63
Original scientific paper
 MIDEM Society
A Novel Approach to Reduce the PMEPR of 
MCPC Signal Using Random Phase Algorithm 
C. G. Raghavendra
1
, Sriranga R
1
, Sanath M Nadig
1
, Siddharth R Rao
1
, N. N. S. S. R. K Prasad
2
1
Ramaiah Institute of Technology, Affiliated to Visvesvaraya Technological University, India,
2
Aeronautical Development Agency, Ministry of Defense, India
Abstract: This paper aims to reduce the Peak-to-Mean Envelope Power Ratio (PMEPR) of a Multicarrier Complementary Phase Coded 
(MCPC) signal. A MCPC signal consists of P subcarriers which are phase modulated by N distinct phase sequences. Each of these P 
subcarriers is spaced by the inverse duration of a phase element, which constitutes an Orthogonal Frequency Division Multiplexing 
(OFDM) signal. A probabilistic approach, namely, Random Phase Updating (RPU) algorithm, is used to reduce the PMEPR of the 
generated MCPC signal. The technique is applied to higher order MCPC signals and a comparison of the peak sidelobe ratio (PSLR) and 
integrated sidelobe ratio (ISLR) is performed. The complex envelopes, autocorrelations and ambiguity functions of the MCPC signal 
obtained by the above mentioned methods are analysed. The Complementary Cumulative Distribution Function (CCDF) is plotted 
to validate the PMEPR reduction obtained by the application of the RPU algorithm which enables us to determine the most suitable 
approach required for radar applications.
Keywords: Integrated Sidelobe Ratio (ISLR); Multicarrier Complementary Phase Coded (MCPC); Orthogonal Frequency Division 
Multiplexing (OFDM); Peak to Mean Envelope Power Ratio (PMEPR); Peak Sidelobe Ratio (PSLR); Random Phase Updating (RPU)
Nov način zniževanja PMEPR MCPC signala z 
uporabo naključnega faznega algoritma
Izvleček: Članek opisuje zmanjšanje vršno-srednjega razmerja moči (PMEPR) večnosilčnega komplementarno fazno kodiranega 
(MCPC) signala. MCPC signal vsebuje podnosilce P , ki so fazno modulirani z N različnimi faznimi sekvencami. Vsak podnosilec P je ločen 
z inverznim trajanjem faznega elementa, ki oblikuje OFDM signal. Za zniževanje PMEPR je uporabljen verjetnostni pristop z naključno 
fazno osvežitvijo (RPU). Tehnika je uporabljena na višjih redih MCPC signala. Opravljanje primerjava razmerja vrhnjega snopa (PSLR) 
in razmerja integriranega snopa (ISLR). Analizirani so kompleksni ovoji, avtokorelacije in nejasne funkcije MCPC signala. Za validacijo 
znižanja PMEPR na osnovi RPU funkcije je uporabljena CCDF funkcija kot najboljši pristop za uporabo v radarju.
Ključne besede: ISLR; MCPC; OFDM; PMEPR; PSLR; RPU
* Corresponding Author’s e-mail: cgraagu@msrit.edu
Journal of Microelectronics, 
Electronic Components and Materials
Vol. 48, No. 1(2018), 63 – 70
1 Introduction
The most important characteristics of a radar signal 
are its range and resolution [1]. In order to improve the 
range of the signal, the pulse width must be increased. 
This hampers its resolution. On the other hand, de-
creasing the pulse width improves the resolution of the 
radar signal but results in deterioration of its range. We 
use pulse compression technique to balance the trade-
off between the range and resolution of the radar sig-
nal. Phase coding of the transmitted radar signal helps 
achieve pulse compression.
The advantage of a multicarrier system over single car-
rier transmission in terms of bandwidth efficiency [2] 
is clearly demonstrated by the Orthogonal Frequency 
Division Multiplexing (OFDM) technique. OFDM tech-
nology forms the foundation for a number of com-
munication systems such as Digital Audio and Video 
Broadcasting, IEEE 802.11g, Digital Subscriber Lines 
(xDSL). The latest applications include LTE and LTE Ad-
vanced. OFDM has also been applied to radar systems 
for object tracking and target detection. This applica-
tion has been realized in different types of multipath 
and clutter environments. 

