Transmission Delay in Large Scale Ad Hoc Cognitive Radio Networksi

Transcription

1 Transmission Delay in Large Scale Ad Hoc Cognitive Radio Networks 1 Transmission Delay in Large Scale Ad Hoc Cognitive Radio Networksi Zhuotao Liu 1, Xinbing Wang 1, Wentao Luan 1 and Songwu Lu 2 1 Department of Electronic Engineering Shanghai Jiao Tong University, China 2 Department of Computer Science University of California, Los Angeles June 15, 2012

2 Transmission Delay in Large Scale Ad Hoc Cognitive Radio Networks 2 Outline Background Motivation Contributions Network Model Percolation Definitions Supercritical Network Subcritical Network Propagation Delay Simulations Conclusions and Future Work

3 Transmission Delay in Large Scale Ad Hoc Cognitive Radio Networks 3 Background Outline Background Motivation Contributions Network Model Percolation Definitions Supercritical Network Subcritical Network Propagation Delay Simulations Conclusions and Future Work

4 Transmission Delay in Large Scale Ad Hoc Cognitive Radio Networks 4 Background Cognitive Radio Networks Cognitive Radio (CR) Networks improved the spectrum efficiency. Primary users have priority to use spectra. Secondary users are opportunistic. Heterogeneity over time and space. Figure: Heterogeneity of CR networks

5 Transmission Delay in Large Scale Ad Hoc Cognitive Radio Networks 5 Background Delay of CR networks Delay or latency is a significant issue for the network architecture and design. Secondary network is suffering from delay penalty. Communication path may be impacted. Waiting for spectrum opportunities.

6 Transmission Delay in Large Scale Ad Hoc Cognitive Radio Networks 5 Background Delay of CR networks Delay or latency is a significant issue for the network architecture and design. Secondary network is suffering from delay penalty. Communication path may be impacted. Waiting for spectrum opportunities. What is the delay performance for secondary network in CR networks?

7 Transmission Delay in Large Scale Ad Hoc Cognitive Radio Networks 6 Background Related Works W. Ren et al., IT 2011 [11] Consider the dynamic connectivity in CR networks through Continuum Percolation Theory [1]. Overall connectivity in secondary network can be established if and only if λ S > λ S and λ PT < λ PT. Z. Kong et al., MOBIHOC 2008 [13] Study the latency in large scale homogenous networks through Subadditive Ergodic Theorem [2]. Delay is ignorable in supercritical network whereas it scales lineally with distance in subcritical network. S. Zhao et al., MOBICOM 2011 [14] Get the more precise description of the delay to distance ration. Great mathematical analysis and excellent simulation work.

8 Transmission Delay in Large Scale Ad Hoc Cognitive Radio Networks 7 Motivation Outline Background Motivation Contributions Network Model Percolation Definitions Supercritical Network Subcritical Network Propagation Delay Simulations Conclusions and Future Work

9 Transmission Delay in Large Scale Ad Hoc Cognitive Radio Networks 8 Motivation Motivation All the previous related work failed to consider the heterogeneity of network while studying the delay. What effect the arbitrariness and diversity of primary network will impose on the performance of secondary network? Is it possible to find a more precise description of the delay to distance ratio?

10 Transmission Delay in Large Scale Ad Hoc Cognitive Radio Networks 8 Motivation Motivation All the previous related work failed to consider the heterogeneity of network while studying the delay. What effect the arbitrariness and diversity of primary network will impose on the performance of secondary network? Is it possible to find a more precise description of the delay to distance ratio? How does the transmission delay scale with distance in large scale ad hoc CR networks?

11 Transmission Delay in Large Scale Ad Hoc Cognitive Radio Networks 9 Contributions Outline Background Motivation Contributions Network Model Percolation Definitions Supercritical Network Subcritical Network Propagation Delay Simulations Conclusions and Future Work

12 Transmission Delay in Large Scale Ad Hoc Cognitive Radio Networks 1 Contributions Contributions Delay scaling is considered under both Boolean Model and Random Connection Model of continuum percolation theory [1]. More precise description of delay to distance ratio has been presented. the exact value, lower bound. Considerable amount of simulation has been conducted to verify the theoretical analysis.

