Sequences with low peak side lobe levels for constant PAPR VSF OFDMA system

Abstract

In multiuser multicarrier systems, constant power schemes are desirable, to reduce the variations in interference power and the requirements on the power amplifier's dynamic range. In this work, variable spreading factor (VSF) orthogonal frequency division multiple access (OFDMA) system is used to support multiple data transmission rates. The effect of using three different spreading sequences, namely, Tent map binary sequences, Zadoff Chu sequences and Orthogonal variable spreading factor codes in VSF OFDMA systems was investigated. Merit factor and peak sidelobe levels (PSL) of sequences were used as metrics for selection of spreading codes and for the study of system performance. It was observed that the use of Tent map and Zadoff Chu sequences with low PSLs resulted in constant peak to average power ratio (PAPR), irrespective of the combinations of data rates used. The use of binary sequences generated from tent map is proposed to reduce PAPR and to maintain constant PAPR. It is an added merit that a large number of chaotic binary sequences with desirable sequence lengths and good correlation property can be generated easily with change in initial conditions.

Full text

International Journal of Applied Engineering Research
ISSN 0973-4562 Volume 8, Number 2 (2013) pp. 9-26
© Research India Publications
http://www.ripublication.com/ijaer.htm
Sequences with Low Peak Side Lobe Levels for
Constant PAPR VSF OFDMA System
Susan R J and Sakuntala S Pillai
Department of Electronics and Communication,
College of Engineering, Thiruvananthapuram 695016, Kerala, India
Corresponding author. E-mail address: susanrj1@gmail.com
Mar Baselios College of Engineering and Technology,
Thiruvananthapuram 695015, Kerala, India
E-mail address: sakuntala.pillai@gmail.com
ABSTRACT
In multiuser multicarrier systems, constant power schemes are desirable,
to reduce the variations in interference power and the requirements on
the power amplifier's dynamic range. In this work, variable spreading
factor (VSF) orthogonal frequency division multiple access (OFDMA)
system is used to support multiple data transmission rates. The effect of
using three different spreading sequences, namely, Tent map binary
sequences, Zadoff Chu sequences and Orthogonal variable spreading
factor codes in VSF OFDMA systems was investigated. Merit factor
and peak sidelobe levels (PSL) of sequences were used as metrics for
selection of spreading codes and for the study of system performance. It
was observed that the use of Tent map and Zadoff Chu sequences with
low PSLs resulted in constant peak to average power ratio (PAPR),
irrespective of the combinations of data rates used. The use of binary
sequences generated from tent map is proposed to reduce PAPR and to
maintain constant PAPR. It is an added merit that a large number of
chaotic binary sequences with desirable sequence lengths and good
correlation property can be generated easily with change in initial
conditions.
Keywords- Peak to average power ratio, OFDMA, variable spreading
factor, chaotic sequences

