8-PAM with low SNR

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4.1 8-PAM with low SNR

For this example, the SNR is 10 dB, the source is unit variance 8-PAM, a 2-tap FSE is used, and the channel is given by $\ensuremath{\mathbf{c}}=\left[\begin{array} {cccc}0.2&0.5&1&-0.1\end{array}\right]^T$ . With these system parameters, $\gamma$ is chosen to be $\gamma_1=1.1905$ via (6) or $\gamma_2=1.4817$ via (8). Using (7), I plotted the cost contour and found that the location of the SE-CMA minima are closer to the MMSE minima when $\gamma$ is chosen via (6).

A numeric simulation was also performed. For 300,000 iterations with $\mu=10^{-4}$ , a portion of the squared-error history is shown in Figure 11.

**Figure 11:** Squared error history for low SNR example
$\begin{figure} \begin{center} \epsfxsize=3in \epsfbox{errdat1.eps} \end{center} \end{figure}$

It is obvious that by using $\gamma_1$ a lower error is obtained.

Therefore, I have shown that in low SNR conditions, using (8) to choose $\gamma$ does not always yield a superior result over the noiseless selection of $\gamma$ via (6). However, this result may be insignificant since any channel with a poor SNR of 10 dB is probably not a good candidate for blind equalization via SE-CMA with an 8-PAM source.

Next: 8-PAM with undermodeled channel Up: Selection of in the Previous: Selection of in the

Andrew Grant Klein
8/12/1998