On Certain Sets of Polyphase Sequences With Sparse and Highly Structured Zak and Fourier Transforms

This paper describes a KM²×M, K ∈ Q, M, KM ∈ Z, Zak space construction of zero correlation zone polyphase sequence sets, of sequence length KM³ and set size KM, with all-zero cross correlation. The construction includes the sets with an (M-1)-point and (T₂M-1)-point zero autocorrelation zone, where T₂ is an arbitrary nontrivial factor of M. All sequences in these sets have sparse, highly structured, semipolyphase finite Zak transforms, with constant nonzero magnitude at M points and zero magnitude at selectable KM³-M points, and sparse, semipolyphase KM³-point discrete Fourier transforms, with constant nonzero magnitude at M² points and zero magnitude at selectable KM³-M² points.