10 Susan R J and Sakuntala S Pillai
Introduction
In broadband wireless networks, the physical layer should facilitate
multiuser/multirate transmission of data, in order to provide users with the
necessary quality of service (QoS) required for integrated services. Wireless
access system optimized for each environment can be realised by controlling
radio parameters in an adaptive manner. The capability of multiple data
transmission rates provides significant advantages in multiuser mobile radio
systems. The data rate can be traded for the improved robustness of
transmission, or it can be adapted to time-varying channel conditions in order
to meet the set error rate criteria. In particular, the rate can be imposed based
on the type of requested service and the available capacity in the system at a
given moment.
Switched packet radio techniques and wideband code division multiple
access like systems, rather than assigned physical channel schemes are required
to support this bandwidth-on-demand environment [1]. To accommodate with
information sources of different data rate requirement, different access schemes
have been employed under direct sequence code division multiple access (DS-
CDMA) scenario [2, 3]. Two multirate transmission schemes applicable
particularly to code division multiple access (CDMA) are the multicode scheme
and the variable spreading factor (VSF) scheme.
In the case of Orthogonal frequency division multiple access (OFDMA)
systems there is flexibility of changing the spreading factor in time domain
and frequency domain, to provide VSF in order for the system to work in
different channel conditions and with different data rates. Spreading data at
variable rate increases peak to average power ratio (PAPR) of OFDMA
system. High PAPR reduces the efficiency and hence increases the cost of the
radio frequency power amplifier. Suitable spreading sequences may be used to
reduce this increase in PAPR. Hence investigation for spreading sequences with
better correlation properties is essential.
It is desirable to keep the advantages of CDMA and Orthogonal Frequency
Division Multiplexing (OFDM) in multicarrier systems, and in the meanwhile
to mitigate the problem of high PAPR. The crest factor of multi-carrier
CDMA (MC-CDMA) systems was shown to be dependent upon the aperiodic
crosscorrelation as well as on the aperiodic autocorrelations of the spreading
codes used [4]. So the spreading sequences employed in MC-CDMA should, in
addition to being mutually orthogonal, must also provide a low PAPR in order
to limit the required linearity range of the power amplifiers used. Constant
power schemes are desirable in multiuser systems, to reduce the variations in
interference power and the requirements on the power amplifier's dynamic
range. Tsai et al. has proposed OFDM-CDMA system that employs polyphase
codes to support variable spreading factors [5]. It was also reported [5] that
OFDM CDMA system using polyphase codes was found to have different
PAPR performance depending on the spreading factor used.
In the last several years, increasing efforts have been devoted to study the
possibility of using chaotic dynamics to enhance the features of communication

Sequences with Low Peak Side Lobe Levels 11
systems [6]. The possibility of generating an infinite number of spreading
sequences for a standard DS-CDMA system by means of chaotic time series
has been reported by Bateni and McGillem [7]. Chaotic sequences have been
proposed for use in multicarrier systems and for reduction of PAPR [8], but
no work has been reported so far of its use in multiple rate support in
OFDMA systems.
The stability of chaotic pseudorandom binary sequences (PRBS) generated
from four different chaotic maps were analysed by Xiang et. al. and it was
concluded that sequences generated from Tent map were stable [9]. It was
reported by Addabbo et. al. that Tent-map-based PRBSs are a viable solution
for the generation of pseudorandom bits and a suitable alternative to traditional
linear feedback shift register sequences [10].
In this paper the use of chaotic Tent map binary sequences has been
proposed for VSF OFDMA and the effect on PAPR was examined.
Performance was compared with that of orthogonal variable spreading factor
(OVSF) codes used widely for variable data rate support and polyphase Zadoff
Chu sequence which have good correlation properties. With Zadoff Chu
sequences and OVSF codes, the data rates that can be supported
simultaneously is limited by the availability of sufficient number of codes
satisfying orthogonality condition. With the use of chaotic sequences a large
number of sequences with desirable correlation property can be generated easily
with change in initial conditions [7]. Security of the system is also enhanced
with the use of aperiodic chaotic sequences [7].
System description and simulation
OFDMA is well matched to bursty multirate, multimedia traffic as it allows
for dynamic allocation of bandwidth resources among the active users. In
OFDMA system total bandwidth is divided into spectrally overlapping,
narrowband subchannels. The subcarriers are allocated using assignment map
defined by subcarrier allocation scheme [11]. Base station allocates to each
user a fraction of subcarriers, preferably in a range where they have channel
with good quality transmission.
Simultaneous transmission of multiple data rate can be achieved by using
spreading codes to spread data with different spreading factors while keeping
the chip rate same for all carriers in the system. Spreading factors are chosen
as per data rate requirement of the user. For realization of multiple rate
spreading, data of low rate users are spread with maximum spreading factors.
PAPR increases with variable spreading of data as highly correlated data
frames have large PAPR. This can be reduced by spreading the data using a
code sequence of desired autocorrelation property since PAPR depends on
autocorrelation of a particular data set [12]. Three different sequences were
used for study in this work, tent map binary sequences, OVSF codes and
Zadoff Chu sequences.

