Binary maximal-length linear feedback shift register sequences (m-sequences) have been successfully employed in communications, navigation, and related systems over the past several years. For the early applications, m-sequences were used primarily because of their excellent periodic autocorrelation properties. For many of the recent systems applications, however, the crosscorrelation properties of such sequences are at least as important as the autocorrelation properties, and the system performance depends upon the aperiodic correlation in addition to the periodic correlation. This paper presents a survey of recent results and provides several new results on the periodic and aperiodic crosscorrelation functions for pairs of m-sequences and for pairs of related (but not maximal-length) binary shift register sequences. Also included are several recent results on correlation for complex-valued sequences as well as identities relating the crosscorrelation functions to autocorrelation functions. Examples of problems in spread-spectrum communications are employed to motivate the choice of correlation parameters that are considered in the paper.

Crosscorrelation properties of pseudorandom and related sequences

A set of equally long finite sequences, the elements of which are either + 1 or - 1, is said to be a complementary set of sequences if the sum of autocorrelation functions of the sequences in that set is zero except for a zero-shift term. A complementary set of sequences is said to be a mate of another set if the sum of the cross-correlation functions of the corresponding sequences in these two sets is zero everywhere. Complementary sets of sequences are said to be mutually orthogonal complementary sets if any two of them are mates to each other. In this paper we discuss the properties of such complementary sets of sequences. Algorithms for synthesizing new sets from a given set are given. Recursive formulas for constructing mutually orthogonal complementary sets are presented. It is shown that matrices consisting of mutually orthogonal complementary sets of sequences can be used as operators so as to per form transformations and inverse transformations on a one- or two-dimensional array of real time or spatial functions. The similarity between such new transformations and the Hadamard transformation suggests applications of such new transformations to signal processing and image coding.

Complementary sets of sequences

A new general class of polyphase sequences with ideal periodic autocorrelation function is presented. The new class of sequences is based on the application of Zadoff-Chu polyphase sequences of length N=sm/sup 2/, where s and m are any positive integers. It is shown that the generalized chirp-like sequences of odd length have the optimum crosscorrelation function under certain conditions. Finally, recently proposed generalized P4 codes are derived as a special case of the generalized chirp-like sequence. >

Generalized chirp-like polyphase sequences with optimum correlation properties

N-shift cross-orthogonal sequences and a complete complementary code derived from them are defined and discussed. A general method for generating this code is also discussed. A synchronous multiple-user spread-spectrum multiple system is proposed that uses N-shift cross-orthogonal sequences. >

N-shift cross-orthogonal sequences

This article is a review of our ongoing research effort to construct a new multicarrier CDMA architecture based on orthogonal complete complementary codes, characterized by its innovative spreading modulation scheme, uplink and downlink signaling design, and digital receiver implementation for multipath signal detection. There are several advantages of the proposed CDMA architecture compared to conventional CDMA systems pertinent to current 2G and 3G standards. First of all, it can achieve a spreading efficiency (SE) very close to one (the SE is defined as the amount of information bit(s) conveyed by each chip); whereas SEs of conventional CDMA systems equal 1/N, where N denotes the length of spreading codes. Second, it offers MAI-free operation in both upand downlink transmissions in an MAI-AWGN channel, which can significantly reduce the co-channel interference responsible for capacity decline of a CDMA system. Third, the proposed CDMA architecture is able to offer a high bandwidth efficiency due to the use of its unique spreading modulation scheme and orthogonal carriers. Lastly, the proposed CDMA architecture is particularly suited to multirate signal transmission due to the use of an offset stacked spreading modulation scheme, which simplifies the rate-matching algorithm relevant to multimedia services and facilitates asymmetric traffic in up- and downlink transmissions for IP-based applications. Based on the above characteristics and the obtained results, it is concluded that the proposed CDMA architecture has a great potential for applications in future wideband mobile communications beyond 3G, which is expected to offer a very high data rate in hostile mobile channels.

A multicarrier CDMA architecture based on orthogonal complementary codes for new generations of wideband wireless communications

A class of binary sequences whose elements are either 1 or -1 and whose autocorrelation function is 0 for all even shifts except the zero shift is discussed. These sequences will be called E sequences. It is proved that every E sequence is paired with another E sequence, its mate, so that the cross-correlation function between them is 0 for all even shifts including the zero shift. Using these sequences, new complete orthogonal function sets are derived. Several other important properties of these sequences are also obtained and the relations among these sequences, Golay's complementary sequences and Welti's quaternary codes are discussed.

M. Hatori

Papers

N-shift cross-orthogonal sequences

Even-shift orthogonal sequences