0.9 Carrier recovery  (Page 15/19)

The direct calculation of $\frac{dx\left(k{T}_s\right)}{d\theta }$ as a filtered version of [link] is only one way to calculate the derivative. Replace this using a numericalapproximation (such as the forward or backward Euler, or the trapezoidal rule). Compare the performance of your algorithmto plldd.m .

Consider the DD phase tracking algorithm when the message alphabet is binary $\pm 1$ .

1. Modify plldd.m to simulate this case.
2. Modify plldderrsys.m to draw the error surface. Is the DD algorithm better (or worse) suited to the binarycase than the 4-PAM case?

Consider the DD phase tracking algorithm when the message alphabet is 6-PAM.

1. Modify plldd.m to simulate this case.
2. Modify plldderrsys.m to draw the error surface. Is the DD algorithm better (or worse) suited to 6-PAM than to 4-PAM?

What happens when the number of inputs used to calculate the error surface is too small? Try $N=100,10,1$ . Can $N$ be too large?

Investigate how the error surface depends on the input signal.

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

TRUE or FALSE: Decision-directed phase recovery can exhibit local minimaof different depths.

This problem uses the $B^3$ $I$ $G$ to test the carrier recovery algorithm of your choice.

1. Currently, the receiver portion of the script in BigIdeal.m “knows” the phase of the carrier. Add a carrier recovery algorithm of your choice to BigIdeal.m so that the receiver can accommodate unknown carrier phases. Run the modified code and usethe carrier recovery algorithm to estimate the phase offset $\Phi$ . State the carrier recovery method used and plot the tracking of $\Phi$ . If the receiver employs preprocessing, take care to design the BPF appropriately.
2. Modify the $B^3$ $I$ $G$ so that a phase offset is introduced. In BigTransmitter.m , set the variable phi=-0.5 , and add a phase offset x_rf=x.*cos(2*pi*rfParams.f_if_tx*... [1:length(x)]'*rfParams.T_t_tx/M+p_noise+phi); where upconversion is performed. Rerun the code. How does the behavior of your algorithm differ?Include plots to justify your claim.
3. Repeat part (b) for the case when phi=1.2 .