Chapter 4 Channel Estimations for MIMO OFDM Systems
4.2 Channel Estimation Techniques for MIMO OFDM System
4.2.3 Channel Estimation with All-pilot Preamble
4.2.3.2 Proposed Method for the Decision of Significant Number of
Q n h n = p n (4.48)
[ ] 1[ ] [ ]
h n =Q n p n− (4.49)
4.2.3.2 Proposed Method for the Decision of Significant Number of Channel Taps
In 4.2.3.1, it is shown that the complexity of LS estimator can be reduced if small is chosen. In Chapter 5, the simulation results show that a proper brings good MSE performance, and the simulations exploit the fact that a proper value of is the number of those most significant taps in time-domain. In [22], the
detection of is not studied for this LS estimator. For this reason, we propose a simple method to improve this drawback of the methods.
K0 K0
K0
K0
According to the simulations in Chapter 5, the mean square error is large when is also large. While decreases and is closed to significant length of the channel, MSE is also reduced. An intuitive idea to decide is to use a large initial
value for coarse estimation. Then a fine estimation of is conducted based on the result of coarse estimation.
K0 K0
K0
K0
The significant length of the channel is defined as the first tap-number at which the multi-path power is below the threshold. With threshold of 10-3, the result falls at a reasonable performance. This criterion is illustrated in Figure 4.15. The overall flow of proposed modification is illustrated in Figure 4.16. The simulations for performance verification will be shown in Chapter 5
0 10 20 30 40 50 60 70
0 0.2 0.4 0.6 0.8 1 1.2 1.4
Delayed tap number
Response Magnitude
Channel impulse response Threshold
Figure 4.15 Criteria for length of the estimated channel
Estimate channels with initial K0
Find the coarse estimations of
channels
Estimated new K0
with coarse estimations
If present K0
equals to previous one?
Estimate channels with present K0
Update K0
Yes No
Figure 4.16 Flow chart for proposed channel length detection algorithm
Chapter 5
Simulations and Comparisons
In this chapter, we will present the simulation results on MIMO OFDM system channel estimation techniques. As we mentioned in Chapter 4, several kinds of pilot arrangements and corresponding estimation techniques are involved in our studies.
After general evaluation on channel estimation techniques, we will discuss channel estimation issues of two popular standard, 802.16a with STC and 802.11n (WWiSE).
5.1 Simulation Environment and Parameters
The studies begin with simulations on a general MIMO OFDM system. Main system features are listed in Table 5.1 for simplicity. The overall system flow is shown in Figure 5.1. In our studies, we assume no synchronization errors in the system (i.e. perfect synchronization). Only inner transceiver is considered, and channel coder will not be considered. Both 802.11n-lke (packet type transmission) and 802.16a with STC (PSAM with STC) systems are also considered in our simulations.
Table 5.1 Simulated 802.11n-like MIMO system parameters Sample Period 50 ns
Total number of carriers 64 Total number of carriers 52 The number of data carriers 48 Symbol period 4µ s Guard Interval 0.8µ s
Modulation QPSK Sampling frequency 20MHz
Carrier spacing 312.5 kHz Normalized Doppler shift frequency 0.01
ST-coding for data STBC Number of Tx/Rx 2-4/1-4
5.1.1 Channel Models
For both 802.11n-like and 802.16a with STC systems, two channel models are considered. The specific static impulse response of each channel model is listed below.
Table 5.2 and Table 5.3 are for 802.11n-like systems. They are indoor wireless model at 5.3 GHz. Table 5.4 is channel model A for 802.16a proposed by ETSI (European Telecommunications Standards Institute). Table 5.4 is a model provided by ATTC (Advanced Television Technology Center). The channels are modeled as Rayleigh fading channels, and we assume uncorrelated between antennas (i.e. the correlation matrices are set to be identity matrices).
