基于有限域理论的最优低碰撞区跳频序列集构造

跳频技术广泛应用于军方无线电通信、移动通信和数据链网络等领域。跳频序列是跳频通信技术的重要一环，影响着通信系统的性能表现。文章基于有限域上的加法群和乘法群，构造一类具有大序列数目的低碰撞区跳频序列集，并证明该序列集在一定条件下关于Peng-Fan-Lee界是最优的。该跳频序列集能有效地消除多址干扰，提升准同步多址通信系统的性能。

The Construction of Optimal Low Hit Zone Frequency Hopping Sequence Set Based on Finite Field Theory

Frequency hopping is widely used in military radio communication, mobile communication and data link network. Frequency hopping sequences play an important role in frequency hopping communication and influence the ability of communication system to a great extent. In this paper, based on the additive group and multiplicative group of finite fields, a construction of low hit zone frequency hopping sequence sets with a large family size was proposed, which has been proved that the sequence sets are optimal with respect to the Peng-Fan-Lee bound under certain conditions. This kind of frequency hopping sequence set can effectively eliminate multiple access interference and improve the performance of quasi synchronous multiple access communication system.