i s f er d
algorithms of the proposed channel e cheme will be introduced. 3 we odified architecture scheme. The simulation result and performance analysis introduce the design methodology, improved archi
This thesis is organ zed a ollows. In chapt stimation s
2, the signal mo els and the detailed In chapter propose the m
will be discussed in chapter 4. Chapter 5 will
tecture of the proposed design and the chip summary of DVB-T/H [28]. Conclusion and future work will be given in chapter 6.
Chapter 2 .
hannel Estimation Algorithms
uce the signal model and the effect of time variant channel in in different categories will be on between developed and the oposed algorithms are also made.
rest in mobile communication research lately. For s, the radio channel is usually frequency selective
me tion of radio channel appears unequal
in b
C
In this chapter, we introd
DVB-T/H system first. The algorithms of channel estimation illustrated in later sections. Some comparison and discussi pr
2.1 Introduction to channel estimation
OFDM is a bandwidth efficient signal scheme for digital communications. In OFDM systems, it has received a lot of inte
wideband mobile communication system
and ti variant. Furthermore, the channel transfer func
oth frequency and time domains. Therefore, a dynamic estimation of the channel is necessary for the demodulation of OFDM signals. In wideband mobile channels, the pilot-based signal correction scheme has been proven a feasible method for OFDM systems.
Most channel estimation methods for OFDM transmission systems have been developed under assumption of a slow fading channel, where the channel transfer function is assumed stationary within one OFDM data block. In practice, the channel transfer function of a wideband radio channel may have significant changes even within one OFDM data block.
Therefore, it is preferable to estimate channel characteristic based on the pilot signals in each individual OFDM data block.
The major goal of channel estimation is to estimate the channel frequency response (CFR)
on the subcarrier. ( )h nl h n t( , ) h ti( ) (n i)
i
δ τ
= =
∑
⋅ − This equation is comprised of the actual channel impulse response (CIR) and the transmission filter. The transmitted signalis 1 1 2 n
channel to be constant during the transmission of one OFDM symbol denoted by ( )h n . l
convolution, and oment, we assume the
Furthermore, when the convolution operation in time domain transfers to frequency domain it
be operation. So the demodula requency domain can
be shown byYl k, = FT y n( ( ))l =Hl k, ⋅Xl k, , and the H is the channel frequency response. l k, l means that it is the lth
comes a multiplication ted data symbol in f F
For time variant channel environments, the CFR will vary as time and frequency. It is ( ( )) N 1 ( ) N
H =FFT h n =
∑
− h n e (2-1)illustrated in ponse will change as time varying because of
the Doppler ef h delay will cause the CFR with selective
Fig.2.1. The channel frequency res fects. Furthermore, the multipat fading in frequency domain.
10
Fig. 2.1 Time variant channel frequency response
The pilot pattern is shown in Fig2.2. In DVB-T pilot carriers are transmitted together with data carriers, so that the channel transfer function is estimated both infrequency and in time. The use of pilots for estimation of the CFR is a main topic of research in OFDM system.
Because of the scatted pilots the interpolation methods are adopted here too [9-11].
In this paper, the channel estimation methods for OFDM systems based on comb-type pilot sub-carrier arrangement are investigated. The channel estimation algorithm based on comb-type pilots is divided into pilot signal estimation and channel interpolation.
2.2 Motivation
OFDM is the most prevalent modulation scheme in modern and future wireless communication systems. However, in mobile reception, a loss of sub-carrier orthogonality due to Doppler spread leads to inter-carrier interference. There are several estimation methods, like Wiener filter [9] and MMSE [12] estimator. Furthermore, there are several ICI cancellation schemes [13]. The complexity of these methods is proportional to the number of adjacent carriers which are used to cancel ICI. Besides, they have an important assumption, that the channel state information (CSI) is known. This assumption is impractical in reality,
Fig. 2.2 Pilot pattern in DVB-T/H systems
especially during mobile environment. Here, we will propose the method which can implement efficiently and realizable methods. In following content, we will introduce the proposed channel estimation scheme.
