The frame structure of DVB-T

Under the 2K mode, a frame is constituted by 68 OFDM symbols. And a super OFDM frame can be constituted by 4 OFDM frames. An OFDM not only transmits information data, but also training data and system parameters which include scattered pilots, continual pilots, and transmission parameter signaling (TPS) data. The pilot signals are used for synchronization and channel estimation.

Figure 2-8 shows the subcarriers for the transmission of data, scattered pilots, continual

pilots, and TPC data.

Figure 2-8 Subcarriers allocation

Within each symbol, a scattered pilot is inserted every 12 carriers. Each scattered pilot jumps forward by three carrier positions in the next symbol. So the scattered pilot will be on the same subcarrier positions every four OFDM symbols. The power level of a scattered pilot is boosted by4

3, and the BPSK data are sent as scattered pilots. The phase of a BPSK signal, either 0 orπ , is decided by the Pseudo Random Binary Sequence (PRBS). The scattered pilots are mainly used to conduction channel estimation. Since the pilots are scattered, the complete channel response must be obtained using interpolation.

Unlike scattered pilots, the positions of the continual pilots are fixed. The power level of the continual pilot is also boosted by4

3, and the BPSK data are sent as continual pilots. The phase of a BPSK signal, either 0 orπ , is also determined by the Pseudo Random Binary Sequence (PRBS). The continual pilots are mainly used for channel estimation and frequency synchronization. The frequency synchronization is also referred to as automatic frequency

Scattered pilot subcarrier Data subcarrier

...

Subcarrier

TPS subcarrier

Continual pilot subcarrier

OFDM Symbol

…

positions for the continuous pilots are given in Table 2-2.

Table 2-2 Subcarrier index for continual pilots

TPS data give information about the current transmission status, including the frame number, QAM size, coding rate, CP size etc. The TPS data are sent through TPS pilots whose locations are given in Table 2-3. The complete TPS information is broadcasted over 68 symbols in one OFDM frame and carried in 68 bits. To lower the error rate, DBPSK is used for the modulation scheme.

Table 2-3 Subcarrier index for TPS pilots

Table 2-4 shows the number of subcarriers allocated for data, scattered pilots, continual pilots, and TPS pilots.

Mode

Carriers 2K Mode 8K Mode total carriers 2048 8192 active carriers 1705 6817 scattered carriers 142/131 568/524 continual carriers 45 177

TPS carriers 17 68

Table 2-4 The number of pilot carriers for 2K and 8K mode

Chapter 3

Joint Time and Frequency Domain Channel Estimation

Consider a specific subcarrier of subcarrier index

i

in an OFDM symbol. We have

y

_i

= h x

_{i i}

+ w

_i , where

y

_i is the frequency-domain received signal,

x

_i is the frequency-domain transmitted signal,

h

_iis the channel frequency response, and

w

_iis the corresponding AWGN noise. It is apparent that if both

x and

_i

y are known,

_i

h can then be

_i estimated. Let

y

_p

= h x

_{p p}

+ w

_p where the subscript denotes the subcarrier in a pilot position.

We can estimate the channel response in the pilot position, denoted by

ˆ h

p, as:

ˆ

^p

p p

h y

= x

(3.1) In the DVB-T system, there is a scattered pilot every 12 subcarriers, as shown in Figure 3-1.

Figure 3-1 Scattered pilots in DVB-T

To obtain the channel responses in data subcarriers, we need to conduct interpolation. In the next two sections, we will describe two simple interpolation techniques, one-dimensional

……

OFDM Symbol

Pilot subcarrier Data subcarrier

...

Subcarrier

and two-dimensional interpolation methods. If the number of pilot subcarriers is not sufficiently large, the interpolated result may not be satisfactory. In this case, the time-domain channel estimation requiring fewer pilots may be used. In the last section, we will describe a recently developed method, a joint time and frequency domain channel estimation method.