12 Susan R J and Sakuntala S Pillai
Generation of sequences
Tent map binary sequences
Chaotic sequences and pseudo noise sequences can have similar spectral and
correlation properties, although chaos can be generated using simple difference
equations. Chaos is deterministic random like process found in nonlinear
dynamical system, and is aperiodic, non converging and bounded [7]. A widely
studied dynamical system capable of exhibiting chaos is the tent map which
can be used to generate chaotic sequence. Tent map is given by equation (2.1)
where n
nRy and (.)f maps state yn to next state yn+1 [13, 14].


cybayfy nn1n 
 (2.1)
The values of parameters taken for the system to exhibit chaotic behavior
are: a ≥ 1, 1.5 ≤ b ≤ 2, c ≤ 1. Depending on the value of parameters, the
dynamics of system can change dramatically exhibiting periodicity or chaos.
The chaotic sequence generated is for all practical purposes non periodic and
non converging [7]. A binary sequence {c(k)} is obtained [15] from chaotic
signal y(k) by equations (2.2) and (2.3). E(y(k)) is the mean value.
E(y(k))}y(k){c(k)


g (2.2)





0z1
0z1
(z)g (2.3)
Aperiodic chaotic sequences for all users were generated with different
initial conditions for the same chaotic map, with parameters a=1, b=1.99 and
c=0.5.
The sequences generated by iterating given chaotic map will diverge to
different trajectories in a few cycles even though their initial conditions differ
by less than 1% [16]. So a large number of chaotic sequences are generated
easily with change in initial condition. There is flexibility in choosing the
spreading gain, as the sequences can be truncated to any length with no loss
in its properties.
Zadoff Chu sequences
The family of Zadoff Chu codes is defined as in equation (2.4)









Noddfore
Nevenfor,e
]k[g
Np)1k(k
j
Npk
j
N
2
(2.4)
where N is the length of the code 0≤k<N and parameter ‘p’ is chosen to be
relatively prime with respect to N [5]. Primitive Zadoff Chu sequences were
generated using integers relatively prime to N in equation (2.4). Codelength N

Sequences with Low Peak Side Lobe Levels 13
for this simulation being 16, values of ‘p’ were taken as 1, 3, 5, 7, 9, 11, 13
and 15.
OVSF codes
OVSF codes are generated recursively by applying Hadamard transform
1,1m,2N, m
N/2N/2
N/2N/2
N







1
c
cc cc
c (2.5)
The maximum number of available orthogonal codes is N.
Correlation properties of sequences
Autocorrelation function (ACF) of a codeword is closely related to its spectrum
[17]. An impulse like ACF results in a nearly flat spectrum, thus giving a
small peak to average power. If 'a' designates a binary sequence of length N,
it can be denoted as a = (a0, a1, ……aN-1), ai є {-1, 1}. Aperiodic
autocorrelation of binary sequence a is another sequence Raa(k) [18].
ki
k1N
0i i
aa aa
N
1
)k(R 



 0 ≤ k ≤ N-1 (2.6)
Usually sequences are sought that have small sidelobes Raa (k) for k ≠ 0.
For two binary sequences a and b, each of length N, the crosscorrelation
function of a and b, Rab(.) is defined as
ki
k1N
0i i
ab ba
N
1
)k(R 



 (2.7)
Two criteria of goodness have widely been used to evaluate and design a
spreading sequence. Off peak auto correlation is typically quantified in terms
of merit factor [18, 19]. The merit factor problem is of considerable practical
interest to communication engineers, as it indicates the smallness of
autocorrelation function. For sequences with aperiodic autocorrelation function
R(n), merit factor (MF) is defined as in equation (2.8)



1N
1
n
2
)n(R2
)0(
2
R
MF (2.8)
Peak sidelobe level (PSL) is also used as a measure of smallness of
aperiodic ACF [20].
)n(R
Nn1 maxPSL 
 (2.9)

