416 IEEE COMMUNICATIONS LETTERS, VOL. 6, NO. 10, OCTOBER 2002
A Technique for Deriving Sets of Orthogonal
Sequences From Binary Parents Which
Preserves Auto-Correlation Properties
Ian Oppermann, Senior Member, IEEE
Abstract—Binary-valued Barker sequences have close to ideal
autocorrelation (AC) properties but are extremely rare. The
11-chip Barker sequence is fundamental to the performance of
the IEEE 802.11 WLAN standard. This letter presents a method
of deriving new sets of sequences from a binary “parent” using
a generalization of the technique derived in [1]. The method
maintains the AC properties of the original binary source and can
be used to produce sequence sets orthogonal to the original. This
technique is applied to produce orthogonal sets of sequences with
Barker-like AC properties.
Index Terms—Barker sequences, complex, orthogonal, spread-
ing sequences.
I. INTRODUCTION
T
HE autocorrelation (AC) properties of spreading se-
quences substantially determine the performance of the
resulting spread spectrum system. The nonzero shift values
seen in the aperiodic AC function indicate the level of interfer-
ence incurred when a multipath component is detected at the
receiver. The mean square sum of the nonzero shift values indi-
cate the degree of “flatness” of the spectrum of the transmitted
signal which is important in fading channels. The degree of
“flatness” is also important in a regulatory sense for operation
in the unlicensed ISM bands. For example, the FCC regulates
the maximum power which may be present in any part of the
band of a signal transmitted in the ISM band. The ideal AC
function for a spreading sequence is a Kroneker delta function
which has a perfectly flat spectrum implying the transmitted
signal is spread uniformly across the occupied band.
The chip Barker sequence was chosen for use in
the IEEE 802.11 WLAN standard due to its almost ideal AC
properties. Fig. 1 shows the normalized aperiodic AC function
of the sequence. Fig. 2 shows the corresponding spectrum of
the sequence. The AC function demonstrates very good side
lobe values at either 0, or . The WLAN standard relies on a
single access channel scheme, so cross-correlation (CC) prop-
erties have not historically been of interest. A problem with
this approach is that neighboring WLAN systems must share
the available spectrum using a carrier sense protocol. If a trans-
mission is detected in any of the available channels, all other
Manuscript received January 18, 2002. The associate editor coordinating the
review of this letter and approving it for publication was Prof. K. Kiasaleh.
The author is with the Centre for Wireless Communications Oulu, University
of Oulu, Oulu, FIN-90014, Finland (e-mail: ian@ee.oulu.fi).
Digital Object Identifier 10.1109/LCOMM.2002.804215.
Fig. 1. AC magnitude for 11 chip Barker sequence.
Fig. 2. Normalized spectrum for 11–chip binary Barker sequence and example
complex set member.
terminals must wait until the channel is clear of traffic. New se-
quences with similar spectral properties would allow multiple
channel access in a true CDMA sense.
A technique developed for generation of complex valued
spreading sequences in [2] has been modified and applied to
1089-7798/02$17.00 © 2002 IEEE