3.1 Interpolation methods

The classical approach for channel interpolation is to construct a polynomial interpolator fitting responses in known samples. The polynomial interpolator can be formulated in various ways, such as the power series, Lagrange interpolation and Newton interpolation. These various forms are mathematically equivalent and can be transformed from one to another. We will use the power series as our polynomial interpolator. Assume that there are some samples available, denoted as

{

x f( ), ( ), , (_o x f1 x f_N)}, where ( )

x f is the amplitude of the signal

_n

( )

x f at frequency f . The polynomial with order

_n N , passing through the N+1 known samples, can be written in a power series form as

2

0 1 2

( ) _N( ) _N ^N

x f

=

P f

=

e

+

e f

+

e f

+ +

e f

(3.2)

where ( )

P f is a polynomial of order

_N N, and

e s are the polynomial coefficients. An

_k' example of the polynomial interpolator is shown in Figure 3-2. As we can see from Figure 3-2 that the fitted polynomial is unique.

f

0

f

1

f

2

f

4

f

5

f

6

f

7

x(f)

frequency

Figure 3-2 Polynomial interpolator

For all the signals in pilot subcarriers, we can write (3.2) into a matrix form.

1 1 1 1

The matrix form can be expressed as:

x = Fe

(3.4) polynomial coefficients, and N is the order of polynomial interpolator. Note thatN is usually small since the computational complexity of the interpolation is proportional to N . In practice, the linear (N=1) and quadratic (N =2) and cubic (N=3) interpolator is often used.

Since M is usually larger than N , the system in (3.4) is overdetermined. So, the polynomial coefficients can be solved by the least-squares (LS) algorithm. With the LS algorithm [5], we then have

H -1 H

e = (F F) F x

(3.5) The simplest polynomial interpolator is the first-order (i.e, the linear) polynomial interpolator. However, the performance is usually not satisfactory. The cubic interpolator being a third-order polynomial interpolator is widely used in real-world applications. It can have better performance while the computational complexity is acceptable.

The one dimensional linear interpolation method uses one OFDM symbol and simply conducts the interpolation for the channel responses in data subcarriers. In order to obtain better performance, we can change the linear interpolation to cubic interpolation in the one dimensional interpolation method. We will discuss the performance of the linear and cubic interpolation methods in the simulation chapter.

The main advantage of the one-dimensional interpolation approach is that it needs only one OFDM symbol and the requirement for the memory size is small. Also, the computational complexity of the one-dimensional linear interpolation is low. However, due to the low density of scattered pilots, this method cannot achieve satisfactory performance in general. To solve this problem, we will introduce the two-dimensional linear interpolation method below.

Since the positions of the scattered pilots are the same for every 4 OFDM symbols, we can conduct interpolation in the temporal domain. The two-dimensional interpolation method uses consecutive OFDM symbols to conduct interpolation both in the frequency and temporal domains. With this approach, the pilot density can be effectively increased. Figure 3-3 shows the linear interpolation in temporal domain. In the figure, the channel responses of the middle OFDM symbol are those we want to estimate (the dotted block). We first interpolate linearly the responses in the temporal domain. The interpolated responses can be seen as pseudo pilots which can be used in the interpolation in the frequency domain. As we can see, the pilot density is increased from 1

12 to 1 3.

Figure 3-3 Interpolation in temporal domain

Since the scattered pilot density is raised to1

3, we can obtain the channel responses in frequency domain more accurately. The two-dimensional interpolation method is better than the one-dimensional interpolation method when the channel responses are highly variant. But the two-dimensional interpolation method needs 7 OFDM symbols to conduct interpolation in both frequency domain and temporal domain. The computational complexity is high and the required memory is large.

In order to obtain better performance, we can also use the cubic interpolation to replace the linear interpolation. The performance comparison of the one-dimensional interpolation methods and the two-dimensional interpolation methods will be shown in the simulation chapter. We will also discuss the performance comparison of the linear and cubic interpolation methods in the simulation chapter.

3.2 Joint time and frequency domain channel estimation

Due to limited pilot signals, channel estimation using the frequency domain interpolation will be degraded when the channel delay spread is large. In this case, the interpolation method may not be able to recover the frequency response, even with the two-dimensional

OFDM Symbol

...

Subcarrier

Pilot subcarrier Data subcarrier Pseudo pilot subcarrier

...

interpolation method.