14 Susan R J and Sakuntala S Pillai
PSL is the largest absolute value of its aperiodic autocorrelations at
nonzero shifts.
System model
Simulations were done using MATLAB. For ease of analysis synchronization
between transmitter and receiver is assumed [21]. Modulation used was
quadrature amplitude modulation. Simulation was done for 16 users,
simultaneously transmitting data with different rates, over a total of 256
subcarriers. Spreading factors (SF) used for simulation include 16 for lowest
rate users, 8 for users with twice the rate and 4 for users with 4 times the
lowest rate.
Data of each user is spread with sequence assigned to the user as per the
data rate requirement before subcarrier mapping. The spread output sequence
{d(k)} is given by equation (2.10)
d(k-iTc)=b(n)c(k-iTc) i = 1,2,…m (2.10)
c(k) represents the spreading sequence, ‘m’ the spreading factor assigned to the
user and Tc the chip period. The data bits b(n)

{-1, 1} were taken as
equiprobable.
The N subcarriers are partitioned into groups with each group having
contiguous subcarriers, so that each user exclusively transmits on a set of
subcarriers, out of a total of N subcarriers. The subcarrier assignment unit
maps data symbols onto the subcarriers assigned to the corresponding user.
The data stream is then divided into blocks and pilots are inserted for channel
estimation.
Data symbols X(k), k = 0,1, …N-1, are given to OFDMA modulator as
sets of length N symbols, to be transmitted on N subcarriers. The N
subcarriers are chosen to be orthogonal, with subcarrier frequency fk = k ∆f,
where ∆f = 1/(NT) and T is the original symbol period. OFDM modulation is
achieved by taking Inverse Fast Fourier Transform (IFFT) of data block to be
transmitted. The sampled version of transmitted complex low pass signal is
given by equation (2.11)
1Nn0eX(k)
N
1
x(n) 1N
0k
Nnkj2π
 


(2.11)
High dynamic range which results from Inverse Discrete Fourier Transform
(IDFT) translates to a high PAPR for OFDMA waveforms. PAPR of OFDM
signal x(t) is defined as (equation 2.12) the ratio between the maximum
instantaneous power and the average power Pav of the signal.
av
2
NTt0 P
])t(x[max
PAPR[x(t)] 
 (2.12)

Sequences with Low Peak Side Lobe Levels 15
The power of OFDM symbol is given by equation (2.13) where R(u) is
the self correlation function of data symbol set [X0, X1, …, XN-1].
 








0ω
k
N
ω
j2π
N
m)k(n
j2π
m
1N
0n
1N
0m n
2R(u)eN)eX(Xx(k)P(k) (2.13)
The average power of antipodal transmit data set is fixed and so the
average power of OFDMA output is also constant according to Parseval’s
theorem and is taken as N. PAPR of transmitted signal is given by equation
(2.14)
N
0ω
k
N
ω
j2π
eR(u)N
average
P
peak
P
PAPR




 (2.14)
From equation (2.14) it can be seen that reducing auto correlation of
transmitted symbol set can reduce PAPR of the system effectively [4].
Spreading sequences can be selected to limit the dynamic range of OFDM
transmitted signal envelope and hence reduce PAPR.
To better approximate the PAPR of continuous time OFDM signals, OFDM
signals are obtained by L times oversampling. L times oversampled time
domain samples are LN point IFFT of data block with (L-1)N zero padding.
Oversampled IFFT output can be expressed as in equation (2.15) with
1NLn0



.



1NL
0k
NL
nkj2π
eX(k)
LN
1
x(n) (2.15)
PAPR increases with L, but does not increase significantly after L = 4. L

4 is sufficient to get accurate PAPR results [17]. The PAPR computed from
the L times oversampled time domain OFDM signal samples can be defined
by (2.16), where E[.] denotes expectation operator.

