Page 22 - Artificial Intelligence in the Age of Neural Networks and Brain Computing

4. Robert Lucky’s Adaptive Equalization, From the 1960s 9

Binary Data Pulses Telephone
Data Transmitter Channel Channel
Stream Output

Strobe

Weights
w 1k
z -1 Summer
w 2k
-1
Tapped z ( SUM ) k +1 q k Received
Delay -1 w 3k  Data
Line z -1 Stream
z -1 Signum
w nk
Â
e k – + d = q k
k
Gate
Error

Strobe
FIGURE 1.5
Decision-directed learning for channel equalization.

The quantized output can accordingly be taken as the desired output, and the differ-
ence between the quantized output and the summed signal will be the error signal for
adaptive purposes. This difference will only be usable as the error signal at times
when the sinc functions are at their peak magnitudes. A strobe pulse samples the
error signal at the Nyquist rate, timed to the sinc function peak, and the error samples
are used to adapt the weights. The output decision is taken to be the desired response.
Thus, decision-directed learning results.
With some channel distortion, the signum output will not always be correct, at
peak times. The equalizer can start with an error rate of 25% and automatically
8
converge to an error rate of perhaps 10 , depending on the noise level in the
channel.
Fig. 1.6A shows the output of a telephone channel without equalization.
Fig. 1.6B shows the same channel with the same dataflow after adaptive equaliza-
tion. These patterns are created by overlaying cycles of the waveform before and af-
ter equalization. The effect of equalization is to make the impulse responses
approximate sinc functions. When this is done, an “eye pattern” as in Fig. 1.6B re-
sults. Opening the eye is the purpose of adaptation. With the eye open and when
sampling at the appropriate time, ones and zeros are easily discerned. The adaptive
algorithm keeps the ones tightly clustered together and well separated from the zeros
which are also tightly clustered together. The ones and zeros comprise two distinct
clusters. This is decision directed learning, similar to bootstrap learning.