64
C.G. Raghavendra et al; Informacije Midem, Vol. 48, No. 1(2018), 63 – 70
However, the multicarrier signals have high variations 
present in the complex envelope. These variations are 
quantified by a parameter, namely Peak to Mean Enve-
lope Power Ratio (PMEPR). Higher value of PMEPR indi-
cates more abrupt variations in the complex envelope 
of the signal and the power amplifier at the transmit-
ter end has to be very sensitive to track these sudden 
variations. Since design of such a sensitive amplifier is 
complicated, reduction of the PMEPR of the radar sig-
nal becomes essential.
The radar signal is phase coded using P4 [3] phase 
sequences which are complementary in nature. This 
helps us to accomplish Pulse Compression. The gener-
ated signal is a MCPC Signal as described by N. Levanon 
in [4]. The only drawback of this signal is its high value 
of PMEPR.
Several attempts have been made to reduce the effect 
of PMEPR in multicarrier schemes and emphasis is on 
data transmission applications, using methods such as 
near- complementary sequence [5], peak power reduc-
tion of OFDM signals with sign adjustment [6], tone 
reservation [7,8] and a joint technique [9]. However 
several authors have investigated to reduce PMEPR in 
multicarrier signals for radar applications. In [10], phase 
modulation is used and in [11] PMEPR is reduced using 
iterative least square algorithm and in [12] genetic al-
gorithm used. The objective of this paper is to address 
the issue of high PMEPR of a MCPC radar signal using 
RPU algorithm whose implementation until now has 
only been restricted to data transmission systems.
2 Characteristics of MCPC Signal
The multicarrier phase-coded signal is based on the 
principle of OFDM technique. It comprises of N subcar-
riers which are phase modulated by N distinct phase 
sequences. The frequencies of the subcarriers are 1/t
b
 
apart, where t
b
 is the duration of each phase element. 
The phase sequences are generated using P4 phase se-
quences.
The equation for generating P4 phase sequence is giv-
en in equation 1.
 
()()
2
11 1, 2,3.....
q
qq qN
N
π
φπ =− −− = (1)
For a 5 x 5 MCPC we generate the P4 phase sequences 
by setting N = 5. The first sequence which is obtained 
by cyclically shifting to attain the other 4 phase se-
quences. The P4 phase sequences obtained are shown 
in Table 1. All the phases are in radians.
Table 1: P4 Phase Sequences
Seq 1
[rad]
Seq 2
[rad]
Seq 3
[rad]
Seq 4
[rad]
Seq 5
[rad]
0 -2.513 -3.769 -3.769 -2.513
-2.513 -3.769 -3.769 -2.513 0
-3.769 -3.769 -2.513 0 -2.513
-3.769 -2.513 0 -2.513 -3.769
-2.513 0 -2.513 -3.769 -3.769
The phase sequence order of a MCPC signal is used to 
indicate the phase sequence which is used to modulate 
a particular subcarrier. For example, a phase sequence 
order of [3 5 2 1 4] involves the phase modulation of the 
first subcarrier with phase sequence 3, second subcar-
rier with phase sequence 5 and so on, where the phase 
sequences are obtained from Table 1.The complex en-
velope [3] of the MCPC signal is given by equation 2.
Using the above equations the complex envelopes for 
MCPC signals having different number of subcarriers 
such as 7 x 7, 9 x 9, 11 x 11, etc. can be generated using 
their respective phase sequences. The block diagram 
for generating the MCPC signal is as shown in Fig. 1.
The PMEPR value for different phase sequence orders is 
 
()
()
,
11
1
exp2 1, 0
2
0,
NN
ps pp qb b
pq
N
Aj ft pu tq tt Nt
st
elsewhere
πθ
==
  +  
−+ −− ≤≤ 
    
=
   


∑∑
(2)
 
()
()
,
,
exp, 0
0,
pq b
pq
jt t
ut
elsewhere
φ

≤≤

=



Where, 
A
p
 is the amplitude weight applied to the subcarriers 
and θ
p
 is the random phase shift introduced by the 
transmitter to each carrier. f p,q
 is the q
th
 phase of the 
p
th
 subcarrier.
Figure 1: Generation of MCPC Signal
illustrated in Table 2.

