In this letter, we investigate the effect of inserting some randomly generated watermarking chips into known spreading sequences in terms of periodic correlations; moreover, we give two design criteria for good watermarked sequences in the sense of: 1) reducing the average correlation value and 2) minimizing the variance of correlations. For n = 2m with even m, we propose a set of 2m-1 punctured bent function sequences of length 2n-1 punctured by the Singer difference set. The maximum non-trivial correlation magnitude of the proposed set turns out to be 2m+1, which is asymptotically two times the Welch bound.
Bibliographical noteFunding Information:
Manuscript received April 7, 2019; accepted April 22, 2019. Date of publication May 7, 2019; date of current version July 10, 2019. This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2017R1A2B4011191). The associate editor coordinating the review of this letter and approving it for publication was S. Majhi. (Corresponding author: Hong-Yeop Song.) M. K. Song, G. Kim, and H.-Y. Song are with the Department of Electrical and Electronic Engineering, Yonsei University, Seoul 03722, South Korea (e-mail: firstname.lastname@example.org; email@example.com; firstname.lastname@example.org).
All Science Journal Classification (ASJC) codes
- Modelling and Simulation
- Computer Science Applications
- Electrical and Electronic Engineering