Study Of Perfect Discrete Signal Pair

The perfect discrete signal has been widely employed in radar, sonar, navigation, telemetry and remote control, signal processing, information encryption, spread spectrum communication and so on. In the past several decades, many researchers devoted to the study of the perfect discrete signal. The perfect discrete signal pair is a new researching direction of the perfect discrete signal, so the research on the perfect discrete signal pair has important theory significance and application significance.Based on the study of discrete signals with good correlation, such as perfect binary array pair, almost perfect binary array pair, perfect punctured binary array pair, some in-depth studies of the perfect discrete signal pair have been developed.Aiming at the unique receiving of binary sequence pair, the uniqueness of low correlation zone sequence pair is put forward and proved. And, the uniqueness of zero correlation zone sequence pair and almost perfect autocorrelation sequence pair is proved as the specific cases of low correlation zone sequence pair. Moreover, the uniqueness of pseudorandom binary sequence pair, almost perfect punctured binary sequence pair, perfect punctured binary sequence pair and pseudorandom punctured binary sequence pair is proved. The unique receiving is guaranteed in theory, when the sequence pairs mentioned above are applied.Two-dimension sequence pair with zero correlation zone is proposed. The transformation properties and existence conditions of two-dimension binary sequence pair with zero correlation zone are studied. The bound on two-dimension sequence pair with zero correlation zone is given. And methods of extension of set size of sequence pair set with zero correlation zone and two-dimension sequence pair set with zero correlation zone are presented.Two-dimension complementary sequence pair with zero correlation zone is proposed. The transformation properties of two-dimension binary complementary sequence pair with zero correlation zone are studied. The bound on two-dimension complementary sequence pair with zero correlation zone is given. And the method of construction of two-dimension ternary complementary sequence pair set with zero correlation zone is presented based on two-dimension binary complementary sequence pair set with zero correlation zone. Two-dimension complementary sequence pair family with zero correlation zone is proposed. The transformation properties of two-dimension complementary sequence pair family with zero correlation zone are studied. The bound on two-dimension complementary sequence pair family with zero correlation zone is given. And the method of construction of two-dimension ternary complementary sequence pair family set with zero correlation zone is presented based on two-dimension binary complementary sequence pair family set with zero correlation zone.Two-dimension periodic complementary sequence pair with zero correlation zone is proposed. The transformation properties of two-dimension binary periodic complementary sequence pair with zero correlation zone are studied. The bound on two-dimension periodic complementary sequence pair with zero correlation zone is given. And the method of extension of set size of two-dimension periodic complementary sequence pair set with zero correlation zone is presented. Two-dimension periodic complementary sequence pair family with zero correlation zone is proposed. The transformation properties of two-dimension binary periodic complementary sequence pair family with zero correlation zone are studied. The bound on two-dimension periodic complementary sequence pair family with zero correlation zone is given. And the method of extension of set size of two-dimension periodic complementary sequence pair family set with zero correlation zone is presented.Binary array pair with two-level autocorrelation is proposed. The transformation properties, Fourier spectrum characters and existence conditions of binary array pair with two-level autocorrelation are studied. Folding construction between binary array pair with two-level autocorrelation and binary sequence pair with two-level autocorrelation, and folding construction among binary array pairs with two-level autocorrelation are given.Punctured binary array pair with two-level autocorrelation is proposed. The transformation properties, Fourier spectrum characters and existence conditions of punctured binary array pair with two-level autocorrelation are studied. Folding construction between punctured binary array pair with two-level autocorrelation and punctured binary sequence pair with two-level autocorrelation, and folding construction among punctured binary array pairs with two-level autocorrelation are given.Aiming at the unique receiving of binary array pair, the uniqueness of binary array pair with two-level autocorrelation is put forward and proved. And, the uniqueness of pseudorandom binary array pair is proved as the specific case of binary array pair with two-level autocorrelation. Moreover, the uniqueness of almost perfect binary array pair and perfect punctured binary array pair is proved. The unique receiving is guaranteed in theory, when the array pairs mentioned above are applied.