]x(n)E[
]x(n)[max
x[n]PAPR 2
2
1NLn0 
 (2.16)
The distribution of PAPR, which bears stochastic characteristics in OFDM
system is expressed in terms of Complementary Cumulative Distribution
Function (CCDF). CCDF of a PAPR as denoted in equation (2.12) is the
probability Pr(.) that PAPR of a data block exceeds a given threshold PAPR0
as given in equation (2.17).
CCDF (PAPR (x(t)) = Pr (PAPR (x(t) > PAPR0) (2.17)

16 Susan R J and Sakuntala S Pillai
CCDF was found for data spread with variable spreading factor for cases,
using OVSF codes, Tent map binary sequences and Zadoff Chu sequences.
For bit error rate (BER) performance analysis the channel is modeled as
slow fading channel with Vehicular A and Additive White Gaussian Noise
(AWGN) channel models. Cyclic prefix (CP) of length greater than channel
impulse response length was added to each OFDM symbol to avoid
intersymbol interference. Due to insertion of CP at the transmitter and removal
of CP at the receiver, the dispersive channel is represented as NxN circulant
matrix. When channel is time invariant within the block, this matrix becomes a
cyclic matrix. Fast Fourier Transform (FFT) of the signal is taken at the
receiver. As IFFT at the transmitter and FFT at the receiver diagonalises the
circulant matrix, inter symbol interference free model of OFDM symbol is
obtained [22]. Minimum Mean Square Error (MMSE) frequency domain
equalization (FDE) can be performed independently for each subcarrier.
Block type pilot channel estimation, has been used under the assumption of
slow fading channel. Block size used for this work is 8. MMSE equalization
weights are obtained from the estimates of channel frequency response of the
subchannels. These weights are used for getting equalized signal for received
data block. Demodulation and despreading is followed by detection to get the
bit estimates. Synchronised chaotic sequences generated in the receiver are used
for despreading of received data.
Root raised cosine (RRC) filtering used for reducing out of band emissions
increases the PAPR of the system [5]. Considering practical systems, the
proposed system was simulated using RRC filter. Roll off factor of 0.25 was
used for simulation.
Results and discussion
In this section the properties of OVSF codes, Tent map binary sequences and
Zadoff Chu sequences were studied and their effect on the PAPR performance
in VSF OFDMA system is presented.
Properties of spreading sequences
The performance of any communication system is closely related to the
properties of the sequences used for spreading. In this work, merit factor and
PSL (peak sidelobe level) were used as measure of suitability of a sequence to
be used for variable rate spreading.
Figure 1 shows aperiodic autocorrelation function of OVSF codes, Tent
map and Zadoff Chu sequences for codelength 16. Off peak autocorrelation
values are high for OVSF codes as can be observed from the figure. It can
also be seen from figure 1, that there is a sharp decrease in the
autocorrelation function for Tent map and Zadoff Chu sequences, which is a
desirable characteristic for OFDMA system.

Sequences with Low Peak Side Lobe Levels 17
Figure 1: Autocorrelation function of OVSF codes, Tent map and Zadoff Chu
sequences for codelength 16
Figure 2 shows cross correlation between two sequences for the OVSF,
Tent map and Zadoff Chu sequences. Tent map sequences were generated
using different initial conditions 0.07 and 0.071 using equation (2.1) with ‘a‘
as 1 and ‘b‘ as 1.99. Zadoff Chu sequences were chosen with values of ‘p’
relatively prime to sequence length N. The sequences gave low
crosscorrelation, hence could be used for multiple data rate spreading in
OFDMA.
Figure 2: Crosscorrelation function of OVSF codes, Tent map and Zadoff Chu
sequences for codelength 16

18 Susan R J and Sakuntala S Pillai
Merit factor and PSL of the sequences were found for codelength 16. For
16 different codes generated by changing initial conditions for map given by
equation (2.1), PSL of Tent map ranges from 4 to 8 and merit factor from
0.76 to 2.7 (figure 3). This is seen to vary slightly depending on initial
conditions, but sequences with low PSL can be chosen easily due to
availability of large number of sequences. For Zadoff Chu sequences,
considering only the 8 sequences with ‘p’ value relatively prime to sequence
length N in equation (2.4), it was observed that PSL ranges from 1.8 to 5,
and merit factor from 2.1 to 7.07 (figure 4). For OVSF codes, PSL values are
in the range from 8 to 14, and merit factor from 0.12 to 0.57 (figure 5).
Observation was that the properties of Zadoff Chu and Tent map sequences
were good compared to that of OVSF codes.
Figure 3: Merit factor and peak sidelobe level of Tent map sequences of
length 16
Figure 4: Merit factor and peak sidelobe level of Zadoff Chu sequences of
length 16

