0.12 Linear equalization  (Page 14/17)

Try the initialization f=[0 0 0 0]' in DMAequalizer.m . With this initialization, can the algorithm open the eye? Tryincreasing m . Try changing the stepsize mu . What other nonzero initializations will work?

What happens in DMAequalizer.m when the stepsize parameter mu is too large? What happens when it is too small?

Add (uncorrelated, normally distributed) noise into the simulation using the command r=filter(b,1,s)+sd*randn(size(s)) . What is the largest sd you can add, and still have no errors? Does the initial value for f influence this number? Try at least three initializations.

Use DMAequalizer.m to find an equalizer that can open the eye for the channel b=[1 1 -0.8 -.3 1 1] .

1. What equalizer length n is needed?
2. What initializations for f did you use?
3. How does the converged answer compare with the designs in Exercises  [link] , [link] , and [link] ?

Modify DMAequalizer.m to generate a source sequence from the alphabet $\pm 1,\pm 3$ . For the default channel [0.5 1 -0.6] , find an equalizer that opens the eye.

1. What equalizer length n is needed?
2. What is an appropriate value of $\gamma$ ?
3. What initializations for f did you use?
4. Is this a fundamentally easier or more difficult task than when equalizing a binary source?
5. How does the answer compare with the designs in Exercises  [link] , [link] , and  [link] ?

Consider a DMA-like performance function $J=\frac{1}{2}\text{avg}\left\{\right|1-y^2\left[k\right]\left|\right\}$ . Show that the resulting gradient algorithm is

Hint: Assume that the derivative of the absolute value is the sign function.Implement the algorithm and compare its performance with the DMA of [link] in terms of

1. speed of convergence,
2. number of errors in a noisy environment (recall [link] ), and
3. ease of initialization.

Consider a DMA-like performance function $J=\text{avg}\left\{\right|1-\left|y\right[k\left]\right|\left|\right\}$ . What is the resulting gradient algorithm?Implement your algorithm and compare its performance with the DMA of [link] in terms of

1. speed of convergence of the equalizer coefficients f ,
2. number of errors in a noisy environment (recall [link] ), and
3. ease of initialization.