Comparisons of All Methods of Time Domain Improvement

'    2

 (5.11)

Then we compute FFT only one time at the first, and the latter channel frequency response can be obtained by the linear operation of the summation of the product of Rayleigh parameter and the^{    2 } .

5.4.1 Comparisons of All Methods of Time Domain Improvement

After simulating our methods on Raleigh fading channel, the LMS adaptation and the exponential average schemes do not perform as well as they do in static channels. There-fore, we take the two methods and the moving average one as well to compare together.

The comparison of the three algorithm is show in Fig. 5.10.

The SER of LMS adaptaion with ^ =1 even amounts to ^{  } , which is the same as guessing the result. That is because the LMS adaptation method uses the pilot informa-tion only at the first symbol, and the step-size parameter in LMS adaptainforma-tion may not be large enough to correct the error caused by the fading channel. The performace improves much when^ =0.5 and 0.2 individually. And the main problem of the exponential average method is that we take all ther former symbols to eliminate the noise term. However, the change in the channel frequency response may cause larger error than the eliminated noise term. Since the downlink frame is composed of^{ ' } symbols where ^ is a pos-tive integer, we could reset the data in the register every six symbols, and the (4.32) then becomes method with ^ =0.2 and 0.5, with and without reset are also shown in Fig. 5.10 and the performance is almost the same. When we use the reset strategy also in the LMS adaptation algorithm, and the result improves.

The moving average scheme, however, does not have a good outcome as we expected.

Though we calculated the coherence time to be 966.788 us with the center frequency =2 GHz, and the channel can be assumed to be static during five symbol times, the simulation of doing average with the data of five symbols did not improve as much as we thought.

The 2-D interpolation has the best performance among all the time domain interpo-lation methods. As in the case of static channels, the four sets of variable location pilots with second-order interpolation in the frequency domain gives the least SER in Fig. 5.11.

In Fig. 5.11, the line marked “ideal” refers to the ideal case when we know the exact channel frequency response. Thus the symbol errors come only from the additive noise.

And the performance difference between the best one among all, which is the four sets variable location pilots with second-order interplation, and the ideal case is about 2.5 dB when the velocity of the receiver is 27 km/h and is about 5 dB when the velocity is 54 km/h.

But there is a shortcome of 2-D interpolation. As we mentioned in the static channel simulation, we needed seven symbols to get enough information for 2-D interpolation. In the first seven symbols, the channel estimation is done by only 1-D interpolation. Thus we can use two kinds of strategies for the first seven symbols and the latter ones seperately.

Note there is also an error floor when the



increases. This is due to the change in the channel frequency response dominates the noise term and therefore, even though the noise decreases, the value of the symbol error rate still remains unreduced.

10 15 20 25 30 35 40 Exponential Average with reset omega=0.2 Exponential Average with reset omega=0.5 Moving Average Exponential Average with reset omega=0.2 Exponential Average with reset omega=0.5 Moving Average

V = 54 km/h

(b)

Fig. 5.10: The SER of the LMS and average all the former algorithm when  = (a) 27 km/h and (b) 54 km/h.

10 15 20 25 30 35 40

Chapter 6

Conclusion and Future Work

6.1 Conclusion

To do the downlink channel estimation in IEEE 802.16a, we got three main points: first, we had to use the pilot carriers to estimate the channel frequency response on the pilot subcarriers. Second, the interpolations are needed to estimate the channel frequency re-sponse on the rest subcarriers. And the third point was to obtain a better estimation by time domain improvement schemes.

We used LS estimator instead of the LMMSE one not only for the complexity con-cern but also dued to the unknown statistical properties of channels. And the three kind of interpolation were compared, linear, second-order, and the cubic spline interpolation.

The four kind of time-domain improvement schemes were moving average, exponential average, the LMS adaptation and the 2-D interpolation.

Out of our expectation, the estimation errors of different interpolations from large to small were cubic spline, second-order, and linear. After doing the 2-D interpolation, the number of pilot carrier increased, and the second-order interpolation started to outperform the linear one as
^ grows. Therefore, not only the
^{ } but also the pilot spacing mattered for the efficiency of the interpolation.

We also found that, although we calculated the coherence time to be 966.788^ with the center frequency^{2 } =2 GHz, and the channel could be assumed to be static during five symbol times. The simulation of doing moving average with the data of five symbols did

not improve as much as we thought.

The 2-D interpolation of four sets of variable location pilots showed the best perfor-mance, but there were extra three multipliers, six adders and seven registers. And the computation complexity was the highest among all. With second-order interpolation, the 2-D interpolation had even a better result. However, to do the 2-D interpolation, there were seven symbols needed to be stored for enough information. The square error be-tween the estimated and the origin channl of the former seven symbols could affect the overall MSE much. For the data stream was not large, this error may dominate the out-come thus an error floor. Regardless the hardware complexity, we could use another structure and algorithm at the beginning to obtain the optimum performance and result.