0.11 Timing recovery  (Page 7/11)

Use clockrecDD.m to “play with” the clock recovery algorithm.

1. How does mu affect the convergence rate? What range of stepsizesworks?
2. How does the signal constellation of the input affect the convergent value of tau ? (Try 2-PAM and 6-PAM. Remember to quantize properlyin the algorithm update.)

Implement a rectangular pulse shape. Does this work better or worse than the SRRC?

Add noise to the signal (add a zero mean noise to the received signal using theM atlab randn function). How does this affect the convergence of the timing offset parameter tau . Does it change the final converged value?

Modify clockrecDD.m by setting toffset=-0.8 . This starts the iteration in a closed eye situation. How many iterations does it take to open the eye?What is the convergent value?

Modify clockrecDD.m by changing the channel. How does this affect the convergence speed of thealgorithm? Do different channels change the convergent value? Can you think of a way to predict (given a channel)what the convergent value will be?

Modify the algorithm [link] so that it minimizes the source recovery error ${(s[k-d]-x\left[k\right])}^2$ , where $d$ is some (integer) delay. You will need to assume that the message $s\left[k\right]$ is known at the receiver. Implement the algorithm by modifying the code in clockrecDDcost.m . Compare the new algorithm with the old in terms of convergence speedand final convergent value.

Using the source recovery error algorithm of [link] , examine the effect of different pulse shapes. Draw the error surfaces(mimic the code in clockrecDDcost.m ). What happens when you have the wrong $d$ ? The right $d$ ?

Investigate how the error surface depends on the input signal.

1. Draw the error surface for the DD timing recovery algorithm when the inputs are binary $\pm 1$ .
2. Draw the error surface when the inputs are drawn from the 4-PAMconstellation, for the special case in which the symbol $-3$ never occurs.