Table 5.2 Static parameters for indoor wireless channel (Model 1) Tap No. Delay (samples) Power (dB)
1 0 0 2 1 -5 3 2 -13 4 3 -19
Table 5.3 Static parameters for indoor wireless channel (Model 2) Tap No. Delay (samples) Power (dB)
1 0 0
2 4 -8
3 5 -15 4 11 -18
Table 5.4 Static parameters for ETSI model A (Model 3) Tap No. Delay (samples) Power (dB)
1 0 0
2 4 -5
3 8 -7
4 12 -8.87 5 20 -10 6 30 -10
Table 5.5 Static parameters for ATTC model E (Model 4) Tap No. Delay (samples) Power (dB)
1 0 0
2 2 -1 3 17 -9 4 36 -10 5 75 -15 6 137 -20
5.2 Channel Estimation for 802.11n-like Systems
In this subsection, different 802.11n-like (block type) MIMO OFDM systems such as all-pilot preamble, scattered preamble, and space-time coded preamble, will be explored. Space-time coded preamble, all-pilot preamble (the same as WWiSE), and scattered preamble are involved in our discussion. Except the pilot arrangement in preamble, all the other system parameters are the same as Table 5.1.
5.2.1 Channel Estimation for Space-Time Coded
Preamble MIMO OFDM
0 5 10 15 20 25 30
10-7 10-6 10-5 10-4 10-3 10-2 10-1 100
SNR in dB
BER
Ideal response (static response) Ideal response (Rayleigh fading)
Estimated response by STC preamble (Rayleigh fading)
(a)
0 5 10 15 20 25 30
10-7 10-6 10-5 10-4 10-3 10-2 10-1 100
SNR in dB
BER
Ideal response (static response) Ideal response (Rayleigh fading)
Estimated response by STC preamble (Rayleigh fading)
(b)
Figure 5.1 BER comparison of space-time coded preamble system (2 x 1) for two different channel conditions (a) Model 1 (b) Model 2
In this kind of MIMO OFDM system, both data and preambles are coded by space-time block code. When receiver starts to extract incoming OFDM symbols, the channel response is obtained by known space-time coded preamble. The channel is estimated of channel is from equations (4.25a) and (4.25b). The assumption of static channels between consecutive symbols is not valid in time-varying channels.
Although noise is suppressed as shown in (4.26a) and (4.26b), the failure of static assumption degrades the performance. In Figure 5.1 (a) and (b), performance degeneration can be observed from the result of the static channel and time-varying channel.
After the decision-direct tracking skill is applied to this system, one can see that the BER curves in both Figure 5.2(a) and 5.2(b) are below the curves without decision-direct channel tracking. It shows that this skill is useful to combat time-varying channels. In Figure 5.3, the estimated responses at both head and tail of the packet are drawn. One can find that they are close to the actual responses. In this simulation, the number of OFDM symbols in a packet is 20, and the forgetting factor α described in equation (4.30) is set to 0.1. The normalized Doppler frequency is 0.1.
T fd
0 5 10 15 20 25 30 10-4
10-3 10-2 10-1 100
SNR in dB
BER
Estimated response by STC preamble (Rayleigh fading)
Estimated response by STC preamble with tracking (Rayleigh fading)
(a)
0 5 10 15 20 25 30
10-6 10-5 10-4 10-3 10-2 10-1 100
SNR in dB
BER
Estimated response by STC preamble (Rayleigh fading)
Estimated response by STC preamble with tracking (Rayleigh fading)
(b)
Figure 5.2 BER comparison of space-time coded preamble system with decision-direct tracking (2 x 1) for two different channel conditions (a) Model 1
(b) Model 2
0 10 20 30 40 50 60 70 0
0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
Subcarrier index
Magnitude
Estimated response at the first symbol of packet Estimated response at the last symbol of packet Actual response at the first symbol of packet Actual response at the last symbol of packet
Figure 5.3 Response plot of space-time coded preamble system with decision-direct tracking (2 x 1) for the first symbol and the last symbol in a
packet
5.2.2 Channel Estimation for All-pilot Preamble
MIMO OFDM
When we further investigate channel estimation in all-pilot preamble MIMO OFDM system, the parameter must be chosen carefully. As mentioned in
Chapter 4, equals to the number of most significant taps in time domain. To illustrate this property, we consider another channel model other than Model 1 and 2.
This channel has a larger delay spread that can demonstrate the influence of . The K0
K0
K0
delay taps of this channel is at 0, 4, 5, and 11 samples. The power attenuation in dB is 0, 4, 5, and 8, respectively.
