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ECEN 661  Modulation Theory
Homework #9
Assignment Date: 4/13/06
Due Date: 4/20/06
1.
Phase Estimation for Binary PAM.
Consider a binary PAM signal of the form
where
is the pulse shape used and the data bits are
. The
received signal is of the form
, where
is the unknown carrier phase on
the received signal and
is white Gaussian noise.
(a) Given that we are able to observe the received signal for a time period totalling
bit intervals
(e.g.,
), find an (approximate) expression for the ML estimate of the carrier phase
. Use
the small SNR approximation
.
(b) Given that we are able to observe the received signal for a time period totalling
bit intervals
(e.g.,
), find a procedure to produce an (approximate) ML estimate of the carrier phase
. Use the large SNR approximation
. In this case, you probably will not be
able to find a closed form expression for the estimate. Instead, see if you can come up with an iter
ative procedure that will converge to the estimate.
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 Spring '11
 Miller

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