Chapter 1 Introduction

Transcription

1 Chapter 1 Introduction 1.1 Overview of Digital TV Broadcasting Recently, Digital television (DTV) systems are going to replace traditional analogue television system because of the fast growing of VLSI technology, information technology and transmission technology. Different from traditional television system, digital television has more advantages, such as better bandwidth efficiency, lower disturbance and high-definition in signal transmission. Digital television systems can provide a HDTV (High Definition TV) program or four to six SDTV (Standard TV) programs by using digital compression in the same traditional channel bandwidth (6MHz). Digital television system also can eliminate some phenomenon such as ghosting, snow and static noise in audio. Therefore, digital television systems provide a high quality image and sound for consumers. Many standards for digital television broadcasting are proposed in the last few years, such as DVB-T [1] (Digital Video Broadcasting-Terrestrial, Europe), ATSC [2] (Advanced Television System Committee, USA), ISDB-T [3] (Integrated Services Digital Broadcasting-Terrestrial, Japan). These standards were recognized by ITU (International Telecommunication Union). Then, the standard DVB-H [4] (Digital Video Broadcasting-Handheld) for portable device such as mobile phone and mobile television system was proposed by European Telecommunication Standard Institute (ESTI). Finally, standard T-DMB [5] (Terrestrial Digital Multimedia Broadcasting) for handheld system has been proposed and put into use in number of countries. Table. 1.1 shows the comparison of there standards. 1

2 Table. 1.1 Comparisons of different broadcasting standards Standard DVB-T/H ATSC ISDB-T T-DMB Modulation COFDM 8-VSB COFDM COFDM Video MPEG-2 MPEG-2 MPEG-2 H.264 Audio ACC AC-3 ACC BSAC Bandwidth 5/6/7/8MHz 6MHz 6MHz 1.5MHz 1.2 DTV System in Taiwan - DVB-T/H In Taiwan, though ATSC has once adopted as the DTV standard in 1998, due to the effort of CTV (China Television), PTS (Public Television Service), FTV (Formosa Television), TTC (Telecom Technology Center) and CTS (Chinese Television System), DVB-T was finally adopted as the standard in The standard DVB-H was also adopted as mobile television standard in In 2005, DTV system was broadcasting in west Taiwan and the proposal E-Taiwan plans to retrieve analog channel in 2006, moreover, TV broadcasting will become all in digital in 2010[6][7]. Digital Video Broadcasting (DVB) was published by Joint Technical Committee (JTC) of European Telecommunication Standard Institute (ESTI), European Committee for Electrotechnical Standardization (CENELEC) and European Broadcasting Union (EBU). DVB family includes DVB-S (Satellite) [3], DVB-C (Cable) [4], DVB-T (Terrestrial) [1] and DVB-H (Handheld) [2]. DVB-T was published in 1997 with COFDM (Coded Orthogonal Frequency Division Multiplexing) transmission technique. Now there are many countries, such as UK, Germany, Norway, Australia, South Africa, India and Taiwan use DVB-T as their DTV transmission standard. Though DVB-T can be applied in mobile environment, the power consumption is not good enough for portable devices. As a result, DVB-H was proposed for low power design and adopted for portable devices. 2

3 1.3 Motivation Since the government of Taiwan adopted DVB-T as DTV standard and decides to revoke all analog channels in 2010, DVB-T products have become a very hot research topic. Some products on market are based on DSP and others on ASIC [8]~[11]. At next few years, digital television broadcasting on handheld device must be the main stream. Thus, a high speed mobile version must be proposed. Since the signal will be transmitted in high speed mobile environment, the design of channel estimation must be more robust to conquer the variation of channel. As many recently proposed communication systems such as ADSL (Asymmetric Digital Subscriber Line), DAB (Digital Audio Broadcasting) and WLAN (Wireless Local Area Network), DVB-T/H also uses OFDM technology. The benefits of OFDM includes high spectrum efficient by orthogonal technology, ability to against multipath interference (Fading) by inserting guard interval and cyclic prefix and can be transmitted in single frequency network (SFN). However, time-variant channel will be a serious problem in handheld systems. It will cause the distortion of the signal. In broadcasting environment, DVB-T/H must solve this problem. Thus, channel estimation is an important part of the receiver. The variation of the channel will cause the distortion and the data information will be destroyed. Traditional channel estimation methods [11][12][15] is too simple to deal with the variation of the channel. The inter-carrier-interference (ICI) will be more serious in mobile environment, so how to solve ICI by channel estimation becomes more important. Many sophisticated channel estimation algorithms [13][14][15] are proposed to deal with channel estimation in mobile environment for DVB. However, their complexities are too high to be implemented in hand held systems. In this thesis, several channel estimation methods are overviewed and their performance are compared. Then, this thesis proposes an Pre-Decision (PD) algorithm and architecture of channel estimation to estimate the time-variation channel. This algorithm can reduce the computation of the 3

4 traditional channel estimation methods and the estimated channel response is more accurate and robust as is compared to other traditional 1-D or 2-D interpolated channel estimation methods. 1.4 Thesis Organization This thesis is organized as follows. In Chapter 2, OFDM will be introduced briefly and DVB- T/H technology will be discussed. Chapter 3 describes the channel estimation algorithms and the proposed PD algorithm. Moreover, performance analysis simulation results and architectures for channel estimation algorithms will be compared. Hardware architecture design of PD channel estimation algorithm and equalizer will be discussed in Chapter 4. The conclusions and future works will be presented in Chapter 5. 4

