51 research outputs found
Cross correlations of Frank sequences and Chu Sequences.
Sets of Frank sequences and Chu sequences are two classes of polyphase sequence with ideal periodic autocorrelation functions, which at the same time have optimum crosscorrelation functions. The authors consider the crosscorrelations of sets of combined Frank/Chu sequences, which contain a larger number of sequences than either of the two constituent sets. It is shown analytically that the crosscorrelations are similar to those of the original sets with one exception, while the autocorrelations remain perfectly impulsiv
Performance Assessment of Polyphase Sequences Using Cyclic Algorithm
Polyphase Sequences (known as P1, P2, Px, Frank) exist for a square integer length with good auto correlation properties are helpful in the several applications. Unlike the Barker and Binary Sequences which exist for certain length and exhibits a maximum of two digit merit factor. The Integrated Sidelobe level (ISL) is often used to define excellence of the autocorrelation properties of given Polyphase sequence. In this paper, we present the application of Cyclic Algorithm named CA which minimizes the ISL (Integrated Sidelobe Level) related metric which in turn improve the Merit factor to a greater extent is main thing in applications like RADAR, SONAR and communications. To illustrate the performance of the P1, P2, Px, Frank sequences when cyclic Algorithm is applied. we presented a number of examples for integer lengths. CA(Px) sequence exhibits the good Merit Factor among all the Polyphase sequences that are considered
Mathematical Properties of the Zadoff-Chu Sequences
This paper is a compilation of well-known results about Zadoff-Chu sequences,
including all proofs with a consistent mathematical notation, for easy
reference. Moreover, for a Zadoff-Chu sequence of prime length
and root index , a formula is derived that allows computing
the first term (frequency zero) of its discrete Fourier transform, ,
with constant complexity independent of the sequence length, as opposed to
accumulating all its terms. The formula stems from a famous
result in analytic number theory and is an interesting complement to the fact
that the discrete Fourier transform of a Zadoff-Chu sequence is itself a
Zadoff-Chu sequence whose terms are scaled by . Finally, the paper
concludes with a brief analysis of time-continuous signals derived from
Zadoff-Chu sequences, especially those obtained by OFDM-modulating a Zadoff-Chu
sequence.Comment: 15 pages, 5 figures, not submitted for publicatio
On the Weight Distribution of Codes over Finite Rings
Let R > S be finite Frobenius rings for which there exists a trace map T from
R onto S as left S modules. Let C:= {x -> T(ax + bf(x)) : a,b in R}. Then C is
an S-linear subring-subcode of a left linear code over R. We consider functions
f for which the homogeneous weight distribution of C can be computed. In
particular, we give constructions of codes over integer modular rings and
commutative local Frobenius that have small spectra.Comment: 18 p
- …