Computer Simulations
4.4 Parameters of channel tracking
4.4.1 Effects of training length
The size of length of training interval will influence the amount of transmitted data symbols. In other words, large length of train interval implies that data symbol of total transmission data will be much more. The accuracy of channel tracking is important in large length of train interval. In this subsection will simulate length of train interval effect for channel tracking structure.
Before seeing these simulations, parameter setting be must first explained. The parameter of system setting is η=67%, Ω=2 and fD =50Hz. Three different methods in will be used these simulations, they are the tracking zero (TZ), channel tracking structure by using LMS algorithm and RLS algorithm. The step-size of LMS algorithm is set to 0.008 and forgetting factor of RLS algorithm is setting 0.995. As mentioned above, we now see MSE of channel in Fig. 4.9.
Figure 4.9 MSE of channel on effect of length of training interval
From Fig. 4.9, as SNR increases, their MSE will improve. TZ (circular point) method is the worst because of no channel tracking. So, when true channel changes, estimated channels are not to following variation of successive two training symbols.
Therefore, its MSE is worst in three methods. The performance of LMS (up-triangular point) method is worse than the RLS (diamond point) method. This is because convergence rate of RLS is faster. In LMS method, it has the slow tracking problem in high SNR and the convergence problem in low SNR, which bill be explained in by Fig. 4.10 and 4.11
Figure 4.10 Profile of MSE with SNR=35dB
Figure 4.11 Profile of MSE with SNR=10dB
Fig. 4.10 and 4.11 are MSE versus length of training interval. From Fig. 4.10, MSE of
the TZ method is the worst because it does not follow to variant channel. LMS method has the problem of slow tracking. Thus, estimated channel is not to following true channel variation. When the length of training symbol is too large, its MSE will be much worse. For RLS method, its convergence rate is very fast. This implies that estimated channel can follow true channel. So basically RLS method is better in its tracking capability and it is not influenced by the size of length of training interval.
Fig. 4.11 is similar to Fig. 4.10, except for the LMS method whose performance is just the opposite. Because, in low SNR, its convergence time needs to be longer.
When length of training interval is smaller, estimated channel has not yet completely followed true channel and it is again reset to do channel tracking. So, in case of longer length of training interval, its MSE will be better.
Next, we will see the SER performance of three methods in Fig. 4.12
Figure 4.12 SER on effect of length of training interval
MSE of channel is very small, their SER is not easy to compare. In this figure, TZ method fails to demodulate data symbol because of its inaccuracy in channel tracking.
4.4.2 The effect of time variant of channel
Effect of time variancy means that time variant channel will influence channel tracking structure. So, this system will be tested by different Doppler frequency shifts.
For convenience, system parameters are η =67%, Λ=100 and Ω=2. Doppler frequency shift is from 50Hz to 500Hz. Step-size and forgetting factor are same as before. MSE versus Doppler frequency shift at SNR=35dB is showed in Fig 4.13 and SER of effect of time variant is showed in Fig 4.14.
Figure 4.13 MSE of channel on effect of time variant
Figure 4.14 SER on effect of time variant
From Fig. 4.13, we can clearly know when Doppler frequency shift increases, their MSE become worse. Although MSE of the RLS method is affected under effect of time variant, but, its performance is the best among these channel tracking methods. Fig. 4.14 is SER of these methods. When Doppler frequency shift is smaller (the group of solid- line), TZ method is slightly worse than LMS and RLS methods and LMS and RLS methods are very similar. With a slow-changing channel, these their MSEs are smaller. When channel changing is very fast (the group of dash- line), their MSE of channel becomes worse. So, their SER are worse than small Doppler frequency. From results of these simulations, we can know when channels are changing very fast, accuracy of estimated channel will be reduced and let their SER become worse.
4.4.3 Efficiency of bandwidth usage
Next, we will test to adjust efficiency of bandwidth usage in channel tracking structure. The parameters are Ω=2 , fD =50Hz and Λ=100 . Efficiency of bandwidth usage of 67%,85% and 100% will be tested in all system. MSE and SER are showed in Fig. 4.15 and 4.16, respectively.
Fig. 4.15 MSE of channel on different bandwidth usage efficiency
Figure 4.16 SER performances on different bandwidth usage efficiency
In Fig. 4.15 and 4.16, the group of solid- line is LMS method and the group of dash- line is RLS method. Fig. 4.14 clearly shows RLS method is slightly better than LMS method. When efficiency of bandwidth usage is larger, their MSE will be worse because of more serious IBI and ICI. But, their MSE can be still accepted. So, their SER are not very bad. In Fig. 4.16, SER of RLS method are a little better than LMS method. Furthermore, as the efficiency of bandwidth usage increases, its performance of SER will be decreased. In a word, large efficiency of bandwidth usage has poor performance of MSE of SER is worse, but its efficiency of bandwidth usage is better.