魏千惠 韓鴻宇
摘要:在高速移動環(huán)境中,傳輸時延和頻率偏移是影響跳頻信號的2大因素.因此,研究在傳輸時延和頻率偏移同時存在下的時頻二維跳頻序列具有重大實用價值.時頻二維漢明相關函數(shù)滿足的理論界是判定跳頻序列性能優(yōu)劣的重要準則.因此,對時頻二維漢明相關函數(shù)進行了研究,并給出了關于時頻二維漢明相關函數(shù)、序列個數(shù)、頻隙個數(shù)、序列長度和頻移范圍的新理論界,證明了劉元慧的理論界以及Peng-Fan界為新理論界的特殊情況.
關鍵詞:跳頻序列; 時頻二維; 漢明相關; 理論界; 多普勒頻移
中圖分類號:TN911.2 文獻標志碼:A 文章編號:1001-8395(2023)05-0706-05
跳頻通信是目前廣泛應用的主要擴頻通信方式.迄今為止,跳頻多址接入(frequency-hopping multiple-access, FHMA)在無線通信領域有著廣泛的應用,如智能電網(wǎng)通信[1]、物聯(lián)網(wǎng)[2]、戰(zhàn)場通信[3].跳頻多址擴頻系統(tǒng)需要發(fā)射機相互之間的干擾盡量維持低的水平.在相同時間下出現(xiàn)同一頻率的發(fā)射信號,則會造成彼此干擾[4].跳頻信號彼此干擾的力度與漢明相關的大小密不可分.因此需要研究跳頻序列的漢明相關特性來更好地評判跳頻通信系統(tǒng)的性能[5-10].一些參數(shù)構成的理論界約束著跳頻序列的漢明相關值.
現(xiàn)有的跳頻序列理論界只考慮了時延的影響.例如,Lempel等[11]研究了當M=1,2的特殊情況時的理論界.Peng等[12-13]研究了時延影響下的Peng-Fan界.在雷達等高速移動環(huán)境下,存在多普勒頻移現(xiàn)象,同時考慮時延、頻移可以更好地實現(xiàn)通信服務.
時頻二維漢明相關的概念由于提出不久,且二維序列設計難度較大,因此現(xiàn)有研究成果不多,主要包括:邊強等[14]給出了時頻二維非周期低碰撞區(qū)跳頻序列的構造,許成謙等[15]給出了時頻二維低碰撞區(qū)跳頻序列的構造和時頻二維無碰撞區(qū)跳頻序列的構造,劉元慧等[16]給出了2類跳頻序列集時頻二維漢明相關性的分析.分析和構造跳頻序列集需要一個評判標準,這個評判標準就是理論界[17-22].目前,關于時頻二維跳頻序列理論界的研究成果不多,理論界體系并不完善,主要包括許成謙等[21]給出的二維相關跳頻偶唯一性和理論界,李鑫等[22]給出的時頻二維部分漢明相關理論界.
本文推導了由跳頻序列的時頻二維漢明相關值、頻隙個數(shù)、序列長度、序列個數(shù)、頻移范圍構成的跳頻序列的時頻二維漢明相關理論界.此理論界對分析和構造最優(yōu)時頻二維跳頻序列集起著重要作用.另外,還證明了現(xiàn)有的劉元慧的理論界以及Peng-Fan界是本文推導的理論界的特例.
1跳頻序列的時頻二維漢明相關函數(shù)的概念
2跳頻序列的時頻二維漢明相關函數(shù)理論界
3結束語
跳頻序列向來都是擴頻通信范疇的基礎理論研究課題.此課題主要涵蓋理論界、序列設計.本文給出了跳頻序列的時頻二維漢明相關函數(shù)的新理論界.該理論界由多個參數(shù)組成,對分析和構造最優(yōu)時頻二維跳頻序列集具有重要的指導意義.并且還證明了劉元慧的理論界以及Peng-Fan界是所推導的新理論界的特殊情況.今后將基于本文推導的新理論界構造具有靈活參數(shù)的最優(yōu)時頻二維跳頻序列集.
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Time-frequency Two-dimensional Hamming-correlated Theoretical
Bound of Frequency Hopping SequenceWEI Qianhui,HAN Hongyu(School of Computer Science, Sichuan Normal University, Chengdu 610101, Sichuan)
Abstract:In high-speed mobile environment, transmission delay and frequency offset are two major factors affecting frequency hopping signal. Therefore, it is of great practical value to study the time-frequency two-dimensional frequency hopping sequence in the presence of transmission delay and frequency offset. The theoretical bound satisfied by the time-frequency two-dimensional Hamming correlation function is an important criterion to judge the performance of frequency hopping sequences. Therefore, the time-frequency two-dimensional Hamming correlation function is studied, and a new theoretical bound on the time-frequency two-dimensional Hamming correlation function, the number of sequences, the number of frequency gaps, sequence length and frequency shift range are given. It is proved that Liu Yuanhuis theoretical bound and Peng-Fan bound are special cases of new theoretical bound.
Keywords:hopping sequence; time-frequency two-dimensional; Hamming correlation; theoretical bound; Doppler shift
(編輯 周俊)