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