Research on theory of binary-third-order cyclic autocorrelation sequences

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. This paper proposes a new concept of perfect binary-third-order cyclic autocorrelation sequences (PBTOCAS), and defines the quasi-perfect binary-third-order cyclic autocorrelation sequences (QPBTOCAS) and the almost perfect binary-third-order cyclic autocorrelation sequences (APBTOCAS). Then, the properties of these binary sequences are studied, and we theoretically prove that binary-third-order cyclic autocorrelation sequences can effectively suppress colored Gaussian noise. Finally, some quasi-perfect binary-third-order cyclic autocorrelation sequences and almost perfect binary-third-order cyclic autocorrelation sequences with short lengths by computer searching are listed. From the observation of the perfect binary-third-order cyclic autocorrelation sequences, we can see that it can well suits engineering applications, remedying the defect of the current Pseudo-noise (PN) code used in very low signal-noise-ratio (SNR) environments.