Comparison of different channel model

In this paragraph, the different channel model is discussed in MSE performance. We fix the training rate as 1/4; the Doppler frequency as 100Hz and 150Hz. Polynomial order is set to two. The MSE performances with different channel model (TV Channel-A and TV Channel-B) are observed in Figure 4.11.

0 5 10 15 20 25 30 35 40 45 50

−55

−50

−45

−40

−35

−30

−25

−20

−15

−10

−5

SNR (dB)

MSE (dB)

TV Channel−A,f_d=150Hz TV Channel−A,f_d=200Hz TV Channel−B,f_d=150Hz TV Channel−B,f_d=200Hz

Fig. 4.11 Channel estimation MSE in TV Channel-A and TV Channel-B and f = _d 150Hz, 200Hz.

The TV Channel-A has the same delay spread with the TV Channel-B. Figure 4.11 is also divided into two parts in order to distinguish the model error and noise error. The first part is low SNR region. The noise error dominates MSE performance in this

section. The second part is high SNR region. The model error dominates MSE performance in this region. The noise error is independent of Doppler frequency and channel model, because these curves overlap in the low SNR region. In high SNR region, the MSE curves have error floor. This error floor is the model error. The model errors in the same Doppler frequency have a little difference between two channel models. MSE performance of TV channel B is a little better than MSE performance of TV Channel A.

We observe sensitivity of the model error and noise error in this section. Then we find that noise error is nonsensitive totally to the channel condition. The noise error is only sensitive to training rate and polynomial order. The model error is sensitive to all parameters observed in this section. In the low SNR region, the noise error dominates the MSE performance. Since the noise error is not sensitive to channel, we can say the sub-symbol polynomial interpolation is robust channel estimation method in the low SNR region. But the width of low SNR region is relative to the model error. In bad channel condition, large Doppler frequency, the model error may be large and cause error floor from a low SNR value.

Chapter 5 Conclusion

Channel estimation of time varying channel is a challenge because of tracking channel variation. We introduce several interpolation techniques to track channel variation. The FPTA or MST with decision directed algorithm is intolerable in simulation results because of large decision error. The linear interpolation is the simplest way to track channel variation, but the large model error will occur in high Doppler frequency environment and low training rate system. In high Doppler shift, variation of channel is more like a polynomial function whose order is more than one.

Low training rate system has a long duration between two training symbol. Linear approach of channel is not suitable for this long duration. In fast fading channel, we propose the sub-symbol polynomial interpolation, together with the MST algorithm to reduce the model error of linear interpolation. We analyze the MSE of sub-symbol polynomial interpolation, and the MSE is divided into two parts. One is the noise error, the other is the model error. For the noise error, we find that it is independent of the Doppler frequency and other statistics of channel. The noise error depends on to training rate and polynomial order. The performance of the noise error becomes worse

by decreasing training rate and increasing polynomial order. The model error is sensitive to the Doppler frequency, statistics of channel, training rate and polynomial order. The model error becomes worse by increasing Doppler frequency, decreasing training rate and decreasing polynomial order.

The MST algorithm can be used in sub-symbol polynomial interpolation. There are two advantages of most significant taps selection. It reduces the computation and suppresses noise. But the MST method has a problem of missing taps. The error floor of MSE will appear when missing taps occurs. In the Chapter 2, we also analyze MSE of MST method under missing taps. The results of analysis reveal that the error floor is equal to the power of missed taps.

In the fast fading channel, we propose sub-symbol polynomial interpolation.

Because it can collect more information of time varying channel, it has better performance than other algorithms which are mentioned before. Combing with most significant taps algorithm, the sub-symbol polynomial interpolation will perform better in noise suppression and load of computation.

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