Low Crest Factor Modulation Techniques for Orthogonal Frequency ...

Ubiquitous Computing and Communication Journal
distributed variable having a mean of zero. And
thus, the absolute value will have Rayleigh
distribution.
The crest factor of the discrete time representation
x(k) is defined as the ratio of the peak magnitude
value and the square root of the average power of
this signal. For the OFDM signal as we mentioned it
have a zero mean and thus the square root of the
average power will be equal to the standard
deviation δ. Thus the crest factor can be written as:
CF = max(x(k )) = max(x(k )) (2)
E ( x 2 ) δ
Note that, the peak to average power ratio, widely
used in literature, is simply the square of the crest
factor. Both quantities coincide, if expressed in
logarithmic scale (dB).
An OFDM system is simulated using Matlab with
512 sub-carriers; We have performed a measure of
normality, i.e., wither the composite time signal
approaches the normal distribution or not, as a
verification of the applicability of central limit
theory to OFDM, and we get the following result as
shown in figure (1)
It can be noticed that the real and imaginary parts of
the OFDM signal completely agree with the normal
distribution.
a. The minimum Euclidean distance amongst
phasors, which is characteristics of the noise
immunity of the scheme
b. The minimum phase rotation amongst
constellation points, determining the phase jitter
immunity
c. The peak to average phasor power, which is a
measure of robustness against non-linear distortion
introduced by power amplifiers.
Fig.(2) Block diagram of OFDM system
Probability
0.999
0.997
0.99
0.98
0.95
0.90
0.75
0.50
0.25
0.10
0.05
0.02
0.01
0.003
0.001
Normal Probability Plot
The Bandwidth efficiency can be increased either by
increasing the Number of signal phase levels, or by
increasing the Number of signal amplitude levels
[6],
1. Increasing the signal amplitude levels has the
drawback that the signal envelope is not constant
and therefore non-linear amplification may cause
spreading of the signal spectrum and increase in
BER.
2. Increasing the Number of phase levels will
highly increase the BER.
-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4
Data
Fig.(1) Normal probability plot of OFDM signal
3. OFDM USING DIFFERENT MODULATORS
In this section we will simulate an OFDM system
as shown in the block diagram in figure (2) using
different modulation techniques.
We have simulated an OFDM system with different
modulation techniques, namely, M-ary PSK, M-ary
QAM (with M=4, 8, 16 and 32) and Minimum Shift
Keying (MSK).
When designing a constellation diagram for a
modulation technique, some considerations must be
given to [5]:
Fig.(3)OFDM Spectrum with different modulation
We have noted that for M-PSK, as M increases no
effect has been occurred to the dynamic range and
the PAR remains nearly the same, while for M-
QAM, as M increases the dynamic range increase
and so the PAR, but both of them agree in the
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