0 10 20 30 40 50 60 70
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Delayed Tap Number
Magnitude
Real impulse response of the channel Estimated channel impulse response
(a)
0 10 20 30 40 50 60 70
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Delayed Tap Number
Magnitude
Real impulse response of the channel Estimated channel impulse response
(b)
0 10 20 30 40 50 60 70 0
0.2 0.4 0.6 0.8 1 1.2 1.4
Delayed Tap Number
Magnitude
Real impulse response of the channel Estimated channel impulse response
(c)
Figure 5.4 Estimated channel responses for three different (a) =15 (b)
=7 (c) =4
K0 K0
K0 K0
From the observation of previous simulations, is a critical factor of performance. To verify the influence of , a static two-ray channel is used for
simulations. In order to evaluate performances of various , the multipath power of each tap is set to a large value to emphasize their difference. The delay taps of this channel is at 0 and 14 samples. The power attenuation in dB is 0 and 3. In Figure 5.5, MSE versus plot is illustrated under noiseless condition with the static two-ray channel. One can see that MSE has the lowest value when equals to 15. The
K0
K0
K0
K0
K0
MSE is large when is smaller than 15 because a significant tap is lost. The MSE increases with when is greater than 15.
K0
K0 K0
0 10 20 30 40 50 60 70
-300 -250 -200 -150 -100 -50 0 50
K0
MSE in dB
Figure 5.5 Averaged MSE versus of an all-pilot preamble system, NT=2, assumed a static two-ray model
K0
0 5 10 15 20 25 30 10-5
10-4 10-3 10-2 10-1 100
SNR in dB
BER in logarithm scale
K0=15, Tx=2 K0=12, Tx=2 K0=10, Tx=2 K0=18, Tx=2 K0=20, Tx=2 K0=22, Tx=2 K0=24, Tx=2
Figure 5.6 BER comparison due to various values, all-pilot-preamble, with NT=2, NR =1, assumed a static two-ray model
K0
The BER comparison is shown in Figure 5.6. The BER versus SNR curves show the same trend as the MSE curve. The curve =15 outperforms all other curves. From this result, one can conclude that the best choice of is length of the channel.
K0
K0
In the following simulations, Rayleigh fading channels are assumed. The power delay profiles are set to Model 1 and Model 2. In a single packet, there are 10 OFDM symbols. From Figure 5.4 to 5.6, we can obtain two conclusions. First, should be
large enough to include all the delay taps in time domain. In 5.4 (b) and 5.4 (c), is smaller than the maximum delay spread (8 in this case). Therefore, there are more noticeable mismatches between estimated taps and the actual taps, than in the case of
K0
K0
enough . Another conclusion is that should not be too large. A more than
enough will include noise and CCI on those null taps. For example, all four major taps are well caught by the extra channel estimator as shown in Figure 5.4 (a), but additional interference can also be observed on those 15 taps ( =15). The mentioned two conditions cause the performance degradation in the channel estimation.
K0 K0
K0
K0
0 5 10 15 20 25 30
10-6 10-5 10-4 10-3 10-2 10-1 100
SNR in dB
BER in logarithm scale
K0=64, Tx=2 K0=48, Tx=2 K0=36, Tx=2 K0=24, Tx=2 K0=12, Tx=2 K0=8, Tx=2 K0=4, Tx=2
(a)
0 5 10 15 20 25 30 10-7
10-6 10-5 10-4 10-3 10-2 10-1 100
SNR in dB
BER in logarithm scale
K0=64, Tx=2 K0=48, Tx=2 K0=36, Tx=2 K0=24, Tx=2 K0=12, Tx=2 K0=8, Tx=2 K0=4, Tx=2
(b)
Figure 5.7 BER comparison due to various values, all-pilot-preamble, with NT=2, NR =1(a) Model 1 (b) Model 2
K0
0 5 10 15 20 25 30
10-6 10-5 10-4 10-3 10-2 10-1 100
SNR in dB
BER in logarithm scale
K0=64, Tx=3 K0=48, Tx=3 K0=36, Tx=3 K0=24, Tx=3 K0=12, Tx=3 K0=8, Tx=3 K0=4, Tx=3
(a)
0 5 10 15 20 25 30 10-6
10-5 10-4 10-3 10-2 10-1 100
SNR in dB
BER in logarithm scale
K0=64, Tx=3 K0=48, Tx=3 K0=36, Tx=3 K0=24, Tx=3 K0=12, Tx=3 K0=8, Tx=3 K0=4, Tx=3
(b)
Figure 5.8 BER comparison due to various values, all-pilot-preamble, with NT=3, NR =1 (a) Model 1 (b) Model 2
K0
0 5 10 15 20 25 30
10-5 10-4 10-3 10-2 10-1 100
SNR in dB
BER in logarithm scale
K0=64, Tx=4 K0=48, Tx=4 K0=36, Tx=4 K0=24, Tx=4 K0=12, Tx=4 K0=8, Tx=4 K0=4, Tx=4
(a)
0 5 10 15 20 25 30 10-4
10-3 10-2 10-1 100