65
Table 2: PMEPR values of MCPC signals for different se-
quence orders
Sequence order PMEPR using P4
[3 5 2 1 4] 4.39
[3 4 5 1 2] 1.73
[3 1 2 5 4] 2.97
[3 2 4 1 5] 3.48
The ambiguity function for the phase sequence order 
[3 5 2 1 4] is depicted in Fig. 2.
Figure 2: Ambiguity Function of MCPC signal
Autocorrelation function is the correlation of a signal 
with a delayed copy of itself as a function of delay [13]. 
The width of the mainlobe gives an idea about the 
range of the radar signal and the sidelobe power levels 
govern the resolution of the signal.
Ambiguity function [14] is a two-dimensional function 
of delay and Doppler frequency that measures the cor-
relation between a waveform and its Doppler distorted 
version. Autocorrelation and the ambiguity function 
together help analyze the target detection capabili-
ties of the radar signal. When we have multiple point 
targets we have a superposition of ambiguity func-
tions. A weak target located near a strong target can 
be masked by the sidelobes of the ambiguity function 
cantered around the strong target. Hence, we have to 
minimize the minor lobes for detection of secondary 
targets. 
The quality of the radar signal can also be assessed us-
ing Peak Sidelobe Ratio (PSLR) and Integrated Sidelobe 
Ratio (ISLR). The Peak Sidelobe Ratio (PSLR) is the ra-
tio between the returned signal of the mainlobe and 
that of the maximum sidelobe power. The Integrated 
Sidelobe Ratio (ISLR) is the ratio of the energy in the 
sidelobes to that contained in the mainlobe. The PSLR 
and ISLR for the conventional 5 x 5 MCPC signal were 
found to be 8.32dB and 3.34dB respectively.
3 Random Phase Updating Algorithm
The only drawback of the MCPC signal is its high value 
of PMEPR. Reducing this quantity will result in the re-
duction of the variations in the complex envelope. This 
issue can be addressed by using one of the methods 
suggested in [5]. However the technique thus adopted 
must not only ensure a reduction in PMEPR but also 
maintain acceptable autocorrelation and ambiguity 
functions. An effective approach is to make use of the 
Random Phase Updating (RPU) algorithm [15] which 
comes under the purview of the probabilistic domain. 
The block diagram for generating the MCPC signal with 
RPU algorithm is shown in Fig. 3.
Figure 3: RPU Algorithm for generation of MCPC signal
The random phase updating algorithm generates 
phases and adds them to the pre-existing P4 phase val-
ues as given by equation 3.
 
() () ()
1
pp p
ii i
φφ φ
−
=+ Δ    (3)
In equation 3, i denotes the iteration, and p denotes the 
subcarrier. (ф
p
)
i
 is the phase of the p
th
 subcarrier in the 
i
th
 iteration and ( Δф
p
)
I
 is the incremental phase added 
to the p
th
 subcarrier in the i
th
 iteration. 
The algorithm uses the number of iterations as the 
control parameter. The incremental phases are gener-
ated based on a particular probability density function 
and added to each subcarrier. Gaussian distribution or 
uniform distributions are used to generate these in-
cremental phases. The complex envelope is obtained 
and the corresponding value of PMEPR is calculated for 
every iteration. Once the required number of iterations 
is carried out, the complex envelope and the phase se-
quences corresponding to the lowest value of PMEPR 
are selected. The autocorrelation function and the am-
biguity function are plotted for the selected complex 
envelope. The flowchart in Fig. 4 describes the random 
phase updating algorithm.
C.G. Raghavendra et al; Informacije Midem, Vol. 48, No. 1(2018), 63 – 70

