1 Connectivity of Wireless Ad hoc Networks Dr. Salman Durrani School of Engineering, College of Engineering and Computer Science, The Australian National University, Canberra, Australia. Dec. 2009

2 Overview Introduction Research Trends in Wireless Communications Open research problems in ad hoc networks Connectivity Analysis Antenna & System Model Analytical framework Results & Conclusions

3 Canberra

4 ASP Academics 8 Academics + 4 NICTA Adjuncts

5 ASP Research Group The Applied Signal Processing Group conducts research in the following application areas: 1.Physical layer Communications (12 PhD students) Telecommunications including Wireless and Mobile Communications Space-Time Signal Processing 2.Signal Processing (9 PhD students) Acoustic and Audio Signal Processing Broadband and Near-field Sensor Arrays and Beamforming Bio-Signal Processing 3.Applied Information Theory (2 PhD students)

6 My PhD Students Xiangyun Zhou (EIPRS Scholarship), Channel estimation in cellular & ad hoc networks. (Jan present) Ali Nasir (ANU International PhD Scholarship), Synchronization in co-operative communication systems. (June 2009-present) Zubair Khalid (EIPRS Scholarship) & Rimla Javaid (ANU PhD Scholarship), commencing 2010.

7 Research Trends IEEE ICC 2009 in Dresden, Germany: paper submissions 1046 accepted papers after peer review (29%) Selected papers presented in oral sessions. On average, 5 to 6 papers being presented in every session. We looked at the number of oral sessions presented for different research topics in GlobeCom and ICC for last 3 years.

8 Research Trends Source: Internal report by PhD student Ali Nasir.

9 Research Trends Research topics in steady state or decline ? Source: Internal report by PhD student Ali Nasir.

10 Research Trends Research topics in steady state or decline ? Source: Internal report by PhD student Ali Nasir.

11 Research Trends Other Research Topics Source: Internal report by PhD student Ali Nasir.

12 Research Trends: Ad Hoc Networks Ad hoc Networks

13 Basic Principles of an Ad hoc Network Formed by wireless nodes which may be mobile. No need (necessarily) for any pre-existing infrastructure. Decentralized operation. Multi-hop communication.

14 Applications: Sensor Networks Networks of typically small, battery-powered, wireless devices. Wide range of applications:- Environmental monitoring, Military surveillance Medical care Home appliance management Industrial monitoring

15 Figure from Lin et. al, IEEE Comm. Mag, April Applications: VANETS Vehicular Ad Hoc Networks comprise vehicle-to- vehicle and vehicle-to-infrastructure communications based on WLAN technologies. (IEEE P1609 WAVE Standards)

16 Applications: Telecomms Networks Ad hoc Networking

17 Research Challenges in Ad hoc Networks Capacity What are the fundamental performance limits (in terms of reliable data rate) for ad hoc networks? Routing How do you efficiently select paths in a network along which to send information? Connectivity If you select any pair of nodes in an ad hoc network, what is the probability they connected? Co-operation 3 node Source, Relay, Destination scenario. Synchronization

18 Connectivity Definitions Connectivity from view-point of a single node:- Average Node Degree: Average no. of direct links that any given node has to other nodes. Probability of node isolation: Probability that a randomly selected node in an ad hoc network has no connections to any other node. Isolated node Average Node degree = 1.8

19 Connectivity Definitions Connectivity from view-point of an entire network:- 1- connectivity: Probability that every node pair in the network has at least one path connecting them. Critical Node density: Node density that yields an almost surely connected network [P (1-con)=0.99]. Path Probability: Probability that two randomly chosen nodes are connected either via a single hop or a multi-hop path.

20 Research Challenges in Modelling Ad hoc network Connectivity Mobility Dynamic network topology Realistic models for mobility Node distribution Uniform Clustered Channel Wireless links subject to shadowing and fading Interference from simultaneous transmissions elsewhere Multiple Antennas Adopted in 3GPP (Release 6), IEEE802.11n, IEEE How does beamforming affect the connectivity of ad hoc networks?

21 Prior Work Closed-form analytical results for connectivity are available for special case of:- Node locations are Poisson, Negligible interference, No mobility, Channel: Path loss & Shadowing, Omni-directional antennas Open Research Problem:

22 Overview Introduction Research Trends in Wireless Communications Open research problems in ad hoc networks Connectivity Analysis Antenna & System Model Analytical framework Results & Conclusions

23 System Model Nodes are distributed in 2D according to Poisson point process. All nodes are equipped with beamforming antennas.

24 Antenna Model Antenna Model is characterized by associated antenna power pattern. Uniform Linear Array or Uniform Circular Array ?

25 Power Pattern Demo (N=8)

26 Antenna Model UCA configuration is chosen:- It has single main lobe. 3 dB beamwidth is constant & independent of main beam direction. For UCA, the directivity G is given by

27 Random Beamforming Core Idea: Each node randomly selects a main beam direction without co-ordination with other nodes. Advantage:- MAC is un-coordinated. Minimal communication overhead and hardware complexity. Disadvantage:- May not be optimal strategy

28 Channel Model Received Signal Power Shadowing affects only the randomness and not the average value of the channel gain. Path Loss Shadowing Beamforming

29 Communication Range Two nodes can communicate with each other if their distance apart is smaller than a given communication range R.

30 Effective Coverage Area With beamforming, the communication range is Effective coverage area is Random variable Shadowing factor Beamforming factor

31 Shadowing factor: Depends on:- path loss  and Shadowing log-normal standard deviation  Key Insight:- Shadowing reduces the effective coverage area (for  > 2). Effect of Shadowing

32 Effect of Shadowing

33 Effect of Beamforming Beamforming factor: ®

34 Effect of Beamforming Beamforming factor: Depends on path loss  Number of antenna elements in the UCA M Does not depend on Shadowing log-normal standard deviation 

35 Effect of Beamforming Beamforming factor values: Key Insight:- For  <3, random beamforming increases the effective coverage area.

36 Overview Introduction Research Trends in Wireless Communications Open research problems in ad hoc networks Connectivity Analysis Antenna & System Model Analytical framework Results Average Node degree Probability of node isolation 1-connectivity Critical node density Path probability Conclusions

37 Connectivity Metrics - P(iso) Probability of node isolation Main Result:- shadowing always increases the probability of node isolation. beamforming, compared to omnidirectional antennas, reduces the probability of node isolation when  <3. Effective coverage Area

38 Connectivity Metrics - P(iso) Verification (effect of shadowing, M=1):-

39 Connectivity Metrics - P(iso) Verification (effect of beamforming, M=1,4 &  = 4 dB ):-

40 Connectivity Metrics -  c Critical node density: node density that yields an almost surely connected network, that is, the density at which P (1-con) = Main Result:- shadowing increases the critical node density.  c can be reduced by using beamforming when  <3.

41 Connectivity Metrics -  c Effect of shadowing No of antennas M=1

42 Connectivity Metrics -  c Effect of beamforming No of antennas M=1,4

43 Conclusions We have presented an analytical model to characterize the effect of random beamforming on the network connectivity.

44 Publications X. Zhou, S. Durrani and H. Jones, "Connectivity Analysis of Wireless Ad Hoc networks with Beamforming," IEEE Transactions on Vehicular Technology, vol. 58, no. 9, pp , Nov S. Durrani, X. Zhou and H. Jones, "Connectivity of Wireless Ad Hoc Networks with Random Beamforming: An Analytical Approach," Proc. IEEE PIMRC, Cannes, France, Sep , Paper PDFs available at:-

45 Thank you for your attention