We conclude that in estimating each ˆ_{Hmodel(m) at the data tone, we need less than (d + 1) complex multiplication on} the average. Thus, it requires about 3 complex multiplication per subcarrier. Our proposed 2-D regression model with TDP requires about 4 complex multiplication if the transform size is 128. Use 2-D regression (3,Lf) needs 7N memory to store those

symbols information, and 2-D regression (4,Lf) needs 11N memory. By using 1-D

channel estimation is not need any extra memory to save symbol information.

3.8

Numerical examples

Numerical behavior of various channel estimates is reported in this section. We assume that QPSK modulation with a rate 1/2 convolutional code is used and perfect timing (frame) recovery is achieved. The 2-D model-based channel estimation with TDP (2D-MB-TDP) algorithm, as indicated in Fig. 3.12, has the best performance amongst those channel estimation algorithms examined. Fig. 3.13 show that the same conclusion holds when Doppler and noise are presented and the system operates in a SFN channel with r.m.s. delay spread of 5.13µs (or equivalently 48 samples). The improvement

with respect to 1D algorithms becomes very significant in this case. When delay spread increases, the coherent bandwidth decreases so that the pilots in frequency domain is not dense enough to properly interpolate the channel response across the whole transmission band. Use a 2-D channel estimation algorithm help overcoming this difficulty.

In Figs. 3.13 and 3.14, regres.(Lt,Lf) denotes that the time-frequency region selected

for 2D modelling contains Lt time pilots and Lf frequency pilots; see Fig. 3.11. These

curves show that it is better to use smaller frequency domain modelling width (fewer frequency pilots) in modelling the channel impulse response. Fig. 3.15 shows that the price we pay for reducing the FFT window size Nt is negligible. Since in the 2K mode,

there are 143 pilots in frequency domain which is not a power of 2, we use 256 points or 128 points FFT instead. 2 4 6 8 10 12 14 16 18 10−7 10−6 10−5 10−4 10−3 10−2 10−1 100 SNR BER 2−D regres. (3,4) 2−D regres.(3,4) + TDP 1−D LS 1−D TDP

Figure 3.12: BER performance comparison of various channel estimates; zero Doppler shift, r.m.s. delay spread = 1.36 µs.

2 4 6 8 10 12 14 16 18 10−6 10−5 10−4 10−3 10−2 10−1 100 SNR BER 1−D TDP 2−D regres. (3,4) 1−D LS 2−D regres. (3,4) + TDP 2−D regres. (3,5) + TDP 2−D regres. (3,5)

Figure 3.13: BER performance comparison of various channel estimates; Doppler fre-quency = 88 Hz, r.m.s. delay spread = 5.13µs.

0 5 10 15 20 25 30 10−6 10−5 10−4 10−3 10−2 10−1 100 SNR BER 2−D regression (3,4) + TDP 2−D regression (3,5) + TDP 2−D regression (3,6) + TDP 2−D regression (3,2) + TDP

Figure 3.14: The effect of the 2D model size on the BER performance; Doppler shift = 88 Hz, r.m.s. delay spread = 9.1245µs.

2 4 6 8 10 12 14 16 10−7 10−6 10−5 10−4 10−3 10−2 10−1 100 SNR BER 2−D regres.(3,4) + TDP, Nt = Np. 2−D regres.(3,4) + TDP, Nt = 128 points. 2−D regres.(3,4) + TDP, Nt = 64 points. 2−D regres.(3,4)

Figure 3.15: The effect of the FFT window size on the BER performance; Doppler frequency = 88 Hz, r.m.s. delay spread = 1.36µs.

Chapter 4

Impulse Noise Suppression

4.1

Background

A radio communication waveform is likely to suffer from several kinds of impairments. Most of them, e.g. thermal, atmospheric, or galactic noise, can be represented by a Gaussian model. However, man-made noise that appears in urban environments created by the electrical self-starter of cars, power lines, heavy current switches, arc welders, fluorescent lights, etc., cannot be assumed to be Gaussian. As they all have a shot duration nature, they are often represented by an impulsive model. Taking the occurring instances of these shot noise into account, we model the impulse noise (IN) as a random train of pulses with a very wideband power spectral density. Detailed impulse noise model in the next section. To eliminate or at least suppress the influence of IN, one has to be able to detect its presence. Detecting the arrivals of impulse noise is discussed in Section 4.3. We then briefly describe the convention impulse noise rejection method–the blanking method in Section 4.4. New IN suppression algorithms are given in Sections 4.5 and 4.6.

4.2

Impulse noise model

We use the IN model based on the Sanchez’s [15] measurements in which two outdoor environments referred to as noisy place and quiet place, respectively are considered. We

will limit our investigation to the noisy place IN model given by i(t) =
i ai  wi (t − ti) (4.1)

This model has three random variables, namely, the pulse duration, pulse amplitude and elapsed time between pulses. The distribution of elapsed time between pulses follows a Gamma distribution, but none of the distribution function is adequate to model the pulse amplitudes or the pulse duration that said by [15]. We choose a static impulse noise model and for the worst-case consideration, we assume that the impulse burst occurs exactly once in every 8th OFDM symbol. We want to emphasize that this is a worst-case assumption since almost all IN occurs much less frequently. We choose the Cook pulse [16] to model the pulse amplitude and the pulse duration, see Fig. 4.1.

-40 -30 -20 -10 0 10 20 30 40 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 Time (us) Im pu ls e Vol tag e ( V )

domain representation of the test pulse sampled

Figure 4.1: The Cook pulse (An impulse noise model).

The received signal r(n) can be expressed as

r(n) = s(n) ⊗ h(n) + w(n) + i(n) (4.2)

4.3

Impulse noise detection

To recover data samples corrupted by IN, the receiver has to be able to determine which samples are IN-corrupted, i.e. to determine if there was an impulse noise in current symbol, and, if yes, to locate its position. The energy detector, also known as radiometer (for detecting the presence of signal or interference), is perhaps the simplest yet efficient algorithm to detect the presence of IN. The sliding window version of the energy detector determines that the IN-corrupted range is [ls, le] where

ls= min l l : l+L−1
k=l yk2 > Υ ! , le= max l l : l
k=l−L+1 yk2 > Υ ! . (4.3)

where L is the mean IN duration.

The simplest way to determine IN location is given by

ip(n) =



1, if r(n) ≥ A0,

0, otherwise (4.4)

where ip(n) is the IN indicator function, i.e., it is nonzero and equal to 1 only if the nth

sample is interfered by IN and A0 is a properly selected threshold. To determine if IN

is present in the mth OFDM symbol we use the channel state indicator CSI(m)

CSI(m) = 1, if

_{(m+1)(N +N}g)−1

n=m(N +Ng)+Ngip(n) ≥ A1,

0, otherwise (4.5)

where A1 is the threshold. (4.3) is more complex than (4.4) but properly outperforms

the latter as it has more parameters for optimization.

4.4

Blanking method

IN-corrupted data samples are very difficult to recover using any conventional ap-proach because of the large noise magnitude. Thus, it is beneficial to blank [13] the IN-corrupted zone, i.e. the sample values within that zone are set to zero. Even with-out further processing the blanking alone reduces the distortion caused by IN if the IN detection is perfect. In other words, the advantage of blanking method is replacing the