Stackelberg Game on Space and Frequency Heterogeneity Analysis in an OFDMA-Based Cognitive Spectrum Leasing

Abstract

With the development of cognitive radio technologies, dynamic spectrum access (DSA) techniques are being regarded as a promising approach to increase the efficiency of spectrum utilization and to solve spectrum scarcity problem. This comes as a greater challenge in a cellular network where there are multiple primary users (PUs) who communicate with their access point while the other secondary users (SUs) want to use PU’s spectrum. On the other hand, heterogeneity in terms of space and frequency can affect the primary users’ decision to release their spectrum to the SUs. In this respect, the present paper is intended to address this issue and thus propose a solution with regard to the reward and punishment policy and equivalent revenue per unit transmission parameter. It has to be noted that both PUs and SUs aim to maximize their utilities in terms of their transmission rate and revenue/payment. Therefore, the proposed model is formulated as a Stackelberg Game, and a unique Nash Equilibrium Point is achieved by analytical procedure. Based on the analyses, the paper presents the conditions under which cooperation will enhance the performance of the whole system. Both analytical and numerical results reveal that the cooperative cognitive radio framework is a promising framework under which the utility of both the primary and secondary systems is maximized.

Appendix

Proof for (14).

$$ \frac{{\partial U_{{s_{j} }} }}{{\partial c_{mj} }} = \frac{{\omega_{mj} \left( {1 - \alpha_{m} } \right)R_{j} \mathop \sum \nolimits_{n \ne j} c_{mn} }}{{\left( {\mathop \sum \nolimits_{n \ne j} c_{mn} } \right)^{2} }} - 1 = 0 ,\quad \forall j \in \left\{ {1, \ldots ,k_{s} } \right\} $$

(25)

$$ \omega_{mn} \overbrace {{\left( {1 - \alpha_{m} } \right)}}^{{A_{m} }}R_{n} \overbrace {{\mathop \sum \limits_{j \ne n} c_{mj} }}^{{k_{m} - c_{mn} }} = \overbrace {{\left( {\mathop \sum \limits_{j} c_{mj} } \right)^{2} }}^{{k_{m} }} $$

(26)

$$ c_{mn} = k_{m} \left( {1 - \frac{{k_{m} }}{{A_{m} \omega_{mn} R_{n} }}} \right) $$

(27)

$$ \overbrace {{\mathop \sum \limits_{n} \left( {c_{mn} } \right)}}^{{k_{m} }} = \mathop \sum \limits_{n} k_{m} \left( {1 - \frac{{k_{m} }}{{A_{m} \omega_{mn} R_{n} }}} \right) \mathop \Rightarrow \limits^{yields} k_{m} = \frac{{A_{m} \left( {k_{{s_{m} }} - 1} \right)}}{{\mathop \sum \nolimits_{n} \frac{1}{{\omega_{mn} R_{n} }}}} \mathop \Rightarrow \limits^{{substituting\; k_{m}\; in\; \left( {31} \right)\,yields }} c^{ * }_{mn} $$

(28)