66
The Gaussian distribution is given by Δф
p
 = N(0, x
2
)
The Uniform distribution is given by Δф
p
 = Unif(0, x
2
)
Here, ( Δф
p
) is the incremental phase generated based 
on a particular distribution. x belongs to {0.1, 0.25, 0.5, 
0.75, 1} for a 5 x 5 MCPC signal. Similarly, x belongs to 
{0.1, 0.25, 0.4, 0.55, 0.7, 0.85, 1} for a 7 x 7 MCPC signal 
and {0.1, 0.21, 0.32, 0.43, 0.55, 0.66, 0.77.0.88, 1} for a 9 
x 9 MCPC signal. For each subcarrier, the incremental 
phases are obtained by calculating the CDF of one of 
the values in the vector '' x which is selected randomly. 
4 Results
In this section, a comparison is made between the con-
ventional MCPC signal and the signal subjected to the 
Random Phase Updating Algorithm for a large number 
of iterations. This technique has been applied to the 
MCPC signal that is based on the cyclic shifts of the 
P4 phase sequences for the order [3 5 2 1 4]. The com-
plex envelope, autocorrelation and ambiguity function 
obtained using the RPU algorithm are plotted against 
those obtained using the conventional method.
In the random phase updating algorithm, the random 
numbers generated can be either repetitive or non-
repetitive in nature. If the random numbers are repeti-
tive, the number of possible combinations is large. For 
a 5 x 5 MCPC signal, there are 5
5
 different combinations 
possible if the random numbers are repetitive and only 
5! combinations if the random numbers are non-repet-
itive. A comparison of the results obtained using both 
the results is made in this section.
Further, for the generation of the incremental phases, 
the random phase updating algorithm uses either 
Gaussian Distribution or Uniform Distribution. A com-
parison of the results obtained using the above men-
tioned distributions along with the two methods of 
generation of random numbers is performed in this 
section.
Due to the random nature of the phase updating pro-
cess, the complex envelope, autocorrelation function 
and ambiguity function need not be unique. However, 
the lowest value of PMEPR for the complex envelope 
remains the same when the number of iterations are 
very large.
It could be observed that the lowest value of PMEPR 
obtained when the random numbers were generated 
in a repetitive manner was almost identical to those 
obtained by generating non-repetitive numbers.
4.1 RPU Using Gaussian Distribution
The results obtained in this subsection illustrate the 
complex envelope, autocorrelation function and the 
Figure 4: Flowchart of the RPU Algorithm
Figure 5: Complex Envelope of MCPC signal using RPU 
algorithm
C.G. Raghavendra et al; Informacije Midem, Vol. 48, No. 1(2018), 63 – 70