5 Chapter 2 OFDM and DVB-T/H Technology 2.1 Concept of OFDM System In this chapter, we will introduce OFDM and DVB-T/H system with special emphasis on baseband receiver. Many of the works are referenced from [14]. Frequency division multiplexing (FDM) haz been published in mid 60s. In FDM, multiple signals are sent at the same time with different sub-channels. OFDM is one kind of FDM, for more bandwidth efficiency, OFDM use orthogonal technique to overlap the sub-channels thus OFDM can sent more information with the same bandwidth. Fig. 2.1 and Fig. 2.2 show the sub-channels in FDM and OFDM. Fig. 2.1 Sub-channels in FDM modulation Fig. 2.2 Sub-channels in OFDM modulation[14] COFDM is an alternative of OFDM, OFDM with channel coding is called COFDM (Coded OFDM) which is adopted by DVB-T. COFDM may reduce the ICI (Inter-Carrier-Interference) and ISI (Inter-Symbol-Interference) by guard interval (GI) insertion. GI is the copy of the last period of 5

6 the current OFDM symbol. GI is inserted between two successive OFDM symbol to prevent the damage caused by multipath effect. Since the multipath effect will cause the ISI phenomenon, for current OFDM symbol, the other sub-paths will cause the inaccuracy of symbol detection. With inaccurate symbol detection, system may find a wrong symbol boundary which may allocate near the exact one. Finding accurate boundary in multipath environment is difficult. Thus, system must tolerate to the inaccurate symbol boundary location. Therefore, the copy of the last period of the current symbol is inserted as the guard interval between two successive symbols. By using this characteristic, the detected boundary which locates before the correct one is able to decode correctly. According to OFDM mathematical function, the transmitted pattern looks like a cyclic shift and the orthogonality of sub-carriers will not be destroyed but only cause a phase rotation. But if the detected boundary locates after the correct one, the orthogonality of the sub-carriers will be destroyed and lead to a wrong decoded answer. The received symbols with multipath effect are shown in Fig = Fig. 2.3 Received OFDM symbols with multipath effect[14] 6

7 2.2 DVB-T/H Technology MPEG-2 Source Coding and Multiplexing As described in Section 2.1, DVB-T/H is the broadcasting system based on OFDM modulation technology. In general, DVB-T/H system can be divided into two parts, transmitter and receiver. Fig. 2.4 shows a DVB-T/H transmitter system block diagram which. MPEG-2 source coding and multiplexing multiplex video, audio and data into an MPEG-2 program stream. Fig. 2.4 Functional block diagram of DVB-T transmission system[14] Channel Coding The channel coding of DVB-T/H system includes the randomizer, inner coder, outer coder, inner interleaver and outer interleaver. The MPEG-2 transport stream will be separated into highpriority (real line in Fig. 2.4) and low-priority (dotted line in Fig. 2.4). Therefore, in a small size monitor or weak signal environment, the receiver can switch a HDTV program into a SDTV program. The MPEG-2 transport stream is organized as fixed length packets (118 bytes) and decorrelated by the block MUX adaptation and energy dispersal. Because the MPEG-2 Transport Stream have a probability to be long 1 or 0 sequences, the synchronization may have some problem. The Exclusive-OR operation with PRBS sequence can efficiently make the energy dispersal and 7

8 make the MPEG-2 Transport Stream sequences random. Fig. 2.5 shows the energy dispersal schematic diagram. Initialization Sequence Enable Clear/randomized data input Data input (MSB first): xxxxxxxx PRBS sequence: Randomized/de -randomized data output Fig. 2.5 Scrambler/descrambler schematic diagram[14] DVB-T uses the nonbinary block coder, Reed-Solomon RS (240, 188, t=8) shorten code, as the outer coder, which have an ability to correct eight errors with the generator polynomial shown in the Eqn. (2.1) p( x) = x + x + x + x (2.1) To avoid to the long sequences of errors, a convolutional byte-wise interleaving with depth I=12 is applied to make the transmitted data sequence being robust to the burst errors. While the data is transmitted in the air, a suddenly short period interference may occur which caused by some known or unknown reasons.as above section described, RS coder is able to correct eight errors most. But sometimes the interference may lead to more than eight errors in a RS package and are unable to be corrected. By using the outer interleaver to interleave the data in a symbol to other symbols may reduce the probability of the burst error. Fig. (2.6) shows the conceptual diagram of the outer interleaver and deinterleaver. 8

9 byte per position =M byte per position =M =I =I-1 FIFO shift register Outer Interleaver Outer Deinterleaver Sync bytes always passes through branch 0 Fig. 2.6 Conceptual diagram of the outer interleaver and deinterleaver[14] To have better Bit-Error-Rate (BER), a punctured convolutional encoder is cascaded,and there are five valid coding rates: 1/2, 2/3, 3/4, 5/6, and 7/8. Higher coding rate means worse performance but higher data carrying ability. Fig. 2.7 shows an example of 1/2 coding rate which means one of toe bits is useful. Fig. 2.7 The mother convolution code of rate 1/2[14] errors. Finally, a block based bit-wise inner interleaver is used to against the Viterbi output burst 9

10 2.2.3 Mapper & Frame After data is coded by two level encoder, all carriers including data and pilots in an OFDM symbol are mapped onto QPSK, 16-QAM, 64-QAM, non-uniform 16-QAM or non-uniform 64- QAM by the mapper. DVB-T/H provides three transmission mode as 2K mode, 4K mode and 8K mode. 4K mode is specially provided in DVB-H. In DVB-T/H, each valid frame consists of 68 OFDM symbols and the scattered pilot cells, continual pilots sub-carriers and TPS sub-carriers are also contained. Four frames constitute one super-frame Reference Signals The pilots cell as scattered pilots, continual pilots and TPS carriers are called Reference signals. These three type reference signals are inserted in all OFDM symbols. Generally, scattered pilots are inserted in unfixed positions, but the continual pilots and TPS carriers are inserted in fixed positions. Eqn. (2.2) shows the mathematical representation of the scattered pilot positions. { k = Kmin + 3 ( l mod 4} + 12 p p integer, p 0, k [ Kmin; Kmax] (2.2) Where k is the frequency index of the sub-carriers and l is the time index of the symbols. Obviously, the location of scattered pilot cell will repeat every four symbol. And K max will be different with different transmission mode. Eqn. (2.3) shows how to generate scattered pilot cells value. Re{ c Im{ c m, l, k m, l, k } = 4/3 2(1/ 2 w } = 0 where w k is the k th data generated by PRBS. k ) (2.3) Fig. (2.8) shows the distribution of scattered pilots. Because of the regular fixed located characteristic, channel estimation can use these scattered pilots to extract channel information. And the channel response can be computed by using time interpolation and frequency interpolation. 10

