Hierarchical Cooperation Improves Delay in Cognitive Radio Networks with Heterogeneous Mobile Secondary Nodes

This paper characterizes the throughput and delay performance of Cognitive Radio Networks (CRNs), where both primary and secondary networks coexist in a unit torus. Specifically, the primary network consists of static primary nodes (PNs) of density <inline-formula><tex-math notation="LaTeX">$n$</tex-math><alternatives><mml:math><mml:mi>n</mml:mi></mml:math><inline-graphic xlink:href="wang-ieq1-2885268.gif"/></alternatives></inline-formula>, which have a higher priority to access the spectrum. In contrast, the secondary network consists of mobile secondary nodes (SNs) of density <inline-formula><tex-math notation="LaTeX">$m=n^{\beta }$</tex-math><alternatives><mml:math><mml:mrow><mml:mi>m</mml:mi><mml:mo>=</mml:mo><mml:msup><mml:mi>n</mml:mi><mml:mi>β</mml:mi></mml:msup></mml:mrow></mml:math><inline-graphic xlink:href="wang-ieq2-2885268.gif"/></alternatives></inline-formula> with <inline-formula><tex-math notation="LaTeX">$\beta \geq 1$</tex-math><alternatives><mml:math><mml:mrow><mml:mi>β</mml:mi><mml:mo>≥</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math><inline-graphic xlink:href="wang-ieq3-2885268.gif"/></alternatives></inline-formula>, which move according to a hybrid random walk mobility model and have opportunistic access to the spectrum without affecting primary packet transmissions. Motivated by the fact that cooperation between primary and secondary nodes leads to possible improvement on the performance of CRNs, as well as the fact that the heterogeneous moving regions of secondary nodes will bring about further improvement, we propose a novel hierarchical cooperative scheduling mechanism, where secondary nodes serve as relays for primary packet transmissions by exploiting their mobility heterogeneity and geographic information. Our findings include: (i) For the primary network, stronger mobility heterogeneity of secondary nodes leads to better delay performance of the primary network, and meanwhile the delay scaling can be significantly reduced to <inline-formula><tex-math notation="LaTeX">$\Theta (n^{\sqrt{\beta /{(4\;\log n)}}}\log ^{3/2}n)$</tex-math><alternatives><mml:math><mml:mrow><mml:mi>Θ</mml:mi><mml:mo>(</mml:mo><mml:msup><mml:mi>n</mml:mi><mml:msqrt><mml:mrow><mml:mi>β</mml:mi><mml:mo>/</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mn>4</mml:mn><mml:mspace width="0.277778em"/><mml:mo form="prefix">log</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:msqrt></mml:msup><mml:msup><mml:mo form="prefix">log</mml:mo><mml:mrow><mml:mn>3</mml:mn><mml:mo>/</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math><inline-graphic xlink:href="wang-ieq4-2885268.gif"/></alternatives></inline-formula> when a near-optimal per-node throughput of <inline-formula><tex-math notation="LaTeX">$\Theta ({1}/{\log n})$</tex-math><alternatives><mml:math><mml:mrow><mml:mi>Θ</mml:mi><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:mrow><mml:mo form="prefix">log</mml:mo><mml:mi>n</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math><inline-graphic xlink:href="wang-ieq5-2885268.gif"/></alternatives></inline-formula> is obtained. (ii) For the secondary network, we also adopt a similar hierarchical cooperative scheduling mechanism, and obtain a near-optimal per-node throughput of <inline-formula><tex-math notation="LaTeX">$\Theta {(1/{\log m})}$</tex-math><alternatives><mml:math><mml:mrow><mml:mi>Θ</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:mrow><mml:mo form="prefix">log</mml:mo><mml:mi>m</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math><inline-graphic xlink:href="wang-ieq6-2885268.gif"/></alternatives></inline-formula> with the delay scaling of <inline-formula><tex-math notation="LaTeX">$\Theta ({m^{1-(1/\sqrt{\log m})}})$</tex-math><alternatives><mml:math><mml:mrow><mml:mi>Θ</mml:mi><mml:mo>(</mml:mo><mml:msup><mml:mi>m</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mo>-</mml:mo><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:msqrt><mml:mrow><mml:mo form="prefix">log</mml:mo><mml:mi>m</mml:mi></mml:mrow></mml:msqrt><mml:mo>)</mml:mo></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math><inline-graphic xlink:href="wang-ieq7-2885268.gif"/></alternatives></inline-formula>. (iii) The delay of secondary source-destination pairs is determined by the moving region of destinations and has no relation with sources. Our work provides deeper understandings of the cooperation, heterogeneous mobility, and geographic information on the performance of CRNs, and sheds light on designing more efficient CRNs.