Yeh’s Algorithm of ICI-reduction Method

Chen’s method of Channel estimation is based on the LS estimation. According to the conclusion in the previous section, this method only takes effect in the all-pilot preamble case. Thus, it is necessary to find out a channel tracking method in the data transmission region where only pilot subcarriers are utilized for the estimation. Yeh [11] proposed a channel tracking method with ICI-reduction technique in line-arly-variant fading channels.

Recall the system model described in Section 2.3. The received signal after DFT is given by

1

G k m when k≠m. Therefore, the channel frequency response at k-th pilot sub-carrier can be obtained by LS estimation introduced in Section 3.2.1

1 The second term on the right hand side of (3.28) represents the estimation error and increases as normalized Doppler frequency, f_nd, becomes large. According to (2.16), the estimation of h_ave( )l can be obtained by DFT-based channel estimation intro-duced in Section 3.2.2

1 2

Besides, (3.15) shows that h_ave( )l is the channel impulse response at the midpoint of the symbol interval when channel variation is approximated to linear fashion, i.e.

( 1, ) ( )

2 ^ave

h n N− l h l

= = . In order to estimate the slopes, α_l’s, of the channel paths within single OFDM symbol by using the two h_ave( )l ’s of the two consecutive OFDM symbols, it is assumed that channel variation within the two consecutive OFDM symbols is linear, i.e. f_nd ≤0.05. Therefore, the slopes of the channel paths can be obtained by

ˆ ( ) ˆ 1( ) de-notes the average response of the l-th channel path of the i-th symbol, and N_CP de-notes the length of the cyclic prefix (CP). This concept is shown in Figure 3.6. The

responding estimated response, respectively. The estimation error is the region be-tween the solid line and the dashed line.

i ( )

Figure 3.6 Linear model between two consecutive OFDM symbols [18]

Thus, the ICI terms in (3.19) can be cancelled by using the estimation of the slope, ˆ_lⁱ

α , and the demodulated data, ˆ ( )X k .

The whole procedure of Yeh’s method is shown in Figure 3.7 modified from [11].

I represent the iteration number. I_max is the number of the iterations. In the first it-eration, the estimation ˆ ( )h_aveⁱ l of h_aveⁱ ( )l suffers from whole ICI and has large error.

Thus, there are still many erroneous data after demodulation. After several iterations, the ICI terms at the pilot subcarriers would be mitigated by the ICI cancellation pro-cedure. The estimation error of ˆ ( )h_aveⁱ l becomes small. A more reliable slope of the

channel path ˆα_lⁱ is obtained. The ICI terms at the data subcarriers would be can-celled more clearly. Therefore, the error floor is reduced.

Although Yeh’s method operates well in the aspect of the performance and the computational complexity, it is only feasible in the assumption circumstance with

nd 0.05

f ≤ . Therefore, this method needs some modification to operate in the targeted fast fading channels. Besides, the performance of this method is bounded by the ICI cancellation method with ideal channel state information, i.e. ICI cancellation in Fig-ure 3.3 and FigFig-ure 3.4.

=0

Figure 3.7 Yeh’s algorithm of ICI-reduction method [11]

3.2.5 Simulation Results

In this section, the performances of the last two mentioned channel estimation methods are evaluated by computer simulations. Multipath Rayleigh fading channels in the simulations are generated by the modified Jakes’ model [9] [10]. The power delay profile is chosen as the “Vehicular A” channel model defined by ETSI for the evaluation of UMTS radio interface proposals [17]. The simulated OFDM system pa-rameters and the channel papa-rameters are listed in Table 3.2 and Table 3.3, respectively.

The 16 pilot subcarriers grouped into 4 groups are equispaced onto the DFT grid, i.e.

the indices of the pilot subcarriers are {0, 1, 2, 3, 16, 17, 18, 19, 32, 33, 34, 35, 48, 49, 50, 51} within 64 subcarriers. These pilot patterns are used for Chen’s method of LS channel estimation. For Yeh’s algorithm of ICI reduction method, the 16 pilot subcar-riers are equispaced along frequency direction, i.e. the indices of the pilot subcarsubcar-riers are {0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60} within 64 subcarriers, due to DFT-based channel estimation. Beside, an all-pilot preamble is attached in front of the data symbols for the initial channel estimation. It is assumed that the maximum path delay time is known at the receiver and that synchronization is perfect.

