On Heterogeneous Sensing Capability for Distributed Rendezvous in Cognitive Radio Networks

Cognitive radio networks (CRNs) have been proposed to solve the spectrum scarcity problem. One of their fundamental procedures is to construct a communication link on a common channel for the users, which is referred to as
rendezvous
. In reality, the capability to sense the spectrum may vary from user to user. We study distributed rendezvous for heterogeneous sensing capabilities in this paper. The licensed spectrum is divided into
$n$
channels,
$U = \lbrace 1,2,\ldots,n\rbrace$
. We denote the sensing capability of user
$i$
as
$C_i \subseteq U$
and the set of available channels (i.e., the channels not occupied by paying users) as
$V_i \subseteq C_i$
. Due to hardware differences, the users may have different sensing capabilities:
$C_i \ne C_j$
, and this is called
heterogeneous sensing capability
. In this paper, we propose efficient algorithms for two scenarios: the fully available scenario where
$V_i = C_i$
and the partially available scenario where
$V_i \subseteq C_i$
. Our idea is to utilize two ‘pointers’ to traverse the sensing capability set, which sets our algorithms apart from the extant rendezvous algorithms. Considering any two neighboring users
$a, b$
, we propose the Traversing Pointer (TP) algorithm that guarantees rendezvous in
$O(\max \lbrace |C_a|,|C_b|\rbrace \log \log n)$
time slots for the fully available scenario. This result is only
$O(\log \log n)$
larger than the theoretical lower bound. Moreover, it removes an
$O(\min \lbrace |C_a|,|C_b|\rbrace)$
factor when compared to the state-of-the-art result (
$O(|C_a||C_b|)$
in S.-H. Wu
et al.
For the partially available scenario, we propose the Moving Traversing Pointers (MTP) and Prime based Moving Traversing Pointers (P-MTP) algorithms that can guarantee rendezvous within
$O((\max \lbrace |V_a|,|V_b|\rbrace)^2\log \log n)$
and
$O(|V_a||V_b|\log \log n)$
time slots respectively, where the latter one combines the pointers and a common technique of plugging in a prime number. The proposed algorithms work more efficiently than the previous best result (
$O(|C_a||C_b|)$
in C.-C. Wu
et al.
under various circumstances. We also conduct extensive simulations and the results corroborate our analyses.