In typical wireless channels, the delay spread may be large, but the number of non-zero taps is small. Since the taps of channel are usually fewer, the unknowns of channel responses in time domain are less than those we need to estimate in the frequency domain. As a result, it is possible for the time-domain approach to have better performance under the same number of pilots. In this subsection, we will describe a newly developed joint time/frequency domain channel estimation method [3], [4].

The first step of the method is to use a two-dimensional interpolation method, with the linear interpolation in the time domain and cubic interpolation in the frequency domain, to obtain the channel responses in the frequency domain. Then, we transform the channel response into the time-domain to obtain the time-domain channel response. One example of the time-domain channel responses is shown in Figure 3-4.

0 20 40 60 80 100

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Tap Delay (Ts)

magnitude

Initial channel estimate in time domain

Figure 3-4 The initial time-domain channel estimate

As we can see, there are only a few significant channel taps. Then, the method locates those taps and estimates their values. The tap searching and the magnitude estimation

algorithms are described in following 3.2.1 and 3.2.2. A more efficient recursive procedure is finally described in 3.3.3.

3.2.1 Tap searching algorithm

As we can see from Figure 3-4, there is a low-pass signal embedded in the channel response. So some fake taps will occur near the significant taps. In this subsection, we outline an iterative method that can solve the problem.

If we take a first-order differentiation to the channel response, the low-pass signal will be removed. The differentiation operation is given by

d k

[ ]=

h k

ˆ[ + −1]

h k

ˆ[ ]( ˆ[

h k

+ , ˆ[ ]1]

h k is

the tap value of different taps). With a threshold, we can find the significant tap by this method. However, if there are consecutive significant taps, the operation can not find all the taps.

Figure 3-5 Channel tap searching method by the first-order differentiation method

Another method to find the taps is simply to compare the magnitude of a tap with a threshold. If it is larger than the threshold, the tap is deemed as a peak (significant tap).

Apparently, some fake taps occurring near the significant taps will also be detected as significant taps.

Channel tap found by the first-order differention method Unfound tap by the

first-order differention method

Figure 3-6 Channel tap searching by thresholding

We can combine the aforementioned two methods to obtain a more reliable method. The idea is to locate the taps in an iterative manner, rather than in one short. Figure 3-7 shows the iterative procedure. First, locate significant the channel taps by the first-order differentiation method (Figure 3-7-(a)) with a high threshold value (Figure 3-7-(b)). In this case, smaller or consecutive significant taps may not be detected. Using the estimation method described in the next subsection, we can estimate the magnitude of those located taps. Then, subtract the channel response formed by the located channel taps from the original channel response (Note that this operation is conducted in the frequency domain). We can then have a residual channel response. Thus, we can transform the response to the time-domain and conduct the tap searching algorithm again (the threshold can be made smaller). Repeat this process until no significant taps are detected.

Unfound channel tap by thresholding Channel tap found by thresholding

Threshold

Figure 3-7 The procedure of the significant tap searching method

3.2.2 LS channel estimator

For a subcarrier of subcarrier index

i

in a particular OFDM symbol, the signal transmitted and passed through the channel can be expressed as

y

_i

= h x

_{i i}

+ w

_i. Let N be the FFT size. We can write the equation for all subcarriers. We have

0 00 0

The LS channel estimator minimize the following squared errors:

Channel taps left after subtracting the detected taps

(b)

(c)

Unfound tap by first-order differention Channel tap that we want to remove found by the first-order differention and thresholding (The ones to be subtracted) Channel tap found by the

first-order differention

ˆ

2

−

LS

y H x

(3.6)

Where

y = [ y y

0

, ,...

1

y

_N−1

]

^T is the frequency domain received signal vector,

[ x x

0

, ,...

1

x

_N−1

]

^T

x =

is the frequency domain transmitted signal vector. Using pilot subcarriers, we can have the LS channel estimator minimize the following squared errors:

2

y

is the frequency domain received vector on pilot

locations, ₀

,

₁

,...