Table 3.2 Simulated OFDM system parameters Operating frequency 3.5GHz

Signal bandwidth 2.5MHz

FFT length 64

Number of piot subcarriers 16 Number of data subcarriers 48

Symbol duration 25.6us Subcarrier spacing 39.1kHz

Modulation QPSK

Channel coding No

Power delay profile ETSI Vehicular A Normalized Doppler frequency 0.083 and 0.040

Table 3.3 ETSI Vehicular A channel environment Tap Relative delay (ns) Average power (dB)

1 0 0.0

2 310 -1.0

3 710 -9.0

4 1090 -10.0

5 1730 -15.0

6 2510 -20.0

0 5 10 15 20 25 30 35 40 45

Figure 3.8 ANMSE performances of Chen’s and Yeh’s methods of channel estimation in the “Vehicular A” channel with f_nd =0.040

0 5 10 15 20 25 30 35 40 45

Figure 3.9 ANMSE performances of Chen’s and Yeh’s methods of channel estimation in the “Vehicular A” channel with f_nd =0.083

0 5 10 15 20 25 30 35 40 45 ICI cancellation 3rd, Ideal CSI ICI-free

FSDMMSE, Chen's LS, pilot FSDMMSE, Ideal CSI Choi's SDMMSE, Ideal CSI

Figure 3.10 BER performances of Chen’s and Yeh’s methods of channel estimation combined with data detection methods in the “Vehicular A” channel with f_nd =0.040

0 5 10 15 20 25 30 35 40 45 ICI cancellation 3rd, Ideal CSI ICI-free

FSDMMSE, Chen's LS, pilot FSDMMSE, Ideal CSI Choi's SDMMSE, Ideal CSI

Figure 3.11 BER performances of Chen’s and Yeh’s methods of channel estimation combined with data detection methods in the “Vehicular A” channel with f_nd =0.083

In Figure 3.8 and Figure 3.9, ANMSE indicates the average normalized mean square error, which is defined as

1 1 2 OFDM symbol defined in Section 2.3. The terms “Chen’s LS, preamble” and “Chen’s LS, pilot” indicate that Chen’s methods of LS channel estimation, introduced in Sec-tion 3.2.3, are applied to the all-pilot preamble and the pilot subcarriers, respectively.

The term “Yeh’s ICI reduction, pilot” indicates that Yeh’s algorithm of ICI reduction method [11] with 3 detection iterations, introduced in Section 3.2.4, is applied to the pilot subcarriers.

In Figure 3.10 and Figure 3.11, the term “ICI-free” indicates the theoretical BER performance of the coherent detection in the time-invariant flat Rayleigh fading channel for the reference of the ICI-free case. The ordinal numbers appended to “ICI cancellation” and “Yeh’s ICI reduction” indicate the numbers of the iterations per-formed in the two methods. The terms “FSDMMSE” and “Choi’s SDMMSE” indicate that the proposed frequency-domain successive detection method with MMSE tion (see Section 4.1) and Choi’s method of successive detection with MMSE detec-tion [7] are adopted in data detecdetec-tion, respectively. The term “Ideal CSI” indicates that ideal channel state information is applied to data detection.

Figure 3.8 and Figure 3.9 illustrate ANMSE performances of Chen’s and Yeh’s methods of channel estimation in the “Vehicular A” channel with f_nd =0.040, and

0.083

fnd = , respectively. Chen’s method applied to the all-pilot preamble has the least channel estimation error of all. It can be viewed as the performance boundary of

Chen’s method applied to any other pilot pattern when the number of pilot subcarriers is less than N. Apparently, the performance degradation of Chen’s method applied to the pilot subcarriers is very large. Under the same ANMSE condition, Yeh’s method with 3 detection iterations applied to the pilot subcarriers has about 4~5dB perform-ance loss compared to Chen’s method applied to the all-pilot preamble when

0.040 ~ 0.083

fnd = . Besides, the channel estimation errors of these methods increase as f_nd becomes large, especially in the high SNR case.

Figure 3.10 and Figure 3.11 illustrate the BER performances of Chen’s and Yeh’s methods of channel estimation combined with data detection methods in the “Vehicu-lar A” channel with f_nd =0.040, and f_nd =0.083, respectively. Because of the large channel estimation error, Chen’s method applied to the pilot subcarriers combined with the proposed detection method has the worst performance of all. There is a large performance degradation compared to the proposed detection method with ideal channel state information. As known in Section 3.2.4, the performance of Yeh’s method is bounded by the ICI cancellation method with ideal channel state informa-tion.

In conclusion, the Yeh’s method is not good enough to reduce the ICI effect under the targeted channel environments. The channel estimation error of the Chen’s method applied to the pilot subcarriers is too large for the proposed detection methods. Thus, it is necessary to develop more reliable channel estimation.

Chapter 4 The Proposed Data Detection and Channel Estimation Methods

In the previous chapter, some existing data detection and channel estimation