where denotes the number of bits associated with the TPS pilot for frame synchronization, and denotes the TPS pilot. The frame timing estimation in (3.17) possesses two advantages: one is that the TPS pilot is more reliable due to the extra protection of the Bose-Chaudhuri-Hocquenghem (BCH) coding. The other is that we only need 16 synchronization bits in one frame, leading to a reduction of computational complexity.
3.4 Channel Estimation in DVB-T Systems
In wideband mobile communication systems, under the assumption of a slow fading channel, in which the channel transfer function is stationary within several OFDM data symbols, preambles or training sequences can be used to estimate the channel response for the following OFDM data symbols. However, in practice, the channel response may significantly vary even within one OFDM data block. Therefore, in DVB-T systems, it is preferable to estimate the channel characteristic based on the pilot signals in each individual OFDM data block. The conventional channel estimation involves a two-stage procedure. First, the channel responses associated with the pilot tones are estimated. Second, interpolation technique is used to obtain channel responses of the data tones. We will introduce two pilot-aided channel estimation methods. One is least square (LS) channel estimation, together with piecewise-linear interpolation. The other is application of low-pass filtering on the transformed pilot tones to reduce the Gaussian noise and ICI effects.
3.4.1 Least Square Channel Estimation with Linear Interpolation
Consider an OFDM system with scattered pilot signals. The received pilot signal in vector form can be given by
scat scat scat scat
scat scat
scat
scat p scat scat p scat
X H
where Xscat, Hscat, and Nscat denote the scattered pilot signals, the corresponding channel responses, and the noise, respectively [32]. According to the LS criterion, the channel transfer function can be obtained by
a rg min 2
scat
scat− scat scat
H Y X H (3.19)
whose solution is given by
, 1
scat LS scat scat
= −
H X Y (3.20)
From (3.20), the channel estimate can be obtained by dividing the received signals by the known scattered pilots. This implies that the LS channel estimator is easier to implement. As the estimation of the channel transfer functions of pilot tones is determined, the channel responses of data tones are then constructed by the linear interpolation technique. Note that we consider a linear interpolation method due to simplicity. With the linear interpolation used, two successive pilot subcarriers are used to compute the channel responses of data subcarriers located between these two pilot tones. Mathematically speaking, the estimated channel response of data subcarrier within the th and th pilot tones is given by number of pilot signals. Its schematic diagram of the pilot-based channel estimation with linear interpolation is shown in Fig. 3.13. It is noteworthy that this method needs
3.4.2 Lowpass Filtering in Transform Domain
LS-based channel estimation can achieve a better performance in a slow fading channel as long as the noise power is moderately small. However, this assumption is impractical due to the fact that a wideband radio channel is usually time-variant, frequency selective, and noisy. The pilot signals may be corrupted by ICI introduced by the fast variation of the mobile channel. In addition, the performance in channel estimation will significantly degrade because of noise. As a remedy, a novel channel estimation incorporating lowpass filtering in the transform domain, as shown in Fig.
3.14, is utilized to alleviate the effects of both ICI and noise [33]. The design involves the following procedure.
1. Rough channel response obtained by LS channel estimation
We first perform initial estimation of the channel responses at pilot locations with a simple LS method used. That is,
scat ls sact p scat
scat scat component consisting of ICI and noise, respectively.
2. Noise and ICI reduction
Since the true channel response Hscat ls, in (3.22) is slowly varying with respect to the noise component Nscat, the “virtual high frequency” and “virtual low frequency”
regions in the transformation of the estimated channel response will be mainly contributed by the true channel response and the noise, respectively. Note that the quotation marks denote the transform domain. An example is shown in Fig. 3.15. This suggests that these two components can be successfully separated by transforming the estimated channel responses of the pilot tones into the transform domain with discrete Fourier transform (DFT) or FFT. The transformation of Hˆscat ls, ( )k is given by is then performed on the transformed data, leading to
( ), 0 , , - -1
where is the “virtual cutoff frequency” of the filter. After filtering, noise and ICI effects can be effectively reduced.
wc
3. Interpolation approach
Under the assumption of slow-variation, the channel transfer function can be viewed as the sum of several sinusoidal functions with respect to k. However, the number and the “virtual frequencies” of the sinusoids vary due to the changing in the mobile radio channel. To avoid the model mismatch problem, we do not transform back to frequency domain and then perform interpolation. Instead, a high-resolution interpolation approach based on zero-padding is used. First, the -sample transform-domain sequence is extended to an -sample sequence by padding with
( ) frequency” region as follows:
,
This -sample sequence , in its physical meaning, is the Fourier transform of the desired estimate of the channel transfer function. By performing an -point inverse DFT/FFT (IDFT/IFFT), the estimated transfer function is obtained as
Nc G q( )
where a denotes normalized coefficient term after IDFT.
4. Dynamic selection of cutoff frequency
According to (3.24), the accuracy of the channel estimation with lowpass filtering is substantially dependent on the “virtual cutoff frequency” . With a large value of selected, noise and ICI effects can only be reduced slightly, while the desired signal will be suppressed with a small value of used. A proper value of can be determined adaptively by the ratio.
wc
wc
wc wc
2 1 2 ten previous OFDM symbols. By a rule of thumb, the ratio
( ) Gscat w
i
R is selected within 0.9 and 0.95.
The channel estimator with lowpass filtering can achieve better performance in the penalty of higher computational complexity. This is because additional operations are necessary for the implementation of a lowpass filter, DFT/FFT, and IDFT/IFFT.