₁

M

T p

= ⎣ ⎡ x

m

x

m

x

m ₋

⎤ ⎦

x

is the frequency domain transmitted pilot signal vector (

m

_i,0≤ ≤

i M

− is pilot location and M is the number of pilots). With the LS 1 algorithm, we then have

(

^H

)

^{-1 H}

p,LS p p p p

H

∧

= x x x y

(3.8)

The LS channel estimator also has a time-domain version. The signal transmitted and passed through the channel can be expressed as

y

_i

= x

_i

gh + w

_iwhere

y

_i is the frequency domain received signal,

x

_i is the frequency domain transmitted signal, h is the channel

response in time domain, g is a row of the DFT matrix,

w

_i is noise. Considering all pilot subcarriers, we can have

Let

0 0 0

Then, we can have a similar formulation as that in (3.7). The LS channel estimator in time domain minimizes the following squared errors:

2

, LS

p D p

−

∧

y X G h

(3.11)

where G is the DFT matrix. And the LS solution to the time domain LS channel estimation is then:

(

^{H H}

)

^{-1 H H}

LS D,p D,p D,p p

∧

=

h G X X G G X y

(3.12)

where

X

_D,pis a diagonal matrix containing pilot signals. The time-domain LS method requires O L( )³ arithmetic operations where L is the maximum channel delay spread. If L is large, the required computational complexity is high. If we only consider L significant taps in whichL is much less thanL, the computational complexity can be reduced. For example, if we only consider

h and

₀

h

_L−1, we only have to use the first and last column of

G and the matrix to inverse in (3.11) becomes a 2 2× matrix.

We then have

(3.13)

,

p D p

+

y = X G'h w

(3.14) where G' is a reduced DFT matrix contain the columns within the dotted block shown in (3.13). In an extreme case, we can only estimate a channel tap at one iteration. The computational complexity is further reduced since the DFT matrix is degenerated to a vector.

3.2.3 Iterative joint time and frequency domain channel estimation

In previous subsections, we have described a low-complexity yet high-performance channel estimator. We called this a joint time and frequency domain channel estimator. The estimation flowchart is shown in Figure 3-8, and the related procedure is summarized as follows: (Notice LSE represents LS error and R represents the LSE threshold)

0 0 0

Figure 3-8 Iterative joint time and frequency domain channel estimation

STEP 1: Use the two-dimensional interpolation method to obtain the initial frequency-domain channel estimate.

STEP 2: Conduct the IFFT of the frequency domain channel estimate to obtain the time-domain channel estimate.

STEP 3: Find the tap with the maximum value (the threshold of tap search is iteration dependent) and use the LS algorithm to estimate the response of the maximum tap.

STEP 4: Compute the least-squares error (LSE) of all located and estimated taps with a

threshold (LSE threshold). If the LSE is greater than the LSE threshold, Conduct the FFT of the channel response estimated in the time domain (with the located and estimated taps) and subtract the resultant response from the

Interpolated frequency domain channel estimate

Subtract the located tap from original response in frequency domain

Force guard band to zero

No YES

channel response estimated in the previous iteration. Note that we have to null the responses in the guard band region. Then, go to STEP 2. If the LSE is smaller than the LSE threshold, stop the iteration.

Note that the LSE is a good indicator telling us when to stop the searching. In other words, it can avoid the redundant operations and reduce the computational complexity for the LS algorithm. In mobile environments, the channel tap positions may change with time suddenly. The LSE can also help us to check whether the channel taps’ positions have changed or not. The iterative operation not only locates the channel taps more precisely, but also requires less computational complexity for the LS algorithm.

As seen, an FFT/IFFT operation is required for each iteration and this will increase the computational complexity significantly. This can be remedied with the following approach.

The main idea is to transfer the response-subtraction operation in the frequency domain to the time domain. Note that the operation conducted in the frequency domain is windowing and subtraction, which can be transferred into convolution and subtraction in the time domain.

The function to be convolved is the sinc filter. In practice, the sinc filter may be difficult to implement. So, we may replace it by some lowpass filter. Since the number of detected taps is expected to be small, the required computational complexity of the convolution operation will not be significant. The modified flowchart of the modified scheme is shown in Figure 3-9.

