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Typical Peak Sidelobe Level of Binary Sequences Noga Alon, Simon Litsyn, and Alexander Shpunt
 

Summary: Typical Peak Sidelobe Level of Binary Sequences
Noga Alon, Simon Litsyn, and Alexander Shpunt
Abstract. For a binary sequence Sn = {si : i = 1, 2, ..., n} {1}n, n > 1,
the peak sidelobe level (PSL) is defined as
M(Sn) = max
k=1,2,...,n-1
|
n-k
i=1
sisi+k|.
It is shown that the distribution of M(Sn) is strongly concentrated, and asymp-
totically almost surely,
(Sn) =
M(Sn)

n ln n
[1 - o(1),

2].
Explicit bounds for the number of sequences outside this range are provided.

  

Source: Alon, Noga - School of Mathematical Sciences, Tel Aviv University

 

Collections: Mathematics