Construction of Asynchronous Relaxed Difference Set of Q-Ary Maximum-Length Channel-Hopping Sequences for Cognitive Radio Wireless Networks

In this letter, a new family of Relaxed Difference Set of Maximum-Length Channel-Hopping (RDSML-CH) sequences is constructed using
$q$
-ary m-sequences in an extension finite field F(
$p^{2s}$
), where
$q=p^{s}>3$
for any prime
$p \ge 2$
and integer
$s \ge 1$
. They have more ways of construction and flexible choices of period than the original RDSML-CH sequences. More importantly, by applying “light-weight” RDSs with fewer consecutive elements and improved channel assignments in the matrix, the maximum-time-to-rendezvous is reduced to
$4q+3$
, which is much shorter than the period, a notable improvement over the original RDSML-CH and similar constructions.