In this paper we assume that the channel is time variant. Therefore, the channel frequency response (CFR) for present symbol should be obtained independently. The proposed channel estimation method based on pilot signals and transform domain processing is depicted in Fig. 2.3.
2.3 Channel estimator for pilot signal
N(K), we will extract the pilot signal YM(K). The first k
Fig. 2.3 Channel estimation function block diagram
Here we will focus on these three parts. First, the estimator can get the CFR at pilot location, and second, filtering can reduce the noise effect. Finally, we can get the CFR of whole symbol by interpolation methods. The three key points will be discussed in following.
When we receive the receiving data Y
ey point is to get the CFR at pilot location HP(K) by YM(K) and known pilot data XP(K).
We can use LS estimator directly byH kˆ ( )p =Y kM( ) /X kp( ). However, this estimator will be easily affected by noise. To reduce the MSE of the LS estimator, we rely on a filter method based in the LS estimator. In fact, in most slowly variant channel environment, this estimator
can get better im
performa t
channel. In order to red average
if the pilot-based estim α1=1 and α0
1,
l k l
H+ +H
provement [14-16]. We propose an adaptive filter which can get better nce in slowly variant channel, and it will not degrade the performance in fast varian
uce the estimation error, the predicted estimated is a weighted
ate and a previous estimated. The formulation is following (2-2), where
=0 initially. The filter diagram is shown in Fig.2.4.
1 l 1,k lHˆl k, l 1Yl 1,k/Xl 1,k lHl k, , l 1, l [0,1]
Fig. 2.4 The filter diagram
he MSE of the estimate. Furthermore, we
prop
T weights αare chosen in order to minimize the
ose an algorithm to decide the weights. Because of the standard, the scatter pilots is four symbols a cycle, here we use three taps FIR. The formulation becomes to (2-3), and MSE is (2-4).
Under this assumption, the first term in (2-4) will dominant the MSE, so we let coefficient of
the first term
We can find the relationship between So we define the weights
(1 ) So the diagram will become to Fig.2.5.
1, Fig. 2.5 The modified filter diagram
In Fig.2.6 we can find the time-variant CFR at someone sub-carrier in Ricean chan different Doppler effects. CFR will change more seriously as Doppler effects increasing.
1.5
50 100 150 200 250
0 300
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4
symbol number @ time axis CFR at 1st pilot subcarrier
Doppler 0Hz Doppler 10Hz Doppler 30Hz Doppler 70Hz
Fig. 2.6 The time variant CFR at 1 pilot subcarrier with Dopst pler
Fig. 2.7 shows the model we use, and we can find Di is like linear variance. We define dynamic channel model in Fig. 2.7.
Fig. 2.7 Block based estimator model & the dynamic channel model We can base on the MSE (2-9) to change the weight βk at each pilot sub-carrier Fig. 2.8.
t filter at each pilot sub-carrier
Because of the standard, the scatter pilots is four symbols a cycle. If we assume the D2=2D1
The MSE in (2-4) becomes to (2-9).
Fig. 2.8 Adaptive weigh
2 1
In this equation, we need to determine the variance of CFR in three symbols E(D2) and
variance of A 2 2
2
WGN E(N /X ). Furthermore, we can find first term in MSE (2-9), as Doppler effects is increasing, the E(D ) will increase too. The second term AWGN noise effect can be average out with larger β. So MSE will trade off in these two terms. We can base on the MSE equation to decide the weight of each pilot sub-carrier.
In static channel, we can find the proposed estimator can get better MSE than without filter design. The CFR variance D is equal to zero in static channel.
2 2
In static channel we can find larger β
=∞
= − = + × − × −
−
⎯⎯⎯→ × − ≤
(2-10)
can get better performance, but in fact the channel will ore time dependent as eans the channel varying too fast over the entation method in later hardware cost than the existing design, but it
2.4 Transform domain processing
, we use a low pass filter to redu
be time variant not only AWGN effects. Furthermore, the channel is m the β lager. When β convergence to 0 which m
previous estimator. We will show the simulation results and implem chapter. We can find it only needs less additional
can get better performance in the slow fading channel.
