Synthesis of a set of real-valued shift-orthogonal finite-length PN sequences

2007

SUMMARYThis paper proposes a real-valued orthogonal periodic sequence of a period N = 2 n derived from a real-valued shift-orthogonal finite-length sequence of length M = 2 n + 1. This paper also explains the principle of a fast correlation algorithm that efficiently executes periodic correlation processing for this real-valued orthogonal periodic sequence. The sidelobe of an aperiodic autocorrelation function for a real-valued shift-orthogonal finite-length sequence (length of M) is 0 except for the right and left ends of the shift. If the subsequent sequence of first values repeatedly overlap the final values of this sequence, a real-valued orthogonal periodic sequence of a period N = M -1 can be obtained. A real-valued orthogonal periodic sequence of a period N = 2 n generated from real-valued shift-orthogonal finite-length sequence of length M = 2 n + 1 is obtained by convoluting partial sequences and based on that controls the number of multiplications and the number of additions to increment on the order of Nlog 2 N without using fast Fourier transformation.

Section: Real-valued Shift-orthogonal Finite-length Sequence Of Lengthmentioning

confidence: 99%

“…8. Section 4 utilizes the real-valued shift-orthogonal finitelength sequence described in Section 3 to express a realvalued orthogonal periodic sequence of period N = M -1 = 2 n using seasonalized convolutions of partial sequences.…”

Section: Introductionmentioning

confidence: 99%

A real‐valued periodic orthogonal sequence derived from a real‐valued shift‐orthogonal finite‐length sequence and its fast periodic correlation algorithm

2007

“…The sequence {a M,i } for which aperiodic autocorrelation function (1) satisfies is called the real-valued shift-orthogonal finite-length sequence [2][3][4]. ε M−1 is called the shift end correlation value.…”

Section: Real-valued Shift-orthogonal Finite-length Sequence and Corrmentioning

confidence: 99%

“…It follows from Eqs. (1) and (2) that Given an arbitrary ε M−1 , the sequence value a M,i is determined [2]. Consider, as an example, the sequence of length 2.…”

Section: Real-valued Shift-orthogonal Finite-length Sequence and Corrmentioning

confidence: 99%

See 1 more Smart Citation

Aperiodic autocorrelation functions of real‐valued shift‐orthogonal finite‐length sequences with round‐off errors

2004

SUMMARYA real-valued shift-orthogonal finite-length sequence is a sequence for which the side-lobe of the aperiodic autocorrelation function is zero except at the two ends. It is effectively used in spread-spectrum communications and other applications. This type of sequence can be synthesized by using element sequences of adequate lengths. Consequently, fast correlation processing can be realized by dividing the process for each element sequence. A problem in this sequence is that the round-off error of its real values has an effect on the correlation characteristics. Therefore, this paper investigates the effect of the round-off error on integrated correlation processing and divided correlation processing. In the former, the mean-square error of the correlation output is inversely proportional to the sequence length. In the latter, it is the sum of the mean-square errors of the element sequences, which are inversely proportional to the respective sequence lengths. Thus, we see that the error of shorter element sequences should be reduced in the latter method in order to speed up correlation processing. This paper considers in particular a method by which the mean-square error is reduced without significantly enlarging the circuit scale.

Fast aperiodic correlation algorithm for real‐valued shift‐orthogonal finite‐length sequence of length 2^ν+1

2007

SUMMARYReal-valued shift-orthogonal finite-length sequences are sequences in which the side lobes of the aperiodic autocorrelation function become 0, except for the endpoints of the shift to both sides, and can be applied in pulse compression radar and spread spectrum communications. In this paper, a fast correlation algorithm for efficiently calculating the periodic correlation function is discussed for real-valued shift-orthogonal finite-length sequences with length M = 2 n + 1. For input data, including a real-valued shift-orthogonal finite-length sequence over a certain range, the value of the aperiodic correlation function is found in a certain shift range. Based on the synthesis of this sequence by the convolution of n + 1 partial sequences, the correlation processing is broken down into correlation processing of the n + 1 stages of partial sequences. As a result, the number of multiplications and the number of additions can be suppressed on the order M log 2 M.