67
ambiguity function obtained for a 5 x 5 MCPC signal 
with phase sequence [3 5 2 1 4] using the RPU algo-
rithm where the incremental phases are generated 
based on Gaussian distribution. Fig. 5, Fig. 6 and Fig. 7 
illustrate the case where the random numbers are non-
repetitive in nature.
Figure 6: Autocorrelation Function of MCPC  Signal us-
ing RPU Algorithm
Figure 7: Ambiguity Function of MCPC Signal using 
RPU Algorithm
Table 3 shows the comparison of PMEPR between con-
ventional method and the RPU algorithm.
Table 3: PMEPR comparison table
Sequence Order PMEPR using conventional 
MCPC Signal
PMEPR using RPU algorithm
Using non-repetitive
 random numbers
Using repetitive
 random numbers
[3 5 2 1 4] 4.39 2.99 2.99
[3 4 5 1 2] 1.73 1.53 1.54
[3 1 2 5 4] 2.97 2.59 2.58
[3 2 4 1 5] 3.48 2.27 2.25
It can be clearly observed that the PMEPR values ob-
tained using both the methods of generating random 
numbers are identical and better than those obtained 
using the conventional method. 
The autocorrelation function shown in Fig. 6 has 
sidelobe power levels at approximately 15dB. This 
shows that the target detection capabilities of the ra-
dar signal are preserved after applying the technique.
From Fig. 7 it can be seen that the sidelobe ridges in the 
ambiguity function are lower for high Doppler shifts 
when compared to the conventional MCPC signal dem-
onstrating that the target detection capabilities have 
been conserved.
The PSLR and ISLR for the MCPC signal after the appli-
cation of the RPU technique were found to be -6.92dB 
and 4.45dB respectively. It can be observed that these 
values are higher than that obtained for the conven-
tional MCPC signal, showing that there is a slight 
degradation in the resolution of the signal. There is a 
trade-off between PMEPR reduction and increased 
sidelobe-power levels. However, this minor disadvan-
tage of distribution of the mainlobe power amongst 
the sidelobes does not compare with the advantage of 
PMEPR reduction.
Figure 8: Complex Envelope of MCPC signal obtained 
by RPU Algorithm
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68
4.2 Using Uniform Distribution
This section demonstrates results obtained when the 
incremental phases are generated based on Uniform 
distribution for the sequence order [3 5 2 1 4]. The 
graphs plotted in Fig. 8, Fig. 9 and Fig. 10 illustrate the 
complex envelope, autocorrelation function and ambi-
guity function respectively for this case. 
The PMEPR comparison between conventional MCPC 
signal and the signal obtained by the application of 
RPU algorithm based on Uniform distribution is illus-
trated in Table 4.
Table 4: PMEPR comparison table
Sequence
Order
PMEPR using Conventional MCPC 
Signal
PMEPR using RPU algorithm
Using non-repetitive random 
numbers
Using repetitive random 
numbers
[3 5 2 1 4] 4.39 3.01 2.99
[3 4 5 1 2] 1.73 1.57 1.53
[3 1 2 5 4] 2.97 2.56 2.60
[3 2 4 1 5] 3.48 2.24 2.26
From Table 4, it can be noted that the PMEPR value has 
considerably reduced for all sequence orders when 
RPU algorithm is incorporated in the phase generation 
process of MCPC signal generation.
The autocorrelation function obtained indicates peak 
sidelobe power levels to be approximately 10dB which 
suggests that the target tracking ability of the signal 
based on Uniform distribution is marginally inferior to 
the signal obtained using Gaussian distribution.
The ambiguity function obtained shows that the sig-
nal has low sidelobe power levels at higher Doppler 
shifts similar to the case when Gaussian distribution is 
used, which is a favourable aspect. The PSLR and ISLR 
were found to be 4.75dB and 7.19dB respectively. The 
resolution of the radar signal is worse than that of the 
conventional MCPC signal and that of the signal ob-
tained using Gaussian distribution but is still effective 
in reducing PMEPR.
4.3 Complementary Cumulative Distribution Function 
(CCDF)
The CCDF curve provides an idea of the distribution of 
power of the complex envelope around the mean. It is 
Figure 9: Autocorrelation Function of MCPC Signal ob-
tained by RPU Algorithm
Figure 10: Ambiguity Function of MCPC Signal ob-
tained by RPU Algorithm
Figure 11: CCDF comparison
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69
a plot of Power levels above the Average Power in dB vs 
Probability of occurrence of that particular power level 
above the mean power in the complex envelope under 
consideration. As the area under the curve increases, 
the power variation around the mean increase and this 
leads to an increased value of PMEPR. Conversely, as 
the area under the curve reduces, the PMEPR also has 
a lower value as the power variations around the mean 