11 Time (Symbol Index) Fig. 2.8 Distribution of scattered pilots Table 2.1 shows the locations of the continual pilots. The values of continual pilots are also generated by PRBS as Eqn. (2.3) shows. The main function of continual pilots is to track carrier frequency offset. 11

12 Table 2.1 Continual pilot carrier position Continual Pilot Indices for Continual Pilot Carriers 2K mode K mode K mode TPS pilots is important in DVB-T/H when transmission. Because there is not any handshaking operation before communication. TPS pilots have 68 different messages in a frame and the messages are shown in Table

13 Table 2.2 TPS signaling information and format Bit Number Purpose/Content S0 Initialization S1 ~ S16 Synchronization word S17 ~ S22 Length indicator S23, S24 Frame number S25, S26 Constellation S27, S28, S29 Hierarchy information S30, S31, S32 Code rate, HP stream S33, S34, S35 Code rate, LP stream S36, S37 Guard interval S38, S39 Transmission mode S40 ~ S47 Cell identifier S48 ~ S53 Reserved S54 ~ S67 Error protection DVB-H For handheld devices, time slicing technology is employed to reduce power consumption. For the purpose to improve the system performance in mobile environment, forward error correction for multiprotocol encapsulated data (MPE-FEC) is adopted with powerful channeling and time interleaving. Since 8K mode has better performance in large single frequency network (SFN) but worse in against Doppler Effect and 2K mode has better performance in against Doppler Effect but not suitable for large SFN, a comprised 4k mode is proposed. Overall, the specification of DVB- T/H is listed in Table

14 Table 2.3 Specification of DVB-T/H Transmission mode 2K, 4K, 8K Number of useful sub-carriers 1705, 3409, 6817 Number of continual pilots 45, 89, 177 Number of scattered pilots 141, 282, 564 Number of TPS pilots 17, 34, 68 Radio frequency (MHz) 45~860 Guard interval 1/4, 1/8, 1/16, 1/32 Bandwidth (MHz) 5, 6, 7, 8 Elementary period (us) 7/40, 7/48, 7/56, 7/64 Channel model Rayleigh, Ricean Forward error correct Convolution code with puncturing Reed Solomon Code (204,188) QPSK, 16QAM, 64QAM, Constellation non-uniform 16QAM, non-uniform 16QAM Required BER after Viterbi decoder Quasi Error Free after Reed Solomon 14

15 Chapter 3 Channel Estimation Algorithm This chapter will focus on channel estimation issue. After the scattered pilot synchronization (SPS) process, which is also called scattered pilot mode detection, channel estimation block collects the scattered pilots and using these values to estimate the channel response. The channel response estimation algorithms by using the scattered pilots will be discussed in this chapter. Finally, a division-free equalizer and three-stage demapping hybrid architecture will be described. 3.1 Pilot-based OFDM System Fig. 3.1 shows the baseband model of a typical pilot-based OFDM system. After the pilots are inserted, the data {X(k)} are modulated and sent to an IFFT and are transformed and multiplexed into {x(n)} as Eqn. (3.1) shows: N 1 x(n) = X(k)e j 2πkn / N,n = 0,1,,...,N 1 (3.1) k= 0 where N is the number of sub-carriers. After guard interval insertion the signals x g (n) can be expressed as Eqn. (3.2). Fig. 3.1 Typical baseband model of OFDM system 15

16 x( N + n), n = L, L 1,..., 1 x g ( n) = (3.2) x( n), n = 0,1,2,..., N 1 where L is the number of samples in the guard interval. The transmitted signal may pass through the frequency selective multi-path fading channel and the received signal can be expressed as: yg ( n) = xg ( n) h( n) + w( n) (3.3) where X denotes convolution, h(n) is the impulse response of the channel and w(n) is the additive white Gaussian noise. After removing the guard interval from y g (n), the received samples y(n) are sent to DFT. The multi-carrier signals can be expressed as: Y ( k) = DFT 1 N 1 { } y( n) = N n= 0 y( n) e j 2πkn/ N, k = 0,1,..., N 1 By selecting suitable guard interval ratio of a symbol, the inter symbol interference (ISI) from OFDM symbols. The demultiplexed samples Y(k) can be expressed as: Y(k) = X(k)H(k) + I(k) + W (k),k = 0,1,...,N 1 (3.5) where W(k) is the Fourier transform of w(n) and I(k) is the Fourier transform of ISI. After FFT, the pilot signals Y p (k) can be extracted from the received signal Y(k) and the channel transfer function H(k) can be also obtained from H p (k). The relationship of transmitted data and channel response may be written as: Y ( k) X ( k) =, k = 0,1,..., N 1 (3.6) H ( k) where H ˆ ( k ) is an estimated value of H(k). Eqn. (3.6) describes one of the major function of FEQ system. If we get the channel response of each sub-carrier, then the source binary information data can be reconstructed after signal demapping. (3.4) From the DVB-T/H Standard, the location of pilot signals can be known exactly as shown in Fig Fig. 3.3 shows the channel estimation operation with pilot signals. 16

