A Family of Single-Channel Spectrally-Null-Constrained Sequences With Low Correlation

Spectrally-constrained sequences (SCSs) with good correlation properties, and low spectral power under the spectral constraint have found many practical applications in communication, and radar systems operating over non-contiguous carriers or frequency slots. In this letter, a construction of single-channel spectrally-null-constrained sequence (SNCS) families with good correlation is proposed. Following the proposed construction, a single-channel polyphase SNCS family with period $N(N$  + 1), and family size $(p-1)$ can be obtained, which has zero power leakage under the spectral constraint $\lbrace 1+a(N+1):a\in \mathbb {Z}_N\rbrace$ , where $N$ is an odd integer, and $p$ is the minimum prime factor of $N$ . Note that the maximum periodic correlation magnitude of the derived single-channel SNCS family is $(N+1)$ , which asymptotically achieves the correlation lower bound as $p$ increasing.