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It is clear from the top plot of
[link] that
converges to a line. What line does it converge to?
Looking carefully at the data generated by
dualplls.m ,
the line can be calculated explicitly. The two pointsat
and
fit a line with slope
and an intercept
. Thus,
or
. Indeed, this was the value used in the
simulation. Reading the final converged value of
from
the simulation shown in middle plot gives
.
is
, which is almost exactly
away from
, the value
used in
phoff .
Use the preceding code to “play” with the frequency estimator.
f0 be from
fc before the estimates
deteriorate?mu ?
Should one be larger than other? Which one?Build a frequency estimator using two SD phase tracking algorithms, rather than two PLLs. How does the performance change?Which do you think is preferable?
Build a frequency estimator that incorporates the
preprocessing of the received signal from
[link] (as coded in
pllpreprocess.m ).
Build a frequency estimator using two Costas loops, rather than two PLLs. How does the performance change?Which do you think is preferable?
Investigate (via simulation) how the PLL functions when there is white noise
(using
randn ) added to the received signal.
Do the phase estimates becomeworse as the noise increases? Make a plot of the standard
deviation of the noise versus the average value of the phase estimates(after convergence).
Make a plot of the standarddeviation of the noise versus the jitter in the phase estimates.
Repeat [link] for the dual SD algorithm.
Repeat [link] for the dual Costas loop algorithm.
Repeat [link] for the dual DD algorithm.
Investigate (via simulation) how the PLL functions
when there is intersymbolinterference caused by a nonunity channel.
Pick a channel (for instance
chan=[1, .5, .3, .1]; )
and incorporate this into the simulation of the received signal.Using this received signal, are the phase estimates
worse when the channel is present? Are they biased? Are theymore noisy?
Repeat [link] for the dual Costas loop.
Repeat [link] for the Costas loop algorithm.
Repeat [link] for the DD algorithm.
"Indirect Frequency Estimation" showed that two loops can be used in concert to accomplish the carrier recovery task:the first loop estimates frequency offset and the second loop estimates the phase offset. This section shows an alternative structurethat folds one of the loops into the lowpass filter in the form of an IIR filter and accomplishes both estimations at once.This is shown in [link] , which looks the same as [link] but with the FIR lowpass filter replaced by an IIR lowpass filter .
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