Cognitive Relaying with Frequency Incentive for Multiple Primary Users

Abstract

This work is directed towards a symbiotic architecture called cognitive relaying with frequency incentive for multiple primary users (CRFI-M). The rationale of CRFI-M is that the primary users (PUs) of a cognitive radio (CR) network, with weak transmission links, seek cooperation from the secondary user (SU) nodes in their vicinity to achieve as much throughput as they can get from their direct links. In return they reward the SUs with incentive frequency bands for their own communication. Each PU has its own distinct bandwidth of operation; however, when relaying through the SU network it can also use the bandwidth of the other PUs to enhance its throughput. Furthermore, the incentive frequency bands may be offered as a complete band-set or interleaved bands. Cross-layer optimization problems are formulated for each of these variants of the CRFI-M paradigm in a multi-hop multi-channel SU network. The frequency incentive that should be awarded to the SUs by each PU is analyzed by means of a utility-based decision-making process, and its efficient utilization is proposed. To make the CRFI-M scheme practically realizable, a MAC scheduling protocol is described. Simulation results are furnished to demonstrate the proof of concept.

Appendix

The variable $u_{m}(q)$ defined in BRR-BSM (problem P1) indicates the occupancy of band $m \in \mathbb M _q$ in the entire network for any session $q$. It is as given by

$$\begin{aligned} u_m(q)=OR_{(i,j)\in \mathbb E } \quad x_{ij}^{m}(q) \quad \quad ...logical \quad OR \end{aligned}$$

We would prefer to write it using arithmetic operations, as they are easier to work with. We use the following lemma:

Lemma For binary variables (0 or 1), multiplication and logical AND operations are identical.

Therefore, we can write,

$$\begin{aligned}&u_m(q)=((OR_{(i,j)\in \mathbb E } x_{ij}^{m}(q))^c)^c \quad ...()^c \quad is \quad complement\\&\Rightarrow u_m(q)=(AND_{(i,j)\in \mathbb E } (1-x_{ij}^{m}(q)))^c \quad \quad ...DeMorgan\text{'}s Rule\\&\Rightarrow u_m(q)=\left(\prod _{(i,j)\in \mathbb E } (1-x_{ij}^{m}(q)) \right)^c \quad \quad \ldots Lemma\\&\Rightarrow u_m(q)=1 - \prod _{(i,j)\in \mathbb E } (1-x_{ij}^{m}(q)) \end{aligned}$$

When we take the sum of all $u_m(q)$, and seek to minimize it, we are in effect minimizing the cumulative band-set used by all the sessions.

The same can be said about $u_m$ defined in ABR-BSM (problem P3).