432 IEEE COMMUNICATIONS LETTERS, VOL. 16, NO. 4, APRIL 2012
Hybrid Carrier CDMA Communication System Based on
Weighted-Type Fractional Fourier Transform
Xue-jun Sha, Member, IEEE, Xin Qiu, and Lin Mei, Member, IEEE
Abstract—Recently, an approach based on carrier scheme
convergence was proposed based on the weighted-type frac-
tional Fourier transform (WFRFT). Meanwhile, in the high-
speed wireless communication systems, code division multiple
access (CDMA) is an efficient technique for interference in the
frequency-selective fading channels. In this letter, we combine the
hybrid carrier (HC) scheme with CDMA and frequency domain
linear equalization. The proposed system can not only provide
the compatibility with single carrier (SC) CDMA and multi-
carrier (MC) CDMA systems, but also achieve a smooth and
seamless transition between the two. The proposed system can
switch to single carrier or multi-carrier scheme under the specific
conditions. Moreover, HC-CDMA outperforms SC-CDMA and
MC-CDMA systems over the frequency-selective fading channel
and single frequency jamming channel.
Index Terms—Hybrid carrier scheme, weighted-type fractional
Fourier transform, code division multiple access.
I. INTRODUCTION
N
OWADAYS, wireless communication area is increas-
ingly in demand of high-spead data transmission. How-
ever, the channel is severely frequency-selective due to paths
with different delays. A promising technique to overcome
the channel frequency selectivity is direct sequence spread
spectrum (DSSS) or code division multiple access (CDMA),
and it has been widely used in existing systems [1]. In view of
the carrier scheme, there are mainly two approaches in CDMA
systems—single carrier CDMA (SC-CDMA) and multi-carrier
CDMA (MC-CDMA) [2].
In SC-CDMA system time spreading is adopted, and each
data symbol occupies the whole bandwidth. While in MC-
CDMA, the data symbols after spreading are modulated in
different sub-carriers, and it can be understood that spreading
is applied in frequency domain. Compared to SC-CDMA
system, MC-CDMA system has a higher spectrum efficiency
and flexibility [3], thus, it has achieved more attention in
recent years [2], [4]. In MC-CDMA system, frequency domain
equalization (FDE) is usually adopted to resist the channel
frequency selectivity [2]. And in order to improve the system
performance further, the research of MC-CDMA is extended
to a multiple-input multiple-output (MIMO) system employing
Alamouti space-time block coding [4]. However, problems
such as high peak to average power ratio (PAPR), which does
not exist in SC-CDMA system, are great challenges to the
multi-carrier scheme [1].
Manuscript received August 4, 2011. The associate editor coordinating the
review of this letter and approving it for publication was W. Ser.
The authors are with the Communication Research Center, Harbin Institute
of Technology, Harbin, Heilongjiang, 150001, P. R. China (e-mail: shaxue-
jun@hit.edu.cn).
This work was supported by the National Natural Science Foundation
General Program of China (61171110).
Digital Object Identifier 10.1109/LCOMM.2012.030512.111681
Convergence of the existing techniques in a common plat-
form will be a main feature for future wireless systems. And
there is also a thriving need to develop integrated mobile
terminals [5]. In order to solve the compatibility issue with
existing systems, [6] proposed a hybrid carrier (HC) commu-
nication system based on the weighted-type fractional Fourier
transform (WFRFT). The HC scheme integrates MC and SC
to achieve a more even time-frequency distribution of signal
energy, and it is thought to have the potential superiority over
the selective fading channels compared to the traditional SC
and MC schemes. In [6] bit error ratio (BER) performance
is also discussed in the simplified fading channel, and the
HC system outperforms SC and MC. In the aforementioned
researches, the channel conditions are simple and the analysis
of interference is not sufficient enough.
We propose a HC-CDMA communication system combin-
ing the WFRFT with the CDMA technique. Spreading is
applied in a certain fractional domain, and the HC charac-
teristic of SC and MC integration is achieved by the WFRFT.
At the receiver frequency domain equalization can further
resist the channel fading and improve the system performance.
Because of unitary property, the data after equalization can be
transformed to the corresponding fractional domain, in which
despreading and demodulation are utilized. In SC-CDMA or
MC-CDMA system, the data symbol is spread in either time
or frequency domain. By this spreading the signal energy can
be distributed uniformly in the spreading domain. Due to its
even and symmetric signal energy distribution in time and
frequency domains, the HC system combined with CDMA is
natural and reasonable, in which spreading is adopted in both
time and frequency domain simultaneously.
The remaining parts of this letter are arranged as follows:
the introductions of the HC scheme and HC-CDMA system
are described in Section II. In Section III, we compare the
performances of the three different carrier scheme CDMA
systems over the multi-path channel and a single-frequency
interference channel. Finally, Section IV concludes the whole
letter.
II. H
YBRID CARRIER CDMA SYSTEM BASED ON THE
WFRFT
A. Hybrid carrier scheme
For a square integrable function g(x), its
Fourier transform and inverse Fourier transform
are G(ω)=1/
√
2π
∞
−∞
g(x)e
−jωx
dx and
g(x)=1/
√
2π
∞
−∞
G(ω)e
jωx
dω. The WFRFT of g(x)
is expressed as a linear weighted combination of four basic
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2012 IEEE