SNR in dB
BER in logarithm scale
K0=64, Tx=4 K0=48, Tx=4 K0=36, Tx=4 K0=24, Tx=4 K0=12, Tx=4 K0=8, Tx=4 K0=4, Tx=4
(b)
Figure 5.9 BER comparison due to various values, all-pilot-preamble, with NT=4, NR =1 (a) Model 1 (b) Model 2
K0
In Figure 5.7 (a) and (b), BER versus SNR curves with different are shown for NT=2. According to previous statements, inadequate ’s have worse
performances than that of exact . However, the lengths of Model 1 and Model 2 indoor wireless channels are not very long, and the multipath powers of last few paths are quite small (smaller than -13 dB). The small taps are not very significant compared with additive noise. For this reason, the performance degradation with small is not obviously in our simulations. When we discuss the simulation results, it is noted that the maximum delay spread of is 3 in Model 1, and 11 in Model 2. In Figure 5.7 (a), =4 provides best performance among several different . In
K0
K0
K0
K0
K0 K0
(b), =8 outperforms other ’s. As a result, decision of is crucial to the
performance of the channel estimation. Set to the maximum delay spread is a good choice. In Figure 5.8 and 5.9, one can see that the influence of CCI increases when the number of transmission antennas is larger. There are significant error floors in high SNR condition while the number is 4. In Figure 5.10 to 5.12, the cases of multiple receiver antennas are simulated. One can see that the receiver diversity provides better performance while multiple receiver antennas are used. For example, the error floor in Figure 5.9(a) is improved in Figure 5.12.
K0 K0 K0
K0
0 5 10 15 20 25 30
10-6 10-5 10-4 10-3 10-2 10-1 100
SNR in dB
BER in logarithm scale
K0=36, Tx=2, Rx=2 K0=24, Tx=2, Rx=2 K0=12, Tx=2, Rx=2 K0=8, Tx=2, Rx=2
Figure 5.10 BER comparison due to various values, all-pilot-preamble, NT=2, NR =2 (Model 1)
K0
0 2 4 6 8 10 12 14 10-6
10-5 10-4 10-3 10-2 10-1
SNR in dB
BER in logarithm scale
K0=36, Tx=3 K0=24, Tx=3 K0=12, Tx=3 K0=8, Tx=3
Figure 5.11 BER comparison due to various values, all-pilot-preamble, NT=3, NR =3 (Model 1)
K0
0 2 4 6 8 10 12
10-6 10-5 10-4 10-3 10-2 10-1
SNR in dB
BER in logarithm scale
K0=36, Tx=4 K0=24, Tx=4 K0=12, Tx=4 K0=8, Tx=4
Figure 5.12 BER comparison due to various values, all-pilot-preamble, NT=4, NR =4 (Model 1)
K0
0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 -60
-50 -40 -30 -20 -10 0 10 20 30 40
K0
MSE in dB
MSE of Estimated Channels (Model 1), Tx=2
(a)
0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64
-40 -30 -20 -10 0 10 20 30 40
K0
MSE in dB
MSE of Estimated Channels (Model 2), Tx=2
(b)
Figure 5.13 Averaged MSE versus of all-pilot preamble system, NT=2 (a) Model 1 (b) Model 2
K0
0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 -40
-20 0 20 40 60 80 100 120
K0
MSE in dB
MSE of Estimated Channels (Model 1), Tx=3
(a)
0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64
-20 0 20 40 60 80 100 120
K0
MSE in dB
MSE of Estimated Channels (Model 2), Tx=3
(b)
Figure 5.14 Averaged MSE versus of all-pilot preamble system, NT=3 (a) Model 1 (b) Model 2
K0
0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 -40
-20 0 20 40 60 80 100 120
K0
MSE in dB
MSE of Estimated Channels (Model 1), Tx=4
(a)
0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64
-20 0 20 40 60 80 100
K0
MSE in dB
MSE of Estimated Channels (Model 2), Tx=4
(b)
Figure 5.15 Averaged MSE versus of all-pilot preamble system, with NT=4 (a) Model 1 (b) Model 2
K0
The MSE versus plot is also shown in Figure 5.13 to Figure 5.15. In the figures, the channels are estimated with SNR set to 40dB. MSE in this plot is the mean of both estimated channels from two antennas. In this case, co-channel interference dominates the MSE performance. One can obtain that if is smaller than the max delay spread (4 in Model 1 and 12 in Model 2), the MSE is relative large due to insufficient . If is chosen to be close to the max delay spread, the
performance is relative good. As grows, the estimated channels include more taps with interference. For this reason, MSE gets larger in this region.