In fact, the CFR would be a smooth curve. According to this property ce the high pass noise effect [11].
p( ) H m ˆ ( )p
H m
Fig. 2.9 The relationship of CFR and noise
In Fig.2.9, we can see that the relationship of CFR and noise. Because of noise we can get the red circle CFR but the perfect CFR is white circle. So the basic concept of filtering is to get a smoother CFR (blue circle) by a LPF. In theory the blue circle H mp( ) will be closer to perfect CFR than red circleH mˆ ( )p .
We can see that, the ener low pass band. In Fig.2.10 we can see the noise effect at high pass band. So we can reduce the noise in high pass band by a LPF. Fig.2.11 is
diagrams.
Fig. 2.10 The CFR of Rayleigh channel @ AWGN 25dB
In filtering processing, first we let the CFR through a FFT transform. The blue signal is the perfect CFR through FFT transform. The red signal is the perfect CFR add noise @ 25dB.
gy is gathered in
noise effect (25dB)
4.5
High pass band
260 270 280 290 300 310 320
0
noise effect (25dB) at high frequency
|FFT(H)|
LPF
Fig. 2.11 The flow diagram From section 2.3 we can get the estimated CFR Ĥp(m).
( ) 1
N m − (2-11)
The noise term N(m)/Xp(m) is a zero mean Gaussian random process. Variation of the true
CFR Hp(m p(m) with
) within one OFDM symbols is much slower than noise term N(m)/X index m. we can use this property to separate the two components by em
domain low-pass filter where the transform domain refers to the “frequency in” in DFT-IDFT transformations. The transform domain representation of
1
the signal component Ĝp(p) is located at the lower frequency band (around p=0 -1), while the noise term is spread over the full band (p=0,…,Np
ng can be realized by simply setting the samples in the “high pass band” to ze
ˆ ( ),0p c, p c p 1
G p p p N p p N
ain index.
As expected
and p=Np -1). The low-pass
filteri ro, that is
( ) 0,
where pc is the cutoff frequency o form domain. Such a low-pass
-f the -filter in the trans
filtering reduces the noise component by an order 2pc/Np. The cutoff frequency pc of the f the transform domain low-pass filter is an important parameter that affects the accuracy o channel estimation. Therefore the pc can be determined from the following relation.
2 2
where the numerator is the energy in the pass-band, the denominator represents the total energy,R∈
[
0.9, 0.95]
, and G pp( ) Gpilot based channel estimation, an efficient interpolation technique is necessary in order to estimate
te domain. The Fig.2.12 shows the 2x1D diagram.
is the average value of ˆ ( )p p of the present data symbol and several previous ones.
2.5 Interpolation process
In DVB-T pilot carriers are transmitted together with data carriers. In block-type
channel at data sub-carriers by using the channel information at pilot sub-carriers. Here we propose the two dimensional interpolation based channel estimation for mobile DVB-T/H reception. As we known, the 2D filtering complexity is much higher than 2x1D filtering, but the performance of 2D filtering is similar to 2x1D filtering [17-19]. Here we will separa interpolation in time domain and in frequency
Fig. 2.12 The 2x1D interpolation processing
2.5.1 Interpolation in time domain
In time direction, the CFR is sampled at time instants Tt =4(Tu+Tg) apart. For mobile channels the correlation between these samples is determined by the bandwidth of the Jakes spectrum with a maximum Doppler frequency f and the residual local frequency offset d
fk
Δ remaining after synchronization. The resulting bandwidth isBt =2(fd + Δfk), and the interpolation is over-sampled by a factor ofrt =Tmax = 1 with respect to the
4 ( )
t t u g
T B ⋅ ⋅ T +T
Nyquist sampling timeTmax t
For interpolation in time domain means that the casual and non-causal taps are used. For
e e non-causal data and the more latency to do
oper
For the received carriers Ck,i, where k denotes the carrier index and i denotes the symbol . Interpolation is only feasible if r > . 1
implem ntation aspect, we need store th
ation. Furthermore, the complexity is dominated by th ded to provide to store the additional OFDM symbols. In other hand, in DVB-T/H systems, we can’t ignore the carrier number in one OFDM symbol (1705 or 17), and each data of subcarrier will be
plex number format.