13 Transmission Delay in Large Scale Ad Hoc Cognitive Radio Networks 1 Outline Background Motivation Contributions Network Model Percolation Definitions Supercritical Network Subcritical Network Propagation Delay Simulations Conclusions and Future Work

14 Transmission Delay in Large Scale Ad Hoc Cognitive Radio Networks 1 Network Model Outline Background Motivation Contributions Network Model Percolation Definitions Supercritical Network Subcritical Network Propagation Delay Simulations Conclusions and Future Work

15 Transmission Delay in Large Scale Ad Hoc Cognitive Radio Networks 1 Network Model Primary Network Primary transmitters: Poisson Point Process P PT(t) with density λ PT. For one primary transmitter, its corresponding receivers are uniformly distributed within its transmission range R p. Time is slotted. Each primary transmitter is associated with an i.i.d. switching renewal process S P(t). E[Q 0 p(t)] β 0 lim Pr(SP(t) = 0) = t E[Q 0 p(t)] + E[Q 1 p(t)], E[Q 0 p(t)] β 1 lim Pr(SP(t) = 1) = t E[Q 0 p(t)] + E[Q 1 p(t)]. Primary network at time slot t: A P(λ PT; S P(t); R p). (A P for simplicity)

16 Transmission Delay in Large Scale Ad Hoc Cognitive Radio Networks 1 Network Model Secondary Network Connection of two secondary nodes are modeled by BM or RCM. BM: connection function h(r) = 1, 0 < r r s. RCM: connection function 0 < f (r s) < f (r) < f (0) < 1, 0 < r < r s. Conditions for the openness of a path π between two secondary nodes. π is established through multiple links; messages can be forwarded by other nodes in π to the destination (Ad-hoc network). G t(λ S; h(r); A P), G t(λ S; f (r); A P): CR networks modeled by BM and RCM, respectively.

17 Transmission Delay in Large Scale Ad Hoc Cognitive Radio Networks 1 Percolation Definitions Outline Background Motivation Contributions Network Model Percolation Definitions Supercritical Network Subcritical Network Propagation Delay Simulations Conclusions and Future Work

18 Transmission Delay in Large Scale Ad Hoc Cognitive Radio Networks 1 Percolation Definitions Percolation for CR Networks For G t(λ S; h(r); A P), the percolation probability p λ is the probability that the connected component containing the origin C 0 O has infinite secondary nodes. The critical density of secondary users is defined as λ c(h(r)) = inf{λ S > 0 : p λ > 0}. λ c(f (r)): percolation density for G t(λ S; f (r); A P). Lemma 1. Two critical percolation densities: λ c(f (r)) > λ c(h(r)).

19 Transmission Delay in Large Scale Ad Hoc Cognitive Radio Networks 1 Percolation Definitions Percolation for CR Networks For G t(λ S; h(r); A P), the percolation probability p λ is the probability that the connected component containing the origin C 0 O has infinite secondary nodes. The critical density of secondary users is defined as λ c(h(r)) = inf{λ S > 0 : p λ > 0}. λ c(f (r)): percolation density for G t(λ S; f (r); A P). Lemma 1. Two critical percolation densities: λ c(f (r)) > λ c(h(r)). If λ S < λ c(h(r)), the secondary network is subcritical. If λ S > λ c(h(r)), the secondary network is supercritical. If λ PT < λ PT, it is com-supercritical. If λ PT > λ PT, it is top-supercritical.

20 Transmission Delay in Large Scale Ad Hoc Cognitive Radio Networks 1 Percolation Definitions Subcritical Secondary Network C 0 O is broken into infinite number of mutually disconnected clusters even no interference from primary network is composed. Overall connectivity cannot be established over entire secondary network. Figure: Subcritical network: mutually disconnected clusters.

21 Transmission Delay in Large Scale Ad Hoc Cognitive Radio Networks 1 Percolation Definitions Supercritical Secondary Network Com-supercritical: C 0 O still exists as λ PT is small. An open path between source and destination can be found over secondary network. Delay tends to zero if ignoring propagation delay. Figure: Com-supercritical network.

22 Transmission Delay in Large Scale Ad Hoc Cognitive Radio Networks 1 Percolation Definitions Supercritical Secondary Network Top-supercritical: C 0 O does not exist as λ PT is large. The open path between source and destination is interfered by primary network. Delay: waiting time for spectrum opportunities. Figure: Top-supercritical network.

