一类跳频序列族的构造和性能分析

级联素数码是由素数码序列时移、频移后级联尝试性构造的一类跳频序列族,具有理想的汉明自相关特性和几乎理想的汉明互相关特性。根据有关数论和代数知识,研究得出级联素数码中关键参数y为素数P的二次非剩余的重要结论,赋予参数y以明确的数学含义,对于进一步研究级联素数码以及素数码在有限扩域GF(P2)上的扩展具有重要意义。对于素数P,共有(P-1)/2个有效y值,从而在GF(P2)上共可构造(P-1)/2个级联素数码族,确定了级联素数码族的个数。此外,还证明级联素数码是一类非重复跳频序列族,并满足最大处理增益、均匀性等性能。

The Construction of a Class of FH Sequences with Its Characteristic Analysis

The Concatenated prime codes are a class of FH sequences tentatively constructed by the concatenation of time-shifted and frequencyshifted versions of prime code sequences,showing ideal Hamming autocorrelation characteristic and nearly ideal Hamming cross-correlation characteristic.Based on the related number theory and the algebra knowledge,the key parameter y is found to be a quadratic nonresidue of prime P,so y is endowed with explicit mathematic meaning.This conclusion is very significant for the study of concatenated prime codes and the evolvement of prime codes to extension Galois fields GF(P2).As for the prime number P,there are in total(P-1)/2 legitimate y values.So it can be concluded that(P-1)/2 concatenated prime codes groups are existed over GF(P2).And the number of concatenated prime codes groups is determined.Besides,it is also analyzed that concatenated prime codes are a class of non-repeating FH sequences.And different properties of concatenated prime codes as FH sequences are listed at the last part.