K0
K0
K0 K0
K0
In Figure 5.16 to Figure 5.19, converge curves of the proposed modification for the LS estimator in 4.2.3.2 are presented. In every OFDM packet, the channel length is estimated again. The curves illustrate the converge of corresponding MSE and values of . In Figure 5.16 to 5.19, one can see that the MSE converge to low value after a few iterations. For the case of four receiver antennas, the curve can’t converge in present simulations. The improvement will be one of the future works.
K0
0 5 10 15 20 25 30
Average MSE of estimated channels (dB)
Converage MSE curve of proposed method (Model 1)
0 5 10 15 20 25 30
Corresponding K0 curve of proposed method (Model 1)
Figure 5.16 MSE and curves versus iteration no. of proposed decision algorithm,
Average MSE of estimated channels (dB)
Converage MSE curve of proposed method (Model 2)
0 5 10 15 20 25 30
Corresponding K0 curve of proposed method (Model 2)
Figure 5.17 MSE and curves versus iteration no. of proposed decision
algorithm,
K0 K0
T 2
N = (Model 2)
0 5 10 15 20 25 30
Average MSE of estimated channels (dB)
Converage MSE curve of proposed method (Model 1)
0 5 10 15 20 25 30
Corresponding K0 curve of proposed method (Model 1)
Figure 5.18 MSE and curves versus iteration no. of proposed decision algorithm,
Average MSE of estimated channels (dB)
Converage MSE curve of proposed method (Model 2)
0 5 10 15 20 25 30
Corresponding K0 curve of proposed method (Model 2)
Figure 5.19 MSE and curves versus iteration no. of proposed decision algorithm,
K0 K0
T 3
N = (Model 2)
5.2.3 Channel Estimation for MIMO OFDM Systems
with Scattered Preamble
The scattered preamble MIMO OFDM system uses partial tones for each antenna to estimate channel parameters. After the responses on pilot tones are estimated by LS-based technique, there are still unknown responses on the non-pilot tones. These unknown values can be obtained by interpolation techniques. In our studies, transform-domain interpolation techniques are considered applied to those equi-spaced pilots. The equi-spaced pilots can be viewed as downsampled version of real channel response, and we can apply transform-domain interpolation techniques in this case.
0 10 20 30 40 50 60 70
0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
Subcarruier Index
Magnitude
Estimated Response by DFT-based Method Real Channel Frequency Response
(a)
0 10 20 30 40 50 60 70
0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
Subcarruier Index
Magnitude
Estimated Response by DCT-based Method Real Channel Frequency Response
(b)
0 10 20 30 40 50 60 70
0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6
Subcarruier Index
Magnitude
Estimated Response by DFT-based Method Real Channel Frequency Response
(c)
0 10 20 30 40 50 60 70
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4
Subcarruier Index
Magnitude
Estimated Response by DCT-based Method Real Channel Frequency Response
(d)
Figure 5.20 Estimated Responses by DFT and DCT-based estimators (a) DFT with sample spaced channel (b) DCT with sample spaced channel (c) DFT with
non-sample spaced channel (d) DCT with non-sample spaced channel
In the following simulations, Rayleigh fading channels are assumed. The power delay profiles are set to Model 1 and Model 2. In a single packet, there are 10 OFDM symbols. The pilots from different antennas are located alternately in all subcarriers of preamble symbol. The estimated responses are shown in Figure 5.20 (a)-(d). In Figure 5.20 (a) and (b), the two estimators are applied to the sample spaced channel described in Table 5.2. As shown in the figure, the estimated responses are not much different. But in Figure 5.20 (c) and (d), we can find that the DFT-based estimator is not good for the non-sample spaced channel while DCT-based estimator works well.
