Study Of Almost Perfect Binary Array Pairs

The perfect discrete signal has already been widely employer in navigation, radar,telemetry and remote control, signal processing, spread spectrum communication,information encryption and so on. In past several decades, a lot of researchers devoted tothe study of some perfect discrete signal. The perfect discretes signals pairs is a newresearch direction of the perfect discrete signals, so the researches on the perfect discretesignal pair has important in the application significance and theory significance.Based on study of discrete signals with some good correlation, such like almost perfectbinary pair, perfect binary array pair, this paper studies it more further. The maincontributions are all followed:(1)The concept of the sequence pairs, some properties of the sequences and theapplications of the sequences pairs in the signal dealing and communication systems areintroduced. On one hand, these concepts lay the foundation for later work and on the otherhand, we can see the sequence pairs can expand the selecting range of the perfect discretesignals.(2)Aiming in the unique receiving of binary array pairs，the uniqueness of the lowcorrelation zone array pairs are proved and put forward. And the uniquences of zerocorrelation zone array pairs and the almost perfect autocorrelation array pair is proved asspecific cases of low correlation zone array pairs. And moreover, based on the theory ofthe formers, the uniquence of the almost perfect binary array pair, pseudorandom puncturedbinary of the array pair is proved. The unique receiving is guaranteed in theory, when thearray pairs mentioned absolved are aoolied.(3)Import of the concept of the almost perfect autocorrelation binary, the charactersand necessary and sufficient conditions of existence of generalized relative difference setpairs are main discussed. Some methods for constructing the generalized relative differenceset pairs are given. And also the Fourier spectrum characters of the characteristic array pairs are given.(4) Based on the sequence theories which are introduced preview, the transformcharacters and the Fourier spectrum and the necessary existence are used to induce the spacethat would be searched by the computer. So the highly active computer searching algorithmof binary array paris is designed. Lastly by using the computer searching, considerable countof array pairs are found with the array length are low then about22.