Multi-parameter performance analysis for decentralized cognitive radio networks

Abstract

In this paper, we investigate the impact of primary user activity, secondary user activity, interface switching, channel fading and finite-length queuing on the performance of decentralized cognitive radio networks. The individual processes of these service-disruptive effects are modeled as Markov chains based on cross-layer information locally available at the network nodes. A queuing analysis is conducted and various performance measures are derived regarding the packet loss, throughput, spectral efficiency, and packet delay distribution. Numerical results demonstrate the impact of various system parameters on the system performance, providing insights for cross-layer design and autonomous decision making in decentralized cognitive radio networks.

Appendix: Two-state SU activity model

Let $X_{n,t} \in \varOmega \left( {X_{n,t} } \right) := \{ 0,1\}$ denote the process that describes the SU activity in channel n at time t, where X _n,t  = 1 if SU activity disrupts the tagged CR node’s communications in channel n at time t, or X _n,t  = 0 otherwise. Taking into account the results in Sect. 3.5, it follows that the SU activity state X _n,t  = 0 corresponds to a residual time of W _n,t  = 0. As a result, we have:

$$ X_{n,t} = \left\{ {\begin{array}{*{20}c} 0 & {if \, W_{n,t} = 0} \\ 1 & {otherwise} \\ \end{array} } \right. $$

(37)

From (37), it follows that $P\left( {X_{n,t + 1} = 0|X_{n,t} = 0} \right) = P\left( {W_{n,t + 1} = 0|W_{n,t} = 0} \right)$. Hence, X _n,t can be modeled as a two-state MC with transition matrix obtained by (38) and (39).

$$ p_{00}^{{X_{n} }} = p_{00}^{{W_{n} }} \;{\text{and}}\;p_{01}^{{X_{n} }} = 1 - p_{00}^{{X_{n} }} $$

(38)

$$ p_{11}^{{X_{n} }} = \frac{{\left( {1 - \pi_{0}^{{W_{n} }} } \right) - \pi_{0}^{{W_{n} }} \cdot \left( {1 - p_{00}^{{W_{n} }} } \right)}}{{\left( {1 - \pi_{0}^{{W_{n} }} } \right)}}\;{\text{and}}\;p_{10}^{{X_{n} }} = 1 - p_{11}^{{X_{n} }} $$

(39)

Accordingly, the limiting distribution of X _n is given as $\pi_{0}^{{X_{n} }} = \pi_{0}^{{W_{n} }}$ and $\pi_{1}^{{X_{n} }} = 1 - \pi_{0}^{{X_{n} }}$.