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ECE 562
Fall 2011
October 20, 2011
HOMEWORK ASSIGNMENT 5
Due Date: November 1, 2011
(in class)
1.
Diﬀerential Detector and Noncoherent Orthogonal Modulation.
Show that for binary
DPSK, the non coherent detector based on the twosymbol interval statistic
Y
n
is the
same as the diﬀerential detector (see notes).
2.
To track or not to track the phase.
Consider a BPSK system with an imperfect phase
reference, and a BDPSK system with diﬀerential detection. Assume that the data rates,
transmit powers, and noise PSD’s for the two systems are the same. Let P
b
(BSPK
, φ
)
and P
b
(BDPSK) denote the respective bit error rates for communication. Find the
value of phase error
φ
for which P
b
(BSPK
, φ
) = P
b
(BDPSK) = 10

6
.
3. In class we saw a ﬁgure from the book by Proakis that depicts a comparison of the
spectral eﬃciency
ρ
versus bit SNR
γ
b
for various modulation schemes at a symbol
error probability of P
e
= 10

5
. Your task in this problem is to produce a similar ﬁgure
for a symbol error probability of P
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This document was uploaded on 02/08/2012.
 Fall '09

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