Sequences with Low Peak Side Lobe Levels 19
Figure 5: Merit factor and peak sidelobe level of OVSF codes of length 16
Performance with Tent map binary sequences
This section presents simulation results of PAPR and bit error rate (BER)
performance of VSF OFDMA system using binary tent map sequences. PAPR
with variable spreading of data was done without codes and using codes for
16 users, for two different sets of data rates. CCDF plots (figure 6) show that
there is an increase in PAPR when variable spreading is done compared to
spreading with same rate. This is due to increase in correlation of the data.
For probability 10-3, the increase was 7 dB and 5 dB for two different
combinations of data rates. Increase in PAPR due to variable spreading could
be reduced by using spreading sequences (figure 6).
Figure 6: PAPR for two different sets of data rates

20 Susan R J and Sakuntala S Pillai
Bit Error Rate for receiver using MMSE FDE was lesser when spreading
sequences were used. BER with the use of chaotic sequences is almost same
as that of OVSF codes (figure 7). For BER 10-3 there is advantage of 1 dB
for both Vehicular A channel and AWGN channel for 16 users.
Figure 7: BER performance in Vehicular A and AWGN channels
Effect of ACF of spreading sequences on PAPR distribution
The effect of ACF of spreading sequences on PAPR distribution was studied
for Tent map binary sequences. Autocorrelation of tent map sequences of
length 16 was plotted in figure 8 when parameter ‘b’ in equation (2.1) takes
values of 1.5 and 1.99. Corresponding CCDF of PAPR was plotted in figures
9 to 10 using sequences generated with same values of ‘b’ for 8 users.
Figure 8: ACF of Tent map sequences with parameter b=1.5 and 1.99

Sequences with Low Peak Side Lobe Levels 21
Figure 9: PAPR for multiple data rates with Tent map sequences, value of
b=1.5
Figure 10 PAPR for multiple data rates with Tent map sequences, value of
b=1.99
The maximum spreading factor used was equal to 16 and each user was
allocated 16 subcarriers. Simulation was done for four different combinations
of data rates. Four different combinations of data rates used for simulation
were (i) 5 users with basic rate R, two with 2R and one user with rate 4R,
(ii) One user with rate 2R, 7 users with rate R, (iii) 4 users with rate 2R, 2
users with rate 4R, 2 users with rate 8R and (iv) 4 users with rate 8R and 4
users with rate 4R. It was observed from these plots that, the PAPR

22 Susan R J and Sakuntala S Pillai
distribution for different combinations of data rates depends on the ACF of
sequences used for spreading.
The ACF for sequences generated with parameter ‘b’ equal to 1.5 had
higher PSL (figure 8) and so the PAPR distribution for different sets of data
rates, were different. The decrease in ACF becomes sharper as value of ‘b’
increases. The resulting PAPR also decreases with this change in ACF.
Observation was that the use of sequences with sharp decrease in ACF
resulted in same PAPR distribution irrespective of combinations of data rates
chosen. It was noted that same PAPR distribution was obtained for Tent map
sequences generated with values of b ≥ 1.95.
PAPR for different sets of data rates were also plotted using Zadoff Chu
sequences and OVSF codes for comparison of the above result. This was done
for 8 users, considering the ease of choosing spreading codes for Zadoff Chu
sequences.
Figure 11 shows PAPR distribution of OFDMA system using OVSF codes
for multiple data rates, with QAM for 8 users. Different distributions were
obtained for different combinations of data rates, with higher PAPR for
combination which have higher data rates.
Figure 11: PAPR for multiple data rates with OVSF codes
PAPR distribution for different combinations of data rates with the use of
Zadoff Chu sequences is plotted in figure 12. Zadoff sequences and Tent map
sequences with good correlation property gave same PAPR distribution. It was
found by Tsai et. al [5] that OFDM CDMA system had different PAPR
depending on the spreading factor used. But with suitable choice of Zadoff
Chu sequences with low PSL, same PAPR distribution was obtained for the
VSF OFDMA system irrespective of the combinations of data rates used.