23 Transmission Delay in Large Scale Ad Hoc Cognitive Radio Networks 2 Outline Background Motivation Contributions Network Model Percolation Definitions Supercritical Network Subcritical Network Propagation Delay Simulations Conclusions and Future Work

24 Transmission Delay in Large Scale Ad Hoc Cognitive Radio Networks 2 Supercritical Network Outline Background Motivation Contributions Network Model Percolation Definitions Supercritical Network Subcritical Network Propagation Delay Simulations Conclusions and Future Work

25 Transmission Delay in Large Scale Ad Hoc Cognitive Radio Networks 2 Supercritical Network G t (λ S ; h(r); A P ) If λ PT < λ PT(λ S) (com-supercritical), γ(λ S, A P) lim d(u,v) T (π) d(u,v) = 0 π is open and messages can be forwarded. If λ PT > λ PT(λ S) (top-supercritical), open pathes cannot be found. Spectrum-to-Hop process is provided: Computation Flow: Spectrum-to-Hop Process (SHP) 1: x, y P S(t), they share a linkage l(x, y) whenever d(x, y) r s. 2: Messages can be forwarded through l(x, y) when it has spectrum opportunities. 3: The expected delay before l(x, y) owning spectrum opportunities is E[l(x, y)]. 4: The minimum number of hops (linkages) in an open path π(u, v) is Q(u, v). 5: The scaling behavior of hops number Q(u, v) is Q(u,v) lim d(u,v) = κ. d(u,v) 6: Obtain γ(λ S, A P) = κ E[l(x, y)].

26 Transmission Delay in Large Scale Ad Hoc Cognitive Radio Networks 2 Supercritical Network G t (λ S ; h(r); A P ) Each link l k in a path is interfered by some primary users: I(l k ). Figure: Interfered region: I(l k ).

27 Transmission Delay in Large Scale Ad Hoc Cognitive Radio Networks 2 Supercritical Network G t (λ S ; h(r); A P ) Step 2: Interfered region I(l k ) for each link: 1. if R p r k 2, ψ = [2πR 2 p F(r k, R p )]λ PT, where F(r k, R p ) = 2R 2 p arccos r k 2R p r k 2. if R p < r k 2 ψ = 2πR 2 pλ PT. 4R 2 p r 2 k 2. The expected number of primary transmitters ψ within I(l k ): πr 2 pλ PT ψ [2πR 2 p F(r s, R p)]λ PT.

28 Transmission Delay in Large Scale Ad Hoc Cognitive Radio Networks 2 Supercritical Network G t (λ S ; h(r); A P ) Step 3: H k (t) = 0 if all the ψ primary transmitters within I(l k ) are sleep. Otherwise, H k (t) = 1. The expected delay for (l k ): T p(l k ) = inf t 0 {t : H k(t) = 0} = X n=0 n(1 β ψ 0 )n β ψ 0 = 1 βψ 0 β ψ 0.

29 Transmission Delay in Large Scale Ad Hoc Cognitive Radio Networks 2 Supercritical Network G t (λ S ; h(r); A P ) Step 4 and 5: (Lemma 3)The minimum number of hops Q(u, v) in one path π(u, v) scales linearly with the distance d(u, v). Q(u, v) lim d(u,v) d(u, v) = κ. The proof is investigated by [13] and [14] through subadditive ergodic theorem.

30 Transmission Delay in Large Scale Ad Hoc Cognitive Radio Networks 2 Supercritical Network G t (λ S ; h(r); A P ) Step 6: γ(λ S, A P) = lim d(u,v) T (π) d(u, v) = Q(u, v) E[T p(l k )] = lim d(u,v) d(u, v) = κ 1 βψ 0 β ψ 0. P Tp(l lim k ) d(u,v),k d(u, v)

31 Transmission Delay in Large Scale Ad Hoc Cognitive Radio Networks 2 Supercritical Network G t (λ S ; f (r); A P ) The most significant issue is to reveal the relationship between G t(λ S; h(r); A P) and G t(λ S; f (r); A P). We introduce the REP algorithm to prove that Lemma 3 still holds for G t(λ S; f (r); A P). Figure: REP algorithm.

32 Transmission Delay in Large Scale Ad Hoc Cognitive Radio Networks 2 Subcritical Network Outline Background Motivation Contributions Network Model Percolation Definitions Supercritical Network Subcritical Network Propagation Delay Simulations Conclusions and Future Work

33 Transmission Delay in Large Scale Ad Hoc Cognitive Radio Networks 3 Subcritical Network Subcritical Network Messages cannot be disseminated among G t(λ S; h(r); A P). Mobility is necessary. Messages is forwarded through Multi-cluster Hop Transmission Process. Figure: Multi-cluster Hop Transmission Process.

