Research on Theory of Almost Perfect Binary-Third-Order Cyclic Autocorrelation Sequences

Abstract

Because higher-order cumulant (HOC) is insensitive to the adding Gaussian noise and symmetry non-Gaussian noise, a new kind of perfect discrete signal with good periodic correlation function is presented, which is the almost perfect binary-third-order cyclic autocorrelation sequences (APBTOCAS). We present the definitions of APBTOCAS and its transformation properties. Based on these properties, we search out an almost perfect binary-third-order cyclic autocorrelation sequence 667 (octal) within length 26. Then, we theoretically prove that binary-third-order cyclic autocorrelation sequences can effectively suppress colored Gaussian noise. Finally, the simulation shows that almost perfect binary-third-order cyclic autocorrelation sequences have such good periodic correlation that they can they are feasible for engineering applications as synchronization codes and multiuser codes, remedying the defect of the current Pseudo-noise (PN) code used in very low signal-noise-ratio (SNR) environments.