Sequences Design With Anti-doppler Properties

With the development of science and technology,pseudo random sequence is widely applied in communication system,cryptography,coding,radar and sonar.Generally,the main indexes to measure the properties of pseudo random sequences are correlation,ambiguity function(two-dimensional correlation),linear complexity and so on.In different engineering systems,the properties of sequence usually directly affect the performance of the system.Therefore,the theoretical study of sequences is mainly devoted to analyzing the properties of existing sequences or designing new sequences with good properties.In 1995,Gong first proposed interleaving method to construct sequences(sets)with long period and good correlation.Subsequently,many scholars have constructed a large number of sequences(sets)with good correlation by using interleaving technique.For example,Zhou et al constructed a kind of low/zero correlation zone sequence sets with flexible length using interleaving technique.In recent years,there have been a lot of studies on the properties of interleaved sequences,such as investigating the pseudo-random properties of interleaved sequences from the autocorrelation properties and considering the linear complexity of interleaved sequences,but the anti-doppler properties of interleaved sequences have not been reported before.Therefore,it is of practical significance to consider the ambiguity function performance of interleaved sequences.In addition,it is urgent to study the performance of other ambiguity functions with good sequences.The main work of this paper is divided into two parts: firstly,we study the ambiguity function of interleaved sequences and derive the ambiguity function of interleaved sequences with low correlation by using exponential sum over finite field.The calculation shows that the amplitude of the cross ambiguity function of the interleaving sequences are determined by the cross ambiguity function of the base sequences and the difference property of the shift sequences.The derivation of the ambiguity function of the constructed sequences by Zhou,Gong and et al also proves that this kind of sequence has good anti-Doppler property.Then,we calculate the second-order ambiguity function of Zadoff-Chu sequence based on the correlation and first-order ambiguity function of sequences.