0 5 10 15 20 25 30 10-6
10-5 10-4 10-3 10-2 10-1 100
SNR in dB
BER
Linear Cubic Spline DFT-based DCT-based
(a)
0 5 10 15 20 25 30
10-7 10-6 10-5 10-4 10-3 10-2 10-1 100
SNR in dB
BER
Linear Cubic Spline DFT-based DCT-based
(b)
Figure 5.21 BER comparisons of various interpolation methods under non-sample spaced channels (a) Model 1 (b) Model 2
The curves shown in Figure 5.21 are BER versus SNR for some major interpolations in non-sample-spaced channel Model 1 and 2. Since Model 2 has stronger frequency selectivity than model 1, it enhances the performance difference between those interpolation techniques. Unexpectedly, the performance of cubic spline interpolation is the worst of all those techniques. This would be against our intuition that cubic spline interpolation has the best function continuity of all those interpolation functions. However, this may be reasonable considering the additive noise effect on the accuracy of the assumed boundary function values and the derivative values of the interpolated segments. Comparing DFT and DCT -based channel estimators, we can find that the DCT-based estimator has better performance than conventional DFT-based estimator. It shows that the aliasing effect due to non-sample spaced channel effect mentioned in Chapter 4 can be mitigated by applying the DCT-based interpolation technique. However, the difference in the 802.11n-like systems is not so obviously compared with 802.16a system. The non-sample spaced effect may be considered to be stronger in typical 802.16a channel (e.g. ETSI A) than Model 1 and Model 2 channels. This is because the power and delay spread are relative large in typical 802.16a channels.
5.3 Channel Estimation for 802.16a OFDMA
with STC
In this section, the channel estimation of 802.16a will be explored. 802.16a is an OFDM system with pilot symbol aided modulation . Therefore there are data tones and pilot tones in a single OFDM symbol. The channel estimation and data detection flows are shown in Figure 5.22. It is noted that interpolation techniques are required
after estimation on pilot tones. Compared to scattered block type MIMO OFDM systems, the estimation is more complicated due to special arrangement in 802.16a.
When it comes to scattered block type systems, the pilot tones for each antenna are regularly distributed in preamble OFDM symbols. However, this is different in 802.16a system. As mentioned in Chapter 3, the pilots are classified into fixed and variable position types in 802.16a OFDMA, and it makes channel estimation more complicated. It will be further explored in this subsection.
Table 5.6 Simulation parameters of 802.16a STC system (2 x 1)
Bandwidth 10Mhz
Sample Frequency 11.42Mhz
Carrier Spacing 5.576KHz
GI Length 22.4µs(256 pts)
OFDM Symbol Length 201.75µs (2048 pts+256 pts)
NFFT 2048 pts
Modulation QPSK
Number of Fixed Pilots 32
Number of Variable Pilots 142
Number of Data Tones 1702
Space Time Coding STBC
Estimate channel response on pilot tones by space-time
coding.
Obtain channel response on data tones by interpolation.
With channel response on all tones, solve STC coded
data.
Figure 5.22 Channel estimation and data detection flow of 802.16a with STC
5.3.1 Pilot Sample Grouping for 2-D Channel
Estimations
For downlink of 802.16a system, each subcarrier appears as an pilot subcarrier once for every four consecutive OFDM symbols. In addition, the pilot tones repeat for every three subcarriers in frequency domain. This arrangement is shown in Figure 5.23 (a)-(c). If we want to compose more pilot subcarriers than in one symbol, we need to combine variable-position pilots from a few consecutive OFDM symbols. We will discuss several possible group schemes in the remaining subsection, and consider both BER and SER performance. Besides, buffer size (number of OFDM symbols reserved to do interpolation) will be considered in the studies.
Scheme 1, merging of multiple symbols: The pilot positions vary cyclically with different offset in consecutive OFDM symbols. One may assume the channel response varies slowly from symbol to symbol in a low mobility environment, and the response won’t change very significantly. A most intuitive solution is to reserve four OFDM symbols in the buffer, and take the response estimated on the only pilot subcarrier as
Scheme 1, merging of multiple symbols: The pilot positions vary cyclically with different offset in consecutive OFDM symbols. One may assume the channel response varies slowly from symbol to symbol in a low mobility environment, and the response won’t change very significantly. A most intuitive solution is to reserve four OFDM symbols in the buffer, and take the response estimated on the only pilot subcarrier as