17 Time (Symbol Index) Fig. 3.2 Pilot signal location of DVB-T/H Fig. 3.3 Channel estimation operation with pilot signals Assume that N p is the pilot number, then the pilot signals X p (m), m=0, 1, 2,, N p-1, are uniformly inserted into {X(k)}. The frequency interval between each pilot signal is usually the same. Assume L-1 is the number of the sub-carriers between two pilot signals, the OFDM signal modulated on the k th sub-carrier can be expressed as: X(k) = X(mL + d) = X p (m),for d = 0 information data,for d =1, 2,..., L 1 (3.7) where d is the sub-carrier number with data information between two pilot signals. The channel response and received data can be expressed as a vector as shown in Eqn. (3.8), Eqn. (3.9) and Eqn. (3.10). 17

18 H p = [ H p (0)H p (1)LH p (N p 1) ] T = [ H(0)H(L)H(2L)LH((N p 1)L) ] T (3.8) Y p = [ Y p (0)Y p (1)LY p (N p 1) ] T (3.9) Y p = X p H p + I p + W p (3.10) where I p is the vector of ICI and W p is the vector of Gaussian noise in pilot signals. In conventional comb-type pilot based channel estimation algorithm, the estimated values of pilot H LS,p signals based on least squares (LS) criterion is given by Eqn. (3.11). [ ] T = X 1 p Y p = Y (0) p H LS,p = H LS,p (0)H LS,p (1)...H LS,p (N p 1) X p (0) Y p (1) X p (1)... Y (N 1) p p X p (N p 1) T (3.11) The LS estimated value of H p is susceptible to Gaussian noise and inter-carrier interference (ICI). By interpolation, the channel response of data sub-carriers H can be obtained. 3.2 Piecewise Interpolation As in the previous sections, the channel response can be obtained from pilot signals. The unknown channel response at data sub-carriers can be approximated by using the known informations of pilot signals through mathematical processing. Piecewise interpolation is one of these processing methods. There are several types of interpolation that may approximate the channel response, such as linear inner interpolation, Gaussian estimation, Cub-Spline estimation and Parabolic estimation, etc[13]. The general piecewise interpolation can be expressed as: M f k H ( k) = Qi ( ) H p( m + i) (3.12) L i= M f where L is the intervals between each pilot signal, k is the index of the data sub-carriers between two pilot signals and Q i (k/l) is the coefficient of the piecewise interpolation. In different 18

19 interpolations, Q i (k/l) will be different. The parameters M i and M f decide the number of the coefficients Q i. The number of Q i means the number of the reference pilots signals when we do interpolation Linear Inner Interpolation The piecewise interpolation of linear inner interpolation can be written as: k k H ( k) = Q0 ( ) H p ( m) + Q1 ( ) H p( m + 1) (3.13) L L where Q 0 (k/l)=1-k/l and Q 1 (k/l)=k/l. Two reference pilot signals are used in linear inner interpolation. Thus, the linear inner interpolation can be expressed as: H (k) = (1 k L )H p(m) + ( k L )H p (m + 1) (3.14) Gaussian Estimation Gaussian Estimation is also called as Gaussian n th order estimation. The solution can be expressed as n th order polynomial, but the computation burden will generally increase by orders. In this section, Gaussian second order estimation will be discussed. The piecewise linear interpolation of Gaussian Estimation can be expressed as Eqn. (3.15). H (k) = Q 1 ( k L )H p(m 1) + Q 0 ( k L )H p(m) + Q 1 ( k L )H p (m + 1) (3.15) where the Q -1 (k/l), Q 0 (k/l) and Q 1 (k/l) are independent coefficients of the three pilot signals, and the values are determined by the distance between the locations of these pilot signals. The values of these coefficients can be expressed as: 19

20 Q 1 ( k L ) = k 2L ( k L 1) Q 0 ( k L ) = ( k L +1)( k L 1) (3.16) Notice that only L an k can effect these coefficients, it means that these coefficients are independent to each other. Q 1 ( k L ) = k 2L ( k L 1) Cubic-Spline Estimation In previous section, It is observed that Piecewise Linear Estimation is an first order interpolation which needs two reference pilot signals and two coefficients. Gaussian Estimation is a second order interpolation which needs three reference pilot signals and three coefficients. The Cubic-Spline Estimation is a third order interpolation, such that it may be expected that Cubic- Spline Estimation needs four reference pilot signals and four coefficients. The Cubic-Spline Estimation can be expressed as: H (k) = Q 1 ( k L )H p(m 1) + Q 0 ( k L )H p(m) + Q 1 ( k L )H p(m +1) + Q 2 ( k L )H p (m + 2) (3.17) Assume that k/l is u, the coefficients can be expressed as: Q 1 (μ) = ( μ 3 ) + (μ2 2 ) (μ3 6 ) Q 0 (μ) =1 ( μ 2 ) (μ2 ) ( μ3 2 ) Q 1 (μ) = μ + ( μ2 2 ) (μ3 2 ) (3.18) Parabolic Estimation Q 2 (μ) = ( μ 6 ) + (μ3 6 ) Parabolic Estimation is similar to Cubic-Spline Estimation. These two estimation are both four order interpolation and the reference pilot signals are all the same. The only difference between 20

