Research on perfect binary correlation sequences based on higher-order cumulant

Current researches define the perfect signal by the inner product of sequence itself and its delay sequence. However, these traditional sequences based on second-order statistics cannot handle colored Gaussian measurement noise automatically. Because higher-order cumulant (HOC) is insensitive to the adding Gaussian noise and symmetrical non-Gaussian noise, a new kind of perfect binary signal with good periodic correlation function based on HOC 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 QPBTOCAS and APBTOCAS with short lengths by computer searching are listed. From the observation of the PBTOCAS, we can see that it can well suit engineering applications, remedying the defect of the conventional pseudo-noise code used in very low signalnoise-ratio environments.