Frequency Hopping Sequences with Optimal Partial Autocorrelation ...
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Frequency Hopping Sequences with Optimal Partial Autocorrelation ...
Jul 1, 2004 - Optimal criteria on partial Hamming autocorrelation. ⢠Partial Hamming correlation function for a period N and a correlation window length.
Coding and Information Theory Lab.
1
Frequency Hopping Sequences with Optimal Partial Autocorrelation Properties
July 1, 2004.
Yu-Chang Eun, Seok-Yong Jin, Yun-Pyo Hong, and Hong-Yeop Song Yonsei University Seoul, Korea
Yonsei University Electrical and Electronic Eng.
Coding and Information Theory Lab.
1
Outline
•
Motives
•
FH Systems
•
Strictly-Optimal FH Sequences
•
Summary & Remarks
Yonsei University Electrical and Electronic Eng.
Coding and Information Theory Lab.
2
Motives
• Most of FH sequences so far have been designed so that – their maximum periodic Hamming correlation is minimized – with the number of hopping slots (frequencies) that is a power of a prime.
• Usually, the correlation window is shorter than the period of the FH sequence. ⇒ A sequence having good partial Hamming autocorrelation ?
Yonsei University Electrical and Electronic Eng.
Coding and Information Theory Lab.
3
Tx & Rx structure of a FH system J (t )
Tx Binary Data
Binary to M-ary Mapper
M-ary Data
d (t )
MFSK Modulator
Frequency Hopping
c (t ) PN Code Generator
Rx
Frequency Synthesizer s (i )
Frequency Dehopping
d' (t ) to noncoherent data detector
PN Code Aquisition & Tracking
c' (t )
PN Code Generator
Frequency Synthesizer s (i )
• Correlation window length – usually shorter than the period of the FH sequence due to the limited synchronization time or hardware complexity – may vary depending on the channel condition
Yonsei University Electrical and Electronic Eng.
Coding and Information Theory Lab.
4
FH sequences with optimal partial autocorrelation properties ¦ Optimal criteria on partial Hamming autocorrelation • Partial Hamming correlation function for a period N and a correlation window length L starting at t,
HXY (τ ; t | L) =
t+L−1 X
h[x(j), y(j + τ )], 0 ≤ τ < N
(1)
j=t
where h[x, y] = 1 if x = y and h[x, y] = 0 if x 6= y. 0
t
t+
t + +L 1
t
t+L 1
Xˆ X 0
Yonsei University Electrical and Electronic Eng.
Coding and Information Theory Lab.
5
• The maximum of the partial Hamming autocorrelation function (p-HAF) H(X | L) =