21 them are the coefficients. Parabolic Estimation can be expressed as: H (k) = Q 1 ( k L )H p(m 1) + Q 0 ( k L )H p(m) + Q 1 ( k L )H p(m +1) + Q 2 ( k L )H p (m + 2) (3.19) Assume that k/l is u and the coefficients can be expressed as: Q 1 (μ) = ( μ 2 ) + (μ2 2 ) Q 0 (μ) = 1 ( μ 2 ) (μ2 2 ) Q 1 (μ) = ( μ2 2 ) + (μ3 2 ) (3.20) Notice that the difference of the coefficients between Cubic-Spline and Parabolic Estimation are not only the different value, but also the difference of the order of u. It means that the computation of Cubic-Spline Estimation is more complex than Parabolic Estimation in the same SNR. Q 2 (μ) = ( μ 2 ) + (μ2 2 ) 3.3 Frequency Domain Channel Estimation The frequency domain channel estimation is aimed at estimating both the channel response and phase error due to symbol timing offset by using the inserted scattered pilots. In this section, three basic channel estimation algorithms, 1-D channel estimation, 2-D channel estimation, 2-D predictive channel estimation, will be discussed and compared. The basic idea of channel estimation is to use the known value of inserted scattered pilots to estimate the channel responses. Three basic channel estimation methods will be discussed below. 21

22 D Channel Estimation One dimensional channel estimation algorithm is the simplest of these three algorithms. Since a scattered pilot is inserted every twelve sub-carriers in a symbol, the easiest way to estimate the channel response is to use the two neighboring scattered pilots to linearly interpolate the channel response of the eleven sub-carriers between them(1-d_1)[15] as Fig. 3.3 shows. Unfortunately, the variation in frequency response is very serious and eleven sub-carriers space is too large to have an accurate approximation. The scattered pilots have three spaces shift for each successive symbol. Due to this characteristic, the space of two neighboring scattered pilots will reduce to two by collecting the scattered pilots of four successive symbols(1-d_2)[14]. This method supposes the time domain variation during four symbols is very small or even none. As Fig. 3.4 illustrates, the n th symbol collects the scattered pilots from the (n-3) th to nth symbols and uses frequency domain linear interpolation operation to approximate the channel response in the middle of the two scattered pilots. For the purpose to reduce the hardware complexity, linear interpolation is adopted as frequency domain interpolation. Channel Response Scattered or continuous pilot Data sub-carrier Virtual pilot Frequency (Sub-carrier Index) Channel Response Scattered or continuous pilot Data sub-carrier Virtual pilot Frequency (Sub-carrier Index) Fig D_1 frequency domain channel estimation using linear interpolation 22

23 Time (Symbol Index) symbol n-3 symbol n-2 symbol n-1 symbol n Scattered or continuous pilot Data sub-carrier Virtual pilot Frequency (Sub-carrier Index) Fig. 3.4 Frequency domain linear interpolation of 1-D_2 channel estimation by collecting scattered pilots of 4 successive symbols The 1-D channel estimation is described mathematically in Eqn. (3.21). SC( n, m) CR( n, m) = SC ( m) exp SC( n 3, m + 3) CR( n, m + 3) = SC ( m + 3) exp SC( n 2, m + 6) CR( n, m + 6) = SC ( m + 6) exp SC( n 1, m + 9) CR( n, m + 9) = SC ( m + 9) exp (3.21) where CR(n,m) is the m th channel response in symbol n, SC(n,m) belongs to scattered pilots and SC exp (m) is the m th expect value. The method shown in Fig. 3.4 comes with a risk. If the channel response in time domain changes serious or not as small as expected, the scattered pilots which don t belong to current symbol are not adequate to represent the channel response of current symbol. As a result, wrong channel response possibly leads to a worse performance. Therefore, the 1-D channel estimation algorithm only suits for time-invariant channel. The channel response in DVB-H environment varies with time seriously, such that the 1-D channel estimation in DVB-H has a very bad performance. 23

24 Quadratic interpolation is another kind of 1-D channel estimation algorithm which takes three successive (real or virtual) pilots as three points of the quadratic equation, and use quadratic equation to calculate the channel response of those sub-tones between the first and the second pilots. As Fig. 3.5 shows, the curve can be sketched by three points, such that the channel response can be approximated. The calculation of this algorithm is more complex than linear interpolation method, and the performance is also worse than those algorithm. This is because the curve can not be approximated precisely by this way due to the distance of the third pilot is too long to the data subcarrier. Thus the estimated channel response will be inaccurate. For example, the information of the third pilot is useless for those sub-carriers between first pilot and second pilot, and if the information of the third pilot is considered when estimating the channel response of those previous sub-carriers, especially in high speed mobile environment it may be a worse result. Fig. 3.5 Quadratic channel estimation After the implementation and simulation of quadratic channel estimation algorithm, the result shows that the channel response cannot be approximated well. These three points which are taken as the quadratic equation reference points cannot advise the accurate information to the current subcarrier and will lead to a much worse performance than using linear interpolation channel estimation algorithms. Thus, we won t take this algorithm into consideration. Instead of inner interpolation, some intuitive methods can be used to reduce the calculation complexity and large storage element caused by inner interpolation. These methods are used to approximate the channel response after collecting scattered pilots and virtual scattered pilots. 24

25 (a) Look Ahead Channel Estimation Algorithm In 1-D channel estimation algorithms, channel response between two pilots is calculated by inner interpolation. Look ahead channel estimation algorithm just takes the previous pilot value as the channel response at next two sub-tones as Fig. 3.6 shows. In this way, channel response will be estimated more quickly by few computation. But the estimated channel response is more inaccurate and the performance will get worse. Scattered or continuous pilot Data sub-carrier Virtual pilot Frequency (Sub-carrier Index) Fig. 3.6 Look ahead channel estimation (b) Look Back Channel Estimation Algorithm Look back channel estimation algorithm is similar to look ahead channel estimation algorithm. Look back channel estimation algorithm takes next pilot value as the channel response at the previous two sub-tones as shown in Fig