Sequences with Low Peak Side Lobe Levels 23
Figure 12: PAPR for multiple data rates with Zadoff Chu sequences
The spreading of data symbols for Zadoff Chu sequences with a spreading
factor M requires M complex multiplications while spreading by binary codes
like OVSF or Tent map binary sequences require M complex additions (or
sign inversions) [5].
It may be concluded that the PAPR distribution is independent of
combinations of data rate used, when the sequences with good autocorrelation
properties are used for spreading. Another useful feature of chaotic sequence is
the availability of large number of sequence sets which can be generated
easily, which is desirable for supporting multiuser communication.
Conclusion
The relationship between PSL and PAPR of VSF OFDMA systems, for three
different spreading sequences, Tent map binary sequences, Zadoff Chu
sequences and OVSF codes was investigated. In the proposed OFDMA system,
subcarriers were assigned to each user after spreading of data with VSF in
time domain. Increase in PAPR due to variable rate spreading could be
reduced with the use of spreading sequences.
In wireless communication systems, working of terminals with constant
PAPR for all data rate combinations is desirable to reduce the interference in
a multiuser environment. It was observed that, with the use of tent map binary
sequences and Zadoff Chu sequences with low PSL, the resulting PAPR was
independent of the combinations of data rates chosen and the CCDF
distribution remained the same. This observation was valid for the cases when
parameter ‘b’ in the Tent map took values greater than or equal to 1.95. The

24 Susan R J and Sakuntala S Pillai
integer values of parameter ‘p’ for Zadoff Chu sequences were chosen to be
relatively prime with respect to the sequence length.
The spreading of data symbols with Zadoff Chu sequences require complex
multiplications while spreading by binary codes like OVSF codes or Tent map
binary sequences require only complex additions or sign inversions. Unlike
other codes used for variable spreading of data, the number of users and the
combinations of multiple rate that is possible with chaotic binary sequences is
not constrained by limited availability of codes. Due to their sensitive
dependence on initial conditions, chaotic systems are able to produce large sets
of uncorrelated sequences with change in initial conditions. This reduces the
complexity of system implementation.
References
[1] Steer, M., 2007, “Beyond 3G,” IEEE microwave mag., pp. 76-82.
[2] Paterson, K.G., 2004, “On codes with low peak-to-average power ratio
for multicode CDMA,” IEEE Trans. Inf. Theory, 50, pp. 550-559.
[3] Nanda, S., Balachandran, K. and Kumar, S., 2000, “Adaptation
techniques in wireless packet data services,” IEEE Commun. Mag., pp.
54-64.
[4] Choi, B., Kuan, E. and Hanzo, L., 1999, “Crest-Factor Study Of MC-
CDMA And OFDM,” IEEE VTC ’99, pp. 233-237.
[5] Tsai, Y., Zhang, G. and Wang, X., 2008, “Polyphase Codes for Uplink
OFDM-CDMA Systems,” IEEE Transactions On Communications, 56(3),
pp. 435-444.
[6] Kurian, A.P., Puthusserypady, S. and Htut, S.M., 2005,“Performance
enhancement of DS/CDMA system using chaotic complex spreading
sequence, ” IEEE Trans. Wireless Commun. 4, pp. 984-989.
[7] Bateni, G.H. and McGillem, C.D., 1994, “A chaotic direct sequence
spread spectrum communication system, ” IEEE Trans. Commun., 42, pp.
1524-1527.
[8] Vitali, S., Rovatti, R. and Setti, G. 2006, “Improving PA Efficiency by
Chaos-Based Spreading in Multicarrier DS-CDMA Systems,” Proc.
International Symposium on Circuits and Systems (ISCAS), pp 1195-
1198.
[9] Xiang, F. and Qiu, S., 2008, “Analysis on Stability of Binary Chaotic
Pseudorandom Sequence,” IEEE communications letters, 12(5), pp 337-
339.
[10] Addabbo, T., Alioto, M., Fort, A., Rocchi, S. and Vignoli, V., 2006,”The
Digital Tent Map: Performance Analysis and Optimized Design as a
Low-Complexity Source of Pseudorandom Bits,” IEEE Transactions on
Instrumentation and Measurement, 55(5), pp 1451-1458.

