ECEN 661  Modulation Theory
Homework #6
Assignment Date: 3/17/08
Due Date: 3/25/08
1. (Text 5.12, 4th edition, modified). In Section 4.3.1 in the text it was shown that the minimum
frequency separation for orthogonality of binary FSK signals with coherent detection is
. However, a lower error probability is possible with coherent detection of FSK if
is increased beyond
.
(a) Show that the optimum value of
is
.
(b) Determine the probability of error for this value of
.
(c) State the gain in dB achieved by using the optimum frequency spacing instead of that which
leads to orthogonal signalling.
2. (Text 5.20, 4th edition, modified) Consider
two 8point QAM signal constellations shown
in the figure. The minimum distance between
adjacent points is 2A.
(a) Determine the average transmitted power for
each constellation, assuming that the signal
points are equally probable.
(b) Which constellation is more power efficient? Also state the difference (in dB) in asymptotic
relative power efficiency of the two signalling schemes.
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 Spring '08
 Miller
 Frequency, Estimation theory, coherent, Quadrature amplitude modulation, Frequencyshift keying, relative power efficiency

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