is reduced.
The graph in Fig. 11 illustrates the comparison between 
the conventional MCPC signal and the signals obtained 
using the RPU algorithm with Gaussian distribution.  
It can clearly be seen that the complex envelope ob-
tained using the RPU algorithm with Gaussian PDF has 
a much lesser area than the conventional MCPC signal 
and hence possesses a much lesser value of PMEPR. 
Thus the results obtained using the CCDF graph are in 
coherence with those shown in Table 3 and Table 4.
4.4 RPU Algorithm applied to Higher Order MCPC 
Signals
In this subsection, the RPU algorithm is applied to 
MCPC signals with greater number of subcarriers to 
assess whether the technique performs favourably 
in different scenarios. From the previous subsections, 
we can observe that the PMEPR value obtained using 
both Gaussian distribution and Uniform distributions 
are identical. Therefore, either of these distributions 
can be used for the reduction of PMEPR. Table 5 and 
Table 6 illustrate the PMEPR comparison between con-
ventional MCPC and MCPC signal obtained using RPU 
algorithm for a 7 x 7 and 9 x 9 MCPC signal respectively. 
The number of possible sequence orders for a 7 x 7 and 
a 9 x 9 MCPC signal are 7! and 9! respectively. Since the 
values are very large, the Table 5 and Table 6 shows the 
sequence orders corresponding to the highest, low-
est and an intermediate value of PMEPR obtained for a 
given order of the MCPC signal. 
Table 5: PMEPR comparison for MCPC of order 7 x7
Sequence 
Order 7 x 7
PMEPR using 
Conventional 
MCPC signal
PMEPR using RPU 
algorithm
[2 5 6 7 4 1 3] 6.14 3.44
[7 1 2 3 4 5 6] 1.92 1.75
[7 1 3 2 6 4 5] 4.01 3.29
It can be inferred that the RPU algorithm delivers prom-
ising results in terms of PMEPR reduction for a 7x7 and 
9x9 MCPC signal and can be suitably applied to higher 
order signals.
Table 6: PMEPR comparison for MCPC of order 9 x 9
Sequence Order 
9 x 9
PMEPR using 
Conventional 
MCPC signal
PMEPR using 
RPU algorithm
[5 9 1 7 2 4 3 6 8] 7.76 3.43
[5 6 7 8 9 1 2 3 4] 1.95 1.57
[5 9 7 1 2 3 6 8 4] 4.86 3.56
The PSLR and ISLR for the discussed signals are shown 
in Table 7.
Table 7: PSLR and ISLR comparison table
Signal PSLR(dB) ISLR(dB)
7 x 7 Conventional MCPC -7.38 5.52
7 x 7 MCPC with RPU -7.35 6.55
9 x 9 Conventional MCPC -7.33 7.04
9 x 9 MCPC with RPU -6.89 7.43
It can be seen that in both 7 x7 and 9 x 9 MCPC signals, 
the conventional MCPC signal has lower PSLR and ISLR 
values than that obtained after application of the RPU 
technique. This shows that the resolution degrades and 
follows the trend of the 5 x 5 case. The advantage of 
PMEPR reduction compensates this limitation.
5 Conclusion
The MCPC signal has many advantages in terms of 
bandwidth efficiency and pulse compression capabil-
ity when compared to other radar signals which makes 
it more suitable for radar applications. Its only limita-
tion is the high value of PMEPR. This paper has success-
fully addressed this drawback through the application 
of the random phase updating algorithm. 
Section IV showed the application of the RPU algo-
rithm based on Gaussian and Uniform distribution 
and both techniques provided favourable results. The 
technique was also found to be successful in reducing 
PMEPR for higher order MCPC signals as well. The CCDF 
further validates the reduction of PMEPR by portraying 
the power distribution about the mean. 
The autocorrelation functions plotted for the complex 
envelopes generated using Gaussian and Uniform 
distribution indicate that the sidelobe levels using 
Gaussian distribution is lesser than that of the Uniform 
distribution. Though the PMEPR values obtained for 
a particular phase sequence is identical in both these 
distributions, the Gaussian distribution fares slightly 
better in resolving the targets due to a lower sidelobe 
power level.
C.G. Raghavendra et al; Informacije Midem, Vol. 48, No. 1(2018), 63 – 70

70
The Random Phase Updating algorithm being an it-
erative approach is computationally intensive and in-
creases design complexity of the radar system. The ran-
dom nature of the procedure makes in-depth analysis 
of the technique difficult. However, the advantages of 
this technique dominate these limitations and can be 
considered as a successful approach to reduce PMEPR, 
aiding the generation of a better MCPC signal.
6 Acknowledgment
The authors are grateful to Department of Electronics 
and Communication, Ramaiah Institute of Technology, 
Bangalore
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Arrived: 09. 01. 2018
Accepted: 27. 03. 2018
C.G. Raghavendra et al; Informacije Midem, Vol. 48, No. 1(2018), 63 – 70