Sequences with Low Peak Side Lobe Levels 25
[11] Stamoulis, A., Liu, Z. and Giannakis, G.B., 2002, “Space-time block-
coded OFDMA with linear precoding for multirate services,” IEEE Trans.
On Signal Process., 50(1), pp. 119-129.
[12] Ochiai, H. and Imai, H., 1998, “OFDM CDMA with peak power
reduction based on the spreading sequences, ” in IEEE Int. conf. on
Commun., pp. 1299-1303
[13] Ruan, H., Yaz, E. E., Zhai, T. and Yaz, Y. I., 2004, “A Generalization
of Tent Map and its Use in EKF Based Chaotic Parameter
Modulation/Demodulation,” 43rd IEEE Conference on Decision and
Control, Bahamas, pp. 2071-2075.
[14] Xing-yuan, W., Qing, Y., 2009, “A block encryption algorithm based on
dynamic sequences of multiple chaotic systems,” Communications in
Nonlinear Science and Numerical Simulation, 14, pp. 574–581.
[15] Morantes, D.S. and Rodriguez, D.M., 1998, “Chaotic sequences for
multiple access,” Electron. Lett., 34, pp. 235-237.
[16] Leon, D., Balkir, S., Hoffman, M. and Perez, L.C., 2000, “Fully
Programmable, scalable chaos based PN sequence generation,” Electron.
Lett., 36, pp. 1371-1372.
[17] Li, X. and Ritcey, J.A., 1997, “M sequences for OFDM peak to average
power ratio reduction and error correction, ” Electron. Lett., 33, pp. 554-
555.
[18] Borwein, P., Choi, K.S. and Jedwab, J., 2004. “Binary Sequences with
Merit Factor Greater Than 6:34,” IEEE Transactions On Information
Theory, Vol. 50, No. 12, pp 3234-3249
[19] Golay, M., 1972,“A class of finite binary sequences with alternate
autocorrelation values equal to zero,” IEEE Trans. Inform. Theory, vol.
IT-18, pp. 449–450.
[20] Dmitriev, D. and Jedwab, J. 2007, “Bounds on the growth rate of the
peak sidelobe level of binary sequences,”Adv. Math. Commun., 1, pp.
461-475.
[21] Husain, I., Husain, S., Khokhar, I. and Iqbal, R. , 2007, “OFDMA as a
technology for the next generation mobile and the Internet, ” in Proc. of
the third int. conf. on Wireless and mobile commun. pp. 14-14.
[22] Han, S.H. and Lee, J.H., 2005,“An overview of peak to average power
ratio reduction techniques for multicarrier transmission, ” IEEE Wireless
Commun., pp. 56-65.

26 Susan R J and Sakuntala S Pillai
Authors biography
Ms. Susan R J received MTech from University of Kerala. She is presently
Assistant Professor at College of Engineering, Trivandrum, Kerala and PhD
candidate at University of Kerala. Her research interests include multiple rate
transmission and multicarrier communication.
Dr. Sakuntala S. Pillai received Ph.D degree in 1989 from University of
Kerala. She is Professor & Dean (R & D), Mar Baselios College of
Engineering, Trivandrum., Kerala State. She has teaching experience of over 40
years, research experience of over 25 years and administrative experience of 8
years. Her research interests include Spread Spectrum Communications, OFDM
systems, OFDMA, Multicarrier communication systems, Error Correcting Codes
etc.