For phase references derived from PLL-based techniques, the phase-offset random variable can be
represented as
where is the SNR of the phase reference signal.
The probability of exactly m errors in a block of N bits is given as
Then the probability of more than M errors within a block of N bits is given as
P(M, N) 1 aM
m0aN
mb # Pe
m # (1 Pe)Nm
P(M, N) aN
mM1aN
mb # Pe
m # (1 Pe)Nm
aN
mb # Pe
m # (1 Pe)Nm
(p f p) f (f)
1
2p # Io(a)
# exp(a cos(f))
POQPSK (f)
1
2
# UPBPSK(f) PQPSK(f)V PQPSK (f)
1
2
# eQaA2Eb
No
# [cos(f) sin(f)]b QaA2Eb
No
# [cos(f) sin(f)]b f
PBPSK (f) QaA2Eb
No
# cos(f)b
f
Pb QaAEb
Nob
Pb
M
4
# c1 erf aAEb log2M
2No bd
Pb
M
2
# QaAEb log2M
No b
Eb
2No Pb
1
2
# e
USEFUL FORMULAS 513
REFERENCES
[1] M. K. Simon, ???A New Twist and the Marcum Q-Function and Its Application,??? IEEE Communications
Letters, Vol. 2, No. 2, Feb. 1998, p. 39??“41.
[2] G. Ferrari and G. E. Corazza, ???Tight Bounds and Accurate Approximations for the BER of DQPSK
Transmission from Novel Bounds on the Marcum Q-Function,??? in: International Symposium on
Information Theory and Its Applications, Oct. 2004.
[3] G. E. Corazza and G.
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