26 Scattered or continuous pilot Data sub-carrier Virtual pilot Frequency (Sub-carrier Index) Fig. 3.7 Look back channel estimation These two channel estimation algorithms can both reduce the calculation of the channel estimation, but the performance of these two algorithms both get worse D Channel Estimation The 2-D channel estimation algorithm[14] will take the time domain variation into consideration. In order to conquer the variation in time domain, 2-D channel estimation(2-d_i) uses the scattered pilots before and after the current symbol to interpolate a virtual scatter pilot of current symbol instead of collecting scattered pilots from the other three previous symbols. As Fig. 3.8 shows, the 2-D channel estimation first collects the scattered pilots from seven continuous symbols and does time domain linear interpolation to approximate the virtual scattered pilots. Then it uses the virtual scattered pilots and scattered pilots to do frequency domain interpolation. When the channel response roughly changes linearly during continuous five symbols, the 2-D channel estimation algorithm will get a better performance. But the 2-D channel estimation method needs to store the sub-carriers at least three symbols before and after to get enough scattered pilots to do time domain interpolation. This means a large storage element is requires, which is at least subcarriers for 8K transmission mode. If the channel varies seriously in five symbol spaces, 2-D 26

27 channel estimation algorithm will not get better, especially in high speed mobile environment. Time (Symbol Index) (a) Channel Response Channel Response Channel Response (b) (c) Fig. 3.8 (a) 2-D channel estimation and (b) time domain linear interpolation of 2-D_I and (c) Frequency domain linear interpolation of 2-D channel estimation 27

28 The 2-D channel estimation can be described mathematically as shown in Eqn SC( n, m) CR( n, m) = SC ( m) exp SC( n 3, m + 3) 1+ SC( n + 1, m + 3) 3 CR( n, m + 3) = 4 SC ( m + 3) SC( n 2, m + 6) 2 + SC( n + 2, m + 6) 2 CR( n, m + 6) = 4 SC ( m + 6) SC( n 1, m + 9) 3 + SC( n + 3, m + 9) 1 CR( n, m + 9) = 4 SC ( m + 9) exp exp exp (3.24) D Predictive Channel Estimation For the purpose to solve the requirement of huge storage memories and keep the characteristic to conquer the time domain variation at the same time, a predictive 2-D channel estimation(2-d_p) algorithm is offered by using time domain external interpolation instead of inner interpolation [12]. The 2-D predictive channel estimation uses two scattered pilots before current symbol and doing external interpolation to predict the channel response of current symbol as shown in Fig. 3.12, Fig and Fig As a result, the storage element for three symbols sub-carriers is saved and an extra storage element for scattered pilots is required. Comparing to the sub-carriers storage element, the storage element for additional scattered pilots is much smaller. But the predictive external time domain interpolation won t work as good as inner time domain interpolation because of the uncertain of prediction. Due to this reason, the 2-D predictive channel estimation is not as good as 2-D channel estimation but better than 1-D channel estimation in time-variant channel. 28

29 K min =0 K max =1704 if 2K K max =3408 if 4K K max =6816 if 8K Time (Symbol Index) symbol n-7 symbol n-6 symbol n-5 symbol n-4 symbol n-3 symbol n-2 symbol n-1 symbol n Scattered or continuous pilot Data sub-carrier Virtual pilot Frequency (Sub-carrier Index) (a) (b) (c) Fig. 3.9 (a) 2-D predictive channel estimation, (b) time domain linear interpolation and (c) frequency domain linear interpolation 29

30 D Middle Point Channel Estimation In this section, 2-D middle point(2-d_m) channel estimation is proposed. 2-D_M channel estimation is the combination of look ahead channel estimation and look back channel estimation. 2-D_M channel estimation use two scattered pilots to estimate the channel response of the current symbol. As Fig shows, the first virtual pilot is estimated by using look ahead algorithm and the third virtual pilot is estimated by using look back algorithm. The second virtual pilot is the average value of those two scattered pilots. 2-D_M channel estimation algorithm can save some storage element and maintain the performance. K min =0 K max =1704 if 2K K max =3408 if 4K K max =6816 if 8K Time (Symbol Index) symbol n-3 symbol n-2 symbol n-1 symbol n symbol n+1 symbol n+2 symbol n+3 Scattered or continuous pilot Data sub-carrier Virtual pilot Frequency (Sub-carrier Index) (a) Channel Response Channel Response Channel Response Time (Symbol Index) Scattered or continuous pilot Data sub-carrier Virtual pilot Time (Symbol Index) Time (Symbol Index) (b) 30

31 (c) Fig (a) 2-D middle point channel estimation, (b) time domain linear interpolation and (c) frequency domain linear interpolation Because these channel estimation algorithms discussed in this section cannot estimate the channel response precisely in high speed mobile environment, a proposed channel estimation algorithm will be described in next section. To reduce the the Doppler effect caused by high speed environment, a concept called Pre-Decision will be introduced and used in channel estimation. 3.4 Pre-Decision Algorithm 2-D channel estimation algorithms described in section 3.3 is in the most common use one. However, the hardware cost, especially the storage unit of 2-D channel estimation is higher than other algorithms. But the performance of 2-D channel estimation algorithm will be terrible in the high mobile environment because the inter-carrier interference (ICI) will be very serious in that environment. Pre-Decision(PD) algorithm is proposed to reduce the inaccuracy when determining the virtual pilots. This section will discuss the Pre-Decision algorithm and the applications on channel estimation algorithms. 31

