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Results

We have implemented both the filters based on RBF and that based on FBF on a TMS-C30 chip. The results were obtained by cross compiling the C code on a TMS-C30 cross compiler. The channel model selected was H(z)=1+0.5z^-1 and the output was mixed with additive white gaussian noise (AWGN). The SNR was varied and all the different types of filters were applied. The BER for different filters are as shown in fig. 3.

**Figure 3:** BER of different equalizers with Channel 1.0 + 0.5z^-1, and varying SNR
$\begin{figure}\hspace{-5mm} \mbox{\centerline{\psfig{figure=fuzzy.ps,height=2.5in}} } \end{figure}$

The decesion boundry for the case of RBF equalizer trained through the clustering algorithm is obtained as shown in fig. 4.

**Figure:** Channel 1.0 + 0.5z^-1, co-channel 0.346(1.0+0.2z^-1),m=2 and $\tau$ =0. $\Diamond$ and + : desired channel states. $\Box$ :inter-channel interference centres, SIR = 10dB, SNR = 20 dB, SINR = 9.6 dB.
$\begin{figure}\hspace{-5mm} \mbox{\centerline{\psfig{figure=fig2.ps,height=2.5in}} } \end{figure}$

If the co-channel interference is also present then the ideal distribution of states and the optimal boundry can be demonstrated as in fig. 5.

**Figure:** Channel 1.0 + 0.5z^-1, co-channel 0.346(1.0+0.2z^-1),m=2 and $\tau$ =0. $\Box$ and + : desired channel states. $\Diamond$ :co-channel interference centres, SIR = 10dB, SNR = 20 dB, SINR = 9.6 dB.
$\begin{figure}\hspace{-5mm} \mbox{\centerline{\psfig{figure=fig1.ps,height=2.5in}} } \end{figure}$

The RBF equalizer decesion function in the case of co-channel interference after being trained is represented in fig. 6.

**Figure:** Channel 1.0 + 0.5z^-1, co-channel 0.346(1.0+0.2z^-1),m=2 and $\tau$ =0. $\Box$ and + : desired channel states. $\Diamond$ :ideal co-channel interference centres and x centres after two phases of training, SIR = 10dB, SNR = 20 dB, SINR = 9.6 dB.
$\begin{figure}\hspace{-5mm} \mbox{\centerline{\psfig{figure=fig3.ps,height=2.5in}} } \end{figure}$

The simulation was performed on a channel with severe distortion, with transfer function H(z)=0.1482+0.8704z^-1+0.1483z^-2, the typical results obtained on the TMS-C30 chip are as follows.

Algo.	Data samples	BER	Clock cycle x 60ns
1	400	0.1125	712175
2	400	0.0925	632260
3	400	0.1125	687256
4	400	0.1200	595126

This simulation was carried out on 400 data samples, and the BER which resulted due to sigmoid function was 0.135. The SNR was low of the order of 7 dB. Algorithm 1 is the simple RBF, 2 is FBF with minimum inference and centre of gravity (COG) defuzzifier [eqn. (7)], 3 is FBF with maximum defuzzifier and product inference [eqn. (8)], 4 is FBF with minimum inference and maximum defuzzifier [eqn. (9)]. Much better results can be obtained if the code is optimized.

The simulation was also done on a severely distorted channel, with transfer function H(z)=0.1482+0.8704z^-1+0.1483z^-2 and a similar co-channel, with SIR=10dB, The BER plots obtained are as shown in fig. 7

**Figure:** Channel 0.1482+0.8704z^-1+0.1483z^-2, co-channel 0.346(H(z)=0.1482+0.8704z^-1+0.1483z^-2),m=3 and $\tau$ =1. SIR = 10dB, SNR = 20dB, SINR = 9.6 dB.
$\begin{figure}\hspace{-5mm} \mbox{\centerline{\psfig{figure=fbf_cci_3.ps,height=2.5in}} } \end{figure}$

Next: Conclusion Up: Fuzzy Equalization of Digital Previous: Results

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1999-02-04

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