34 Transmission Delay in Large Scale Ad Hoc Cognitive Radio Networks 3 Subcritical Network Subcritical Network Delay is composed by waiting delay for both connectivity and spectrum opportunities: Delay = cluster to cluster transmission delay + waiting delay for spectrum opportunities = T P(Υ) + T S(Υ).

35 Transmission Delay in Large Scale Ad Hoc Cognitive Radio Networks 3 Subcritical Network Subcritical Network Delay is composed by waiting delay for both connectivity and spectrum opportunities: Delay = cluster to cluster transmission delay + waiting delay for spectrum opportunities = T P(Υ) + T S(Υ). T P(Υ) d(u,v) 1 E[M h(r) (λ S,A P )+r s]. T S(Υ) d(u,v) 1 β η 0 β η 0 E[M h(r) (λ S,A P )+r s].

36 Transmission Delay in Large Scale Ad Hoc Cognitive Radio Networks 3 Subcritical Network Subcritical Network Delay is composed by waiting delay for both connectivity and spectrum opportunities: Delay = cluster to cluster transmission delay + waiting delay for spectrum opportunities = T P(Υ) + T S(Υ). T P(Υ) d(u,v) 1 E[M h(r) (λ S,A P )+r s]. T S(Υ) d(u,v) 1 β η 0 β η 0 E[M h(r) (λ S,A P )+r s]. γ(λ S, A P) 1 β η 0 E[M h(r) (λ S,A P )+r s].

37 Transmission Delay in Large Scale Ad Hoc Cognitive Radio Networks 3 Propagation Delay Outline Background Motivation Contributions Network Model Percolation Definitions Supercritical Network Subcritical Network Propagation Delay Simulations Conclusions and Future Work

38 Transmission Delay in Large Scale Ad Hoc Cognitive Radio Networks 3 Propagation Delay Impact of propagation delay Assume that the propagation delays τ is the same for different links. For supercritical network, a constant is added as the delay. (i) γ(λ S, A P) = κτ if λ PT < λ PT(λ S); (ii) if λ PT > λ PT(λ S), γ(λ S, A P) = κ ( 1 βψ 0 β ψ 0 + τ) For subcritical network, the maximum size of one cluster is bounded by min{m h(r) (λ S, A P)}. γ(λ S, A P) 1 β η 0 E[min{M h(r)(λ S, A P), rs τ } + rs].

39 Transmission Delay in Large Scale Ad Hoc Cognitive Radio Networks 3 Simulations Outline Background Motivation Contributions Network Model Percolation Definitions Supercritical Network Subcritical Network Propagation Delay Simulations Conclusions and Future Work

40 Transmission Delay in Large Scale Ad Hoc Cognitive Radio Networks 3 Simulations Simulations Constant ψ and κ are got through simulation. Figure: Simulation for constant ψ and κ.

41 Transmission Delay in Large Scale Ad Hoc Cognitive Radio Networks 3 Simulations Simulations γ(λ S, A P): delay to distance ratio. Figure: γ(λ S, A P ) converges to a constant. Figure: γ(λ S, A P ) increases with λ PT.

42 Transmission Delay in Large Scale Ad Hoc Cognitive Radio Networks 3 Conclusions and Future Work Outline Background Motivation Contributions Network Model Percolation Definitions Supercritical Network Subcritical Network Propagation Delay Simulations Conclusions and Future Work

43 Transmission Delay in Large Scale Ad Hoc Cognitive Radio Networks 3 Conclusions and Future Work Conclusions In this paper, we have studied the transmission delay in large scale ad hoc CR networks by analyzing the ratio of delay to distance γ(λ S, A P). For com-supercritical CR networks, γ(λ S, A P) = 0. For both top-supercritical G t(λ S;h(r);A P) and G t(λ S;f (r);a P), γ(λ S, A P) = κ 1 βψ 0 In the subcritical network, γ(λ S, A P) > 1 β η 0 E[M h(r) (λ S,A P )+r s]. Propagation has been investigated to generalize our results. We do considerable simulation to verify our theoretical analysis. β ψ 0.

44 Transmission Delay in Large Scale Ad Hoc Cognitive Radio Networks 3 Conclusions and Future Work Future work γ(λ S, A P) has not been investigated for subcritical RCM network. More precise description of γ(λ S, A P) for subcritical BM network. Capacity and delay tradeoff (Our MOBICOM 2012 submission).

45 Transmission Delay in Large Scale Ad Hoc Cognitive Radio Networks 4 Conclusions and Future Work Q&A Thank you!