32 3.4.1 Pre-Decision Algorithm Fig Pre-Decision algorithm block diagram for channel estimation Fig is the block diagram of Pre-Decision algorithm, the block Time Domain Channel Response Computation is used to detect the sub-carrier mode (2K, 4K or 8K) and compute the channel response at time domain by using inner interpolation or outer interpolation. Sub-carrier mode detection is like guard interval mode detection. The power of the pilot is higher than the other sub-carriers, such that the positions of those pilots can be found and the mode can be detected after autocorrelation. When mode detection is done, the channel response at time direction can be computed by inner interpolation or outer interpolation. Fig Function block diagram of Pre-Decision algorithm As Fig shows, the block Pre-Decision includes five sub-blocks, the first sub-block is Response/Data Transform which is used to calculate the data vector (24 bits, real part 12 bits and imagine part 12 bits) of these virtual pilots from the channel response. After response/data transform, the data vector will be sent to the second sub-block Hard Demapper [14]. Hard demapper is used to define the QAM vector (6 bits) of each virtual pilot by using the data vector. In fact, the function of this sub-block is to do error correction. This is because all the data vectors are 32

33 mapped on the QAM constellation and transmitted from transmitter to receiver. Then the channel effect will cause distortion on the data. Thus, we can observe the error of each virtual pilot on the QAM constellation as shown in Fig The function of hard demapper can be described as Eqn. (3.25). After hard decision, the error can be cancelled and a decided QAM vector (6 bits) is sent to the third sub-block. Fig Error correction of Pre-decision algorithm i Pre Decision = arg min( distance( QAM ( i), Xˆ ( n distance( QAM ( i), Xˆ ( n X Pre Decision ( n p, m i p p, m p ) = QAM ( i )) = Pre Decision ( QAM ( i) Xˆ ( n ) p, m p ))) p, m p ))( QAM ( i) Xˆ ( n p, m p )) * (3.25) where QAM(i) is the QAM point of those 64 possible value on the constellation map, and i is the index of the QAM point. X Pre-Decision (n p,m p ) is the estimated virtual pilot. And the subscript p is the position index of virtual pilot. The third block is Pre-Decision Vector Decoder which is used to compute the data vector (24 bits, real part 12 bits and imagine part 12 bits) of virtual pilot after decision. Then the data vector will be sent to the fourth sub-block. The fourth sub-block is Data/Response Transform which is used to calculate the new channel response. The operation of Data/Response Transform 33

34 is similar to the Response/Data Transform sub-block and the function of these two sub-blocks are both division. After these four operations, the new channel response can be computed and will be sent to the fifth sub-block Stop-And-Go (SAG). The fifth sub-block SAG is used to reduce the penalty when wrong decision is made. We can observe that if the estimated virtual pilot is near the correct QAM point, the hard demapper can refine the correct value of the virtual pilot, then the error between the estimated virtual pilots and QAM point can be used to correct the estimated channel response. In the other hand, if the estimated virtual pilot is located in the area that results in wrong QAM value, the channel estimation error will be increased and the result will be worse. As Fig shows, the virtual pilot may be near the edge between two QAM regions. Then the wrong decision is possibly made in this case. Thus, we define a danger area between two successive QAM regions. If the data vector is located in the danger area, the new channel response will not be adopted and the original channel response will be sent to the next block. Then the penalty when wrong decision is made can be reduced. Fig Danger area for Stop-Ang-Go scheme After the Pre-Decision process, the new channel response are sent to the block Frequency Domain Channel Response Computation to compute the new frequency domain channel response. Pre-Decision algorithm may increase the accuracy when the virtual pilot is calculated and this 34

35 algorithm can be used in different channel estimation algorithm. In the next sections, we will discuss how Pre-Decision algorithm is applied in other channel estimation algorithms Pre-Decision Algorithm with 1-D Channel Estimation Fig (a) shows the channel response in frequency domain and (b) shows the channel response in time domain. (a) (b) Fig (a) Channel response in frequency domain and (b) channel response in time domain 1-D Channel Estimation is the simplest way to estimate the channel response, but the 35

36 performance is the worst. We use Matlab software to simulate the performance. The simulation environment is 2K transmission mode symbols with 1/4 guard interval, zero CFO, and surviving from Rayleigh channel with 70 Hz Doppler spread. Fig shows the comparison between 1-D _1 channel estimation and 1-D_1 channel estimation with PD algorithm. In order to compare the difference between two algorithms, we choose the 100th sub-carrier to observe the time domain variation of channel. Even though the original virtual pilots can be replaced by the new virtual pilots, the improvement is limited because the estimated virtual pilots are almost located in danger area or near the wrong QAM point. (a) (b) Fig (a) 1-D channel estimation and (b) 1-D channel estimation with PD algorithm 36

37 3.4.3 Pre-Decision Algorithm with 2-D Channel Estimation Fig shows the channel response estimated by 2-D channel estimation with Pre-Decision. After applying Pre-Decision, many errors can be reduced by slicer, and the estimated channel response is more accurate. (a) (b) Fig (a) 2-D_I channel estimation and (b) 2-D_I channel estimation with PD algorithm 37

38 3.4.4 Pre-Decision Algorithm With 2-D Predictive Channel Estimation Fig shows the channel response approximation of 2-D predictive channel estimation without Pre-Decision and with Pre-Decision respectively. Although most error can be reduced by slicer, but some virtual pilots can not be estimated precisely. (a) (b) Fig (a) 2-D_P channel estimation and (b) 2-D_P channel estimation with PD 38

39 3.4.5 Pre-Decision Algorithm with 2-D Middle Point Channel Estimation Fig shows the channel response approximation of 2-D middle point channel estimation without Pre-Decision and with Pre-Decision respectively. Though 2-D middle point channel estimation can reduce the storage element, but the channel response cannot be approximated precisely. Pre-Decision can reduce the error to compensate the disadvantage of 2-D middle point channel estimation. (a) (b) Fig (a) 2-D_M channel estimation and (b) 2-D_M channel estimation with PD 39