e memory nee
68 com
index. For CFR Ĥk,i at carriers Ck,i to be estim CFR at pilot carriers where k=12n+i*3+1, n is an integer and 0<n<142 (in 2k mode).
ated. Ĥk,i is the estimated
A. 1 -order predictive [17] st
The CFR is predicted using the nearest 2 CFR by setting the CFR value equal to the extrapolate value of these 2 CFR value as Fig.2.13 shows.
Frequency index
The linear extrapo bols to
predict the CFR of
Fig. 2.13 1 -order predictive interpolation in tim
lation is adopts CFR estimated at scatter pilots in the latest 7 sym currently received symbol at those carriers.
3, 1 3, 5
In this scheme, the extrapolation uses pilots only on previously received symbols and currently receiving symbol, no additional storage are needed. Therefore, it only eeds storage for previous CFR at pilot sub-carriers
n .
B. Linear interpolation
The Linear interpolation is shown in Fig.2.14
Currently
r interpolation is adopts CFR estimated at scatter pilots in the lates to interpolate the CFR of compensating symbol at those carriers.
3, 1 3, 5
In this scheme, it needs storage for 3 OFDM symbols for implementation of its non-causal properties, because after compensating symbol which data didn’t compensate yet.
So the memory is quite only needs storage for
CFR
ages in table 2-1. Although both are two taps interpolation methods, but linear interpolation needs store more 3 OFDM symbols, and the latency is 3 OFDM symbols time.
large. Then, before the compensating data, it at pilot sub-carriers.
We make comparison for the two methods in memory stor
Table 2-1 storage requirem St
ents for interpolation in time domain orage requirements (2K mode) Latency 1st-order predictive 1138 (569*2) carriers 0 symbols Linear interpolation 5684 (3*1705+569) carriers 3 symbols
2.5.2 Interpolation in frequency domain
After interpolation in time domain between scattered pilots, we can get estimated CFR every three subcarriers. Then, we use these sampled CFR to interpolate the whole CFR at the rest data subcarriers. Since the interpolation in time domain is done, the sample interval in frequency domain is from 12 fc to 3fc, where fc is the subcarrier spacing. Here, we use Linear, Parabolic, Second-order, and Cubic, four methods for interpolation in frequency domain, where Ĥ(k) is the result of the interpolation in frequency domain, k is the sub-carrier index.
Hp(m) = H(3* <3(m+1), and
=k/3-m.
nomial int oint base-poin x(i)} can be
range form . 2.15.
m) is the CFR after interpolation in time domain, where 3m<k μ
Classical poly erpolation of an N-p t set {ti, performed by the Lag ulas [18-19]. It shows in Fig
0( ) '( ) k 0 k k
Fig. 2.15 Polynomial interpolation in frequency domain
A. Linear interpolation
2
is only 1/3 or 2/3 two kinds of values, so the taps can be calculated in advance,
E between these interpolation methods. As we know, high order tter performance than low order interpolation. But if we concern the noise effects, the MSE of high order interpola r than low order interpolation. The criteria are MSE, and the fo n in following equation (2-21).
2
and save in the registers.
Next we discuss the MS
interpolation will use more samples to get smother curves, and gets be
tion will not be always bette rmulation detail is show
| ( ( )) k | }2
MSE=
∑
Cj× Hj Nj+ −H(2-21)
ferent coefficients. The coefficients are listed on table 2-2, and the
ferent in each interpolation curve, so the higher order can get better
[ ])Hj Hk
In the same channel conditions, we can find that different interpolation methods which MSE will depend on dif
relationship is listed on table 2-3.