Figure 3-9 Joint time and frequency domain channel estimation with time domain filtering

3.2.4 Improved joint time and frequency domain channel estimation

One problem associated with method described above is that the estimation of a significant tap may be affected by the other significant taps. An improved method was then proposed in [4]. The main idea is to conduct a re-estimation for all significant taps. After all the taps has been estimated, we can conduct the re-estimation of one tap by subtracting the channel response contributed from the other taps and using the LS method shown above.

Using the approach, the estimation accuracy can be improved. The procedure is summarized below. Figure 3-10 show the flowchart of the method. Note that the channel taps can be re-estimated more than one time until the satisfactory result is obtained.

Interpolated frequency domain channel estimate

IFFT

Tap searching algorithm

LS algorithm

Low pass filter

Compute LSE Locate tap

Find the tap value we locate

Subtract the located tap from original response in time domain

LSE>R?

STOP No YES

STEP 1: With the channel estimation method described above, we get L significant

taps. We can order

h

_k’s and start from the maximum one.

STEP 2: With the FFT operation, we obtain the frequency response for a subcarrier of

the other taps (the subcarrier index is

i

), denoted as

h

_i

'

.

STEP 3: For a specific pilot position, say p, we can subtract the response contributed

by

h

_p

'

. Let the transmitted pilot signal be

x

pand the received pilot signal be

y

_p. We then have

' '

p p p p

y = y − x h

(3-14)

STEP 4: Using all y

_p

'

s, we can conduct the LS channel estimator to re-estimate the

designated tap.

STEP 5: Check if all taps are re-estimated. If no, then select the next largest tap and go

to STEP 2.

Figure 3-10 Improved joint time and frequency domain channel estimation

The dotted block is the improved LS algorithm which will be used in the next Chapter. It contains the iterative channel tap searching and improved LS operation.

STOP

Channel estimation result in Figure 3-9

Subtract the response in

frequency domain

of the selected tap from

Chapter 4

Proposed Joint Time and Frequency Channel Estimator for DVB-T Systems

As discussed in Chapter 3, the channel estimation with a two-dimensional interpolation requires 7 OFDM symbols. The computational complexity is high and the memory to store the OFDM symbols is large. For one symbol in the first three or the last three OFDM symbols (in a frame), we cannot collect 7 symbols (three before and three after) for channel estimation and the performance in these areas will degrade. Another problem is that the channel cannot have large variation in the selected 7 OFDM symbols. Thus, the methods described in Chapter 3 are only applicable in slow-fading environments. In this chapter, we will propose a new method to overcome this problem for DVB-T systems.

The proposed method uses only one OFDM symbol to conduct the channel estimation.

As known, the pilot density is low in DVB-T systems. Direct estimation will result in poor performance. Our idea is to use decisions as pseudo pilots, which will be referred to as pseudo pilots in the sequel, such that the pilot density can be effectively enhanced. The proposed algorithm can be summarized as follows.

1. Obtain an initial channel estimate with one OFDM symbol.

2. Use the estimate with the LS algorithm to conduct data detection.

3. Use some detected data as pseudo pilots and conduct channel re-estimation.

4. Use the re-estimated channel with the LS algorithm to conduct data re-detection.

In the following subsection, we will describe each step in details.

4.1 Initial channel estimation with one OFDM symbol

As discussed in Chapter 3, we also conduct an initial frequency-domain channel estimate by pilot information and transfer it to time domain. However, we do not conduct interpolation. Since the pilot density is low, the initial estimate is not accurate. As known, the pilot subcarriers are uniformly spread in the frequency domain. If we only estimate the channel response with those in pilot subcarriers, it is equivalent to conduct a sampling on

As discussed in Chapter 3, we also conduct an initial frequency-domain channel estimate by pilot information and transfer it to time domain. However, we do not conduct interpolation. Since the pilot density is low, the initial estimate is not accurate. As known, the pilot subcarriers are uniformly spread in the frequency domain. If we only estimate the channel response with those in pilot subcarriers, it is equivalent to conduct a sampling on

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