Uplink MC-DS-CDMA using ZCZ sequences for
frequency-selective block-fading channels
D.J. Basilio, Member, IEEE, L.P. Linde, Senior Member, IEEE, and B.T. Maharaj, Member, IEEE
Department of Electrical, Electronic and Computer Engineering, University of Pretoria, Pretoria, South Africa
Email: s23361850@tuks.co.za, llinde@postino.up.ac.za, sunil.maharaj@up.ac.za
Abstract—In this paper, a time and frequency (TF) domain
spreading multicarrier direct sequence code division multiple
access (MC-DS-CDMA) scheme employing zero correlation zone
(ZCZ) sequences, designed specifically for quasi-synchronous
uplink transmissions, is proposed to exploit frequency and
temporal diversity in frequency-selective block-fading channels.
This is in contrast to previously proposed schemes designed
only to exploit frequency diversity in frequency-selective slow
fading channels. Almost optimal quadriphase ZCZ sequences
are employed to minimize multi-user interference (MUI) in the
uplink channel. Joint detection is employed at the receiver using
the optimal maximum likelihood (ML) detector and sub-optimal
minimum mean square error (MMSE) detector. When using
the ML detector, the proposed system showed a performance
improvement of 2.7 dB at a BER of 10
−4
over a previously
proposed scheme designed only to exploit frequency diversity.
I. Introduction
Among the multicarrier code division multiple access
(CDMA) schemes proposed in the literature, we can
distinguish between two different approaches: frequency-
domain spreading, as in multicarrier CDMA (MC-CDMA)
systems [1], and time-domain spreading, as in MC
direct-sequence CDMA (MC-DS-CDMA) systems [2, 3].
Conventional MC-DS-CDMA does not achieve frequency
diversity without introducing redundancy [2, 3], and thus
there is a trade-off between data throughput and performance.
In [4], an amalgam of MC-CDMA and MC-DS-CDMA
known as time and frequency (TF) domain spreading MC-
DS-CDMA was proposed to achieve frequency diversity,
without introducing redundancy. TF-domain spreading MC-
DS-CDMA relies on joint detection at the receiver, and
generally has higher receiver decoding complexity compared
to conventional uncoded MC-DS-CDMA. Recently, a TF-
domain spreading MC-DS-CDMA scheme employing zero
correlation zone (ZCZ) time domain spreading sequences
was proposed for the quasi-synchronous uplink channel
[5]. The benefit of employing ZCZ time domain spreading
sequences in the uplink is that they are capable of reducing
multi-user interference. Over the duration of the ZCZ, both
the cross-correlation and the auto-correlation properties of the
spreading sequences are zero, and thus there is no interference
between users separated by propagation delay differences that
are within the ZCZ (interference-free window). However, the
system in [5] is only designed to obtain frequency diversity
in frequency selective slow fading channel conditions and
does not consider the time selectivity of the wireless channel.
In this paper the authors present a system model for
TF-domain spreading MC-DS-CDMA that exploits frequency
and temporal diversity in frequency selective block-fading
channel conditions, where the fading coefficients are constant
over one fading block but are independent from block to
block [6, 7]. It has been shown that the diversity gain in
block-fading channels can be improved by coding across
multiple fading blocks [6, 7]. Thus, the proposed system is
able to achieve frequency and temporal diversity instead of
just the frequency diversity achieved in [5]. Quadriphase ZCZ
sequences are employed as time-domain spreading sequences
to reduce multi-user interference (MUI) in the uplink. Joint
detection is done at the receiver using the optimal maximum
likelihood (ML) detector and the minimum mean square
error (MMSE) detector [8]. Simulation results reveal that the
proposed system performs better than the system proposed
in [5], due to the additional temporal diversity exploited in
block-fading channel conditions.
Notation: Column vectors (matrices) are denoted by
boldface lower (upper) case letters. Superscripts
T
and
∗
denote the transpose and complex conjugate operations,
respectively; diag(d
1
, . . . , d
P
) denotes a P ×P diagonal matrix
with diagonal entries d
1
. . . d
P
. I
N
is the N ×N identity matrix
and 0
N×M
is the N × M all zero matrix. F
P
is the P × P
discrete Fourier transform (DFT) matrix. The cardinality of a
set or the magnitude of an element is denoted by |.| and dxe is
the smallest integer larger than x. The remainder of division
of x by y is denoted by (x)mod(y).
II. Construction of ZCZ sequences
Traditional orthogonal spreading sequences, such as or-
thogonal Gold sequences and Walsh-Hadamard sequences [9],
exhibit non-zero off-peak cross-correlations, which limits the
achievable performance in asynchronous or quasi-synchronous
scenarios. However, ZCZ sequences exhibit an interference
free window over which both the cross-correlation and auto-
correlation function are zero. Consequently, ZCZ sequences
are able to suppress MUI in the quasi-synchronous uplink
channel. We denote a set of ZCZ sequences as (L
seq
, M
seq
, Z
0
)-
ZCZ, where L
seq
is the sequence length, M
seq
is the sequence
family size and Z
0
is the one-sided ZCZ length in chips. For
a sequence set {s
q
}
M
seq
q=0
with family size M
seq
, and sequence
length L
seq
, the periodic correlation characteristics of ZCZ
23 - 25 September 2009, Nairobi, Kenya
978-1-4244-3919-5/09/$25.00 ©2009 IEEE