Abstract
We present an N-dimensional generalisation of the two-dimensional block-circulant perfect array construction by Blake et al. As in Blake et al, the families of N-dimensional arrays possess pairwise good zero correlation zone (ZCZ) cross-correlation. Both constructions use a perfect autocorrelation sequence with the array orthogonality property (AOP).
Highlights
This paper presents a generalization of the 2-dimensional block-circulant array construction by [Blake, 2013]
The ratio of zero to non-zero cross-correlation values is larger for higher dimensional arrays
We show that Sk from Construction II has perfect autocorrelation (k1 = k2) and Sk1, Sk2 has good cross-correlation (k1 = k2)
Summary
This paper presents a generalization of the 2-dimensional block-circulant array construction by [Blake, 2013]. We begin by stating the 2-dimensional construction for families of arrays with perfect autocorrelation and good cross-correlation as given in [Blake, 2013]. Sk = [Si,j ]k = aj c(j mod d)w⌊j/d⌋+k(j mod d)+i for 0 ≤ i < n, 0 ≤ j < m, a has the AOP for the divisor d, 0 < k ≤ m, and w = m/d. We construct a family of k N -dimensional perfect arrays, Sk, such that
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