40 3.5 Channel Compensation and Demapper Eqn. (3.26) shows the channel compensation theorem, and it needs a divider to eliminate the channel effect. After the channel compensation, the equalized data sub-carriers will be sent to the demapper and the demapper will find out the QAM value of the current data sub-carrier according to the minimum distance between the data sub-carrier and each QAM point on the QAM constellation map. Finally, the equalized and demapped data sub-carrier will be the result. SC( n, m) X ( m) = SC( n, m) = X ( m) CR( m) CR( m) (3.26) Since the divider will cause high cost of hardware design, divider free architecture is preferred as [15] and [16] described. As Eqn. (3.26) shows, the denominator will be multiplied to both sides and X(m) is supposed to be the answer of SC(n,m)/CR(m) which is unknown yet. Because the value of X(m) is one of 64 QAM points, such that X(m) can be replaced by those 64 possible values in constellation map. By finding the minimum distance we can define the most like-hood value of X(m). Then the demapper outputs the demapping result which the point represents. This procedure can be thought as changing the constellation map boundary with a scale which the value is the denominator. In DVB-T/H, the 64 QAM may be applied such that the X(m) has 64 possible value. That means 63 comparators and 64 multipliers are required in this method. Therefore, in [6] a threestage demapping algorithm is proposed to reduce the hardware cost. This algorithm is based on dichotomy method, and X(m) can be found by three times of boundary comparison on constellation map as Fig shows. Therefore, few reference value is needed and the hardware design can be implemented by using three comparators and three multipliers. 40

41 Location region after stage 1 Location region after stage 2 Location region after stage 3 Fig Three-stage Demapper[14] Eqn. (3.27) shows the divider free method in detail. = = SCre( n, m) + isc CR ( m) + icr ( n, m) = X ( m) [ SCre( n. m) + iscim( n. m) ] [ CRre( m) icrim( m) ] [ CRre( m) + iceim( m) ] [ CRre( m) icrim( m) ] [ SC ( n. m) + isc ( n. m) ] [ CR ( m) icr ( m) ] = re CR ( m) 2 + CR ( m) + ix ( m) [ SC ( n. m) + isc ( n. m) ] [ CR ( m) icr ( m) ] re 2 2 [ X ( m) + ix ( m) ] [ CR ( m) + CR ( m) ] re re im im re im im im re im re re re 2 im im ( m) im im (3.27) let F F 1 2 = = [ SC ( n. m) + isc ( n. m) ] [ CR ( m) icr ( m) ] re [ CR ( m) ] 2 + CR ( m) 2 re im im where SC re (n,m) and SC im (n,m) are the real part and image part of SC(n,m) and so do CR xx (m) and X xx (m). There are two ways to cancel the denominator. One is multiplying the denominator to the right side and the other is to multiply the conjugate of the denominator to both numerator and denominator. In the first method, left side becomes a complex number and the right side becomes a complex number multiplication. In the second method, numerator is still a complex number but the denominator becomes an integer number. After moving the integer denominator to the right side, re im 41

42 the operation is finished. This method makes the complex division become two integers division and makes the right side multiply the denominator as a scale. Comparing to the first one, the second operation uses an integer multiplier, which can be simplified by several adders, to scale the constellation map instead of a complex multiplier. 3.6 Performance Simulation And Comparison A benchmark Average Square Error (ASE) is used to determine the accuracy when channel estimation algorithms is used to estimate the channel response. ASE can be described as: ˆ H ASE = E(( H H ) ( H Hˆ )) Ref Ref (3.28) where H Ref is the reference channel response and H is the estimated channel response. The performance simulation results are shown in Fig The simulation environment is 2K transmission mode symbols with 1/4 guard interval, zero CFO, and surviving from Rayleigh channel with 70Hz Doppler spread. We simulate the 100th sub-carrier in all symbols to compare the performance when channel varies in time domain. Under the time variant channel, the 2-D middle point channel estimation algorithm is the worst because 2-D middle point channel estimation has few channel information. If Pre-Decision is added, 2-D middle point channel estimation algorithm is still the worst. Pre-Decision cannot improve 2-D middle point channel estimation very much when the variation of time is too serious because Pre-Decision cannot keep up with the variation of time. In this case, Stop-And-Go scheme will come to work to use the original virtual pilots to estimate new channel response and the improvement won t be as good as 2-D channel estimation. 2-D inner interpolation channel estimation without Pre-Decision can approximate the channel response better than 2-D middle point channel estimation and 2-D outer interpolation channel estimation, such that the error between the reference channel and the estimated channel will be much smaller than 2-D middle point channel estimation and then Pre-Decision can easily correct 42

43 the error and help 2-D channel estimation get better performance. Fig ASE of each algorithm for different SNR The 1-D algorithm theoretically needs to store four symbols scattered pilots. The scattered pilot number is 142/284/568 for 2K/4K/8K as defined in [7]. The (n-3) th symbol s scattered pilots are only used to compensation for the n th symbol and can be overwritten by the n th symbol s scattered pilots after used. Therefore, the maximum scattered pilot storage is reduced from four to three symbol s scattered pilots. The 2-D_I algorithm needs to store additional three symbols pilots, which includes the scattered pilots. Therefore, the 2-D_I algorithm needs to store scattered pilots from the (n-1) th symbol to the (n-3) th symbol and all pilots from the (n) th symbol to the (n+2) th symbol. For 2-D_P algorithm, it only needs to store scattered pilots form the (n-1) th symbol to the (n-7) th symbol and no data pilot is required to be stored. For 2-D_M algorithm, it needs to store the pilots from (n-1) th symbol to (n-3) th symbol and the sub-carriers from (n-1) th symbol to (n-2) th symbols. Overall, the 2-D_I with PD channel estimation has the best performance with an unreasonable large storage elements requirement. The 2-D_P with PD channel estimation has a better performance than 2-D_M with PD channel estimation and 1-D with PD channel estimation under dynamic channel and a little worse performance under static channel. The storage elements required 43