Odd-periodic Autocorrelation Research Articles

The 4-adic complexity of quaternary sequences with optimal odd-periodic autocorrelation magnitude

The 4-adic complexity of quaternary sequences with optimal odd-periodic autocorrelation magnitude

New quaternary sequences with optimal odd-periodic autocorrelation magnitude

A quaternary sequence is said to be optimal if its odd-periodic autocorrelation magnitude equal to 2 for even length, and 1 for odd length. In this paper, we propose three constructions of optimal quaternary sequences: the first construction applies the inverse Gray mapping to four component binary sequences, which could be chosen from GMW sequence pair, twin-prime sequence pair, Legendre sequence pair, and ideal sequences; the second one generates optimal sequences from quaternary sequences with optimal even-periodic autocorrelation magnitude; the third one gives new optimal quaternary sequences by applying the sign alternation transform and Gray mapping to GMW sequence pair and twin-prime sequence pair. In particular, some proposed sequences have new parameters.

On three conjectures of binary sequences with low odd-periodic autocorrelation

This paper provides a complete answer to three conjectures of Parker about low odd-periodic autocorrelation of sixteen cyclotomic binary sequences in Parker (2001), and also gives new binary sequences with low odd-periodic autocorrelation.

Odd-Periodic and Periodic Complementary binary sequences

Two or more sequences are called an Odd-Periodic Complementary binary sequences Set (OPCS) if the sum of their respective odd-periodic autocorrelation function is a delta function. In this paper, the definition of OPCS is given and the construction method of OPCS is discussed. The relation of the OPCS with the Periodic Complementary binary sequences Set (PCS) is pointed out, and some new PCSs are obtained based on such relation.

Binary and quadriphase sequences with optimal autocorrelation properties: a survey

Time-discrete signals with good autocorrelation properties are used in various applications in communications engineering. From an implementation point of view, usually sequences with a small phase alphabet and a maximal energy efficiency, i.e., a uniform envelope, are most favorable. For this reason, known methods as well as several new construction techniques of binary and quadriphase sequences with optimal or best known autocorrelation properties are discussed in this correspondence. In many cases, the achievable correlation properties can be improved significantly if a single zero element per sequence is accepted. These almost binary and almost quadriphase sequences are considered as well. The optimality criteria used include the maximum absolute sidelobe and the merit factor of the periodic and the odd-periodic autocorrelation function, respectively. For sequence lengths of up to 44 in the binary case and up to 32 in the quadriphase case, the best known parameters obtained by computer search are compared with the constructed results.

Cubical binary arrays with perfect odd-periodic autocorrelation

Three-dimensional arrays with good autocorrelation functions are required in multidimensional signal processing. A generalized folding procedure is derived that permits the construction of such arrays from good correlating sequences for many array sizes. This method is applied to the construction of cubical binary arrays with a single zero element and odd-periodic autocorrelation function with zero sidelobes.

Mismatched filtering of odd-periodic binary sequences

Binary sequences with perfect periodic autocorrelation functions, as required in communications, radar, and measuring, are not known for any lengths >4. As a possible remedy, mismatched filtering can be used to entirely suppress any sidelobes of the periodic autocorrelation function at the expense of a reduced signal-to-noise ratio (SNR). In this work, the mismatched filtering method is extended to the odd-periodic autocorrelation function whose technical implementation is no more complex than that of periodic sequences. A new class of odd-periodic binary sequences is constructed that exist for many more lengths and exhibit significantly lower mismatched filtering losses than any known periodic sequences.

Binary arrays with perfect odd-periodic autocorrelation

Arrays with good autocorrelation functions are required for coded aperture imaging. A generalized folding procedure is derived that permits the construction of arrays with good correlation properties from well correlating sequences for many array sizes. This synthesis method is applied to the construction of approximately square binary arrays with a single zero element and perfect odd-periodic autocorrelation functions. In addition, new binary arrays with constant sidelobes of their periodic autocorrelation functions (uniformly redundant arrays) can be generated with the generalized folding method.