We can find that the first term in (2-21) will enhance the noise effect with high order interpolation in comparison of ( 2)
j
∑
Cj . In table 2-3 we can find the enhance term of each method. In the formulation, the other terms effects will be difmethod. In fact the CFR would be a smooth performance without noise effects.
(ex: 2 [ 2] (2 [ ] [ ]) (2
However, the noise effect term ( Cj E Nj2) [ 2]
∑
j will be worse with higher order interpolation. So there will be a crossover in simulation with different SNR noise. We can use the equation (2-21) to determine the crossover point with different channels.ssover po
e coefficients list
C2 C3
The noise term will be dominant at low SNR< crossover point, but the other term effect will be dominant at high SNR> cro int. Then we can choose the better interpolation method for different channel cases.
Table 2-2 th
C0 C1
Average 0 0.5 0.5 0
Linear 0 0.3333 0.6666 0
Lagrange (2 order) -0.1111 0.8889 0.2222 0 Lagrange (3 order) -0.0617 0.7407 0.3704 -0.0494
Table 2-3 the coefficients relationship
Average Linear Lagrange (2 order) Lagrange (3 order)
(Cj2)
∑
0.5 0.5555 0.8519 0.69212CiCj
∑
0.5 0.4444 0.1481 0.3078∑
2Cj 2.0 2.0 2.0 2.0Chapter 3
Channel Equalization Algorithms
, we in lization algorithms, and we w how the
ritical path is the complex division operation. The division model is dominant hardware cost nd power consumption in channel equalizer. So we can simplify this division model and
ow the results of saving hardware cost and power consumption in later sections.
to channel equalization
e the bandwidth into many ding. Therefore, the equalization for each subcarrier becomes simple in frequency domain, ly a one-tap equalizer to compensate the channel fading effects. In OFDM–based
.
In this chapter troduce the channel equa ill s
c a sh
3.1 Introduction
It is mentioned in Chapter 2. In OFDM system, it will divid
subcarriers, so the channel frequency response of each subcarrier can be considered as flat fa
and it is on
communication systems, the received signal R[k] can be expressed by [ ] [ ] [ ] [ ]
R k =S k H k⋅ +N k
Where S[k] is the transmitted signal, H[k] is the CFR, and N[k] is AWGN noise. The , (3-1)
estimated signal Ŝ[k] can be obtained by dividing the estimated CFR, Ĥ[k] from channel stimation.
propose one new method to simplify divider complexity without
transferring receiving data by
, (3-2)
In related research, there was other approach via changing receiving data format to achieve divider-free method [20]. Here, we keep up the full-time complex dividing operation with new approach. We
format. In the same time, we replace the division operation
re
and a few registers to implement.
3.2
In channel equalizer, it contains a complex number division. One complex division operation includes two real number divisions. As we know, the division hardware cost is proportional to square of word-lengths, but the signal bus needs sufficient digits to represent receiving signals in order to get enough accuracy. In DVB-T/H system, it will provide higher clock rate for 64Qam and Viterbi decoder. So we can reuse the hardware by raising clock rate.
Furthermore, we can optimize the saturation cases and don’t need to add word-length to get enough decimal fractions of the quotient. Then according to multi-cycles division, we can use the shift-subtraction structure to simplify the hardware efficiently.
In addition, the division gate count is about 62.8% of equalizer, and the cycle time of DVB
3.3 Proposed division scheme
First, we introduce the format notations. In complex divider, the equation can be expressed by:
currence step based algorithm [21]. In recurrence step algorithm, it only requires an adder (substracter)
Motivation
-T/H systems for 8Mhz channels is about 109ns. Due to the long cycle time and the high hardware cost of long digits dividers, we propose a low cost architecture to implement the equivalent divider.
s and n is at structure is show
are (m1, n1 ll produce some
intermediate 1, 2n1).
α. When
the output da α. The complex
division includes two real ore, in order
to get n2 bits in decimal ac t n2 bits left. The dividend beco
to get n2 bits in decimal ac t n2 bits left. The dividend beco