Mobility Increases the Capacity of Ad-hoc Wireless Networks

1. Mobility Increases the Capacity of Ad-hoc Wireless Networks • Delbert Huang • EE206 • Spring 2001

3. Motivation • Original work by Knopp and Humblet. • Problem: • Uplink in the single cell, with multiple users communicating to the basestation via time-varying channels • Maimum System Throughput Solution: • Schedule at any one time only the user with the best channel to transmit to the basestation. • Rational Behind It: Multiuser Diversity Gain: • In a system with many users, there is likely to be a user with a very good channel at any one time. • Result: • Good: • Overall system throughput is maximized, • Bad: • Different user might suffer differ delays – Qos? • Packet has to be buffered until the channel becomes strong relative to other users. • Applicable to application where there is a loose time constraint – seconds delay

4. Introduction • Moral Of The Lesson: • Multi-user Diversity can be exploited to increase the throughput of the system with tradeoff the delay. • This Paper Is About: • Stretching end-to-end delay to be order of minutes or hours such that even more diversity gain can be obtained, thus Ad-hoc can be infinitely scaled.

6. Scalability Problem • Original work by Gupta and Kumar • Problem: • Studying the capacity of fixed ad-hoc networks, where nodes are randomly located but are immobile and each source node has a random destination to which it wants to communicate. • Observation: • As the number of nodes per unit area n increases, the throughput per source destination (S-D) pair decreases approximately like which is the upper performance bound even allowing for optimal scheduling, routing, and relaying (you name it) of packet in the networks. • Reason: • Long-range direct communication between many user pairs is infeasible, due to excessive interference caused as what we saw in the last slide. As the result most communication has to occur between nearest neighbors, at distances of order with each packet going through many other nodes(serving as relays) before reaching the destination. The number of hops in a typical route is of order

7. Conclusion 1 • Moral Of The Lesson: • For fixed ad-hoc networks, scalability of such networks is not possible, as the traffic per S-D pair actually goes down to zero ,since much of the traffic are about relaying packets to destination and actual throughput per S-D pair is small in comparison. • Key Assumption Made by the Gupta and Kumar: • The nodes are fixed, but not mobile

8. Let’s Tackle the ProblemFirst Try • Problem: • Scalability issue that was faced in the Gupta and Kumar paper. • Next Hop Requirement: The throughput capacity of the node is constrained by the mutual interference of concurrent transmission between nodes, so communication has to occur between nearest neighbors. • Key Assumption Made Here: • Let’s get rid of the key assumption made by Gupta and Kumar- That is make the nodes mobile instead fixed. • Solution Proposed: • Since the nodes are mobile, why not transit only when the source and destination nodes are close together, at the distance of at distances of order which met the imposed requirement. As the result, we do not have relay any packet between source and destination, so most of the traffic between nodes are all about just transferring desired packet, which should solve the scalability issue, or does it really?

9. Conclusion 2 • Results: • Good: • O(n) concurrent successful transmissionsas a whole system per time slot O(1) successful transmission per node per time slot is possible • Bad: • New Problem arrived: • The fraction of time desired S-D pair node are nearest neighbors is too small, of the order of . • Per S-D throughput vanishes as user n gets large (O(1)*O(1/n)=O(1/n)) • Direct communication doesn’t work

11. Second Try • Problem: • 1. The fraction of time desired S-D pair node are nearest neighbors is too small, of the order of . –> if we solve this, we effectively solve the scalability problem. • Next Hop Requirement: The throughput capacity of the node is constrained by the mutual interference of concurrent transmission between nodes, so communication has to occur between nearest neighbors. • Key Assumption Still Holds: • 1. The nodes are mobile not fixed. • Solution Offered: • For each source node to distribute its packets to as many different nodes that temporarily buffer packets as possible, then these serve as mobile relay nodes and whenever they get close to the final destination, they hand the packets off to the final destination.

13. Rational Part 1 • Rational Behind It: • Sincere there are many different relay nodes(n-2 nodes can serve as relay nodes), the probability that at least one is close to the destination is significant. Furthermore, each packet only goes though at most one relay node, and hence the throughput can be kept. Problem solved. • Recall Motivation in : • Uncertainty: channel impairment(such as multipath fading, shadowing by obstacles, and interference from other users). • Multiuser Diversity Gain: • In a system with many users, there is likely to be a user with a very good channel at any one time.So, on average system seems to have a good channel all the time.

14. Rational Part 2 • In parallel, • Uncertainty: channel impairment (in terms of nodes are not close enough to do the next neighbor routing) –Next Hop requirement. • Exploit the node mobility as a type of multiuser diversity. Distributing packets to many different intermediate nodes which have independent time-varying channels to the final destination. (Make as much user as possible and each holding some pieces of packet you are sending.) • In a S-D pair with many nodes, there is likely to be a node with a very good channel (meaning close to the destination while holding a piece of your packet) at any one time. So, overall S-D pair seem to have a good channel (meaning seems the source is right next to the destination), because the network topologies changes significantly over time due to user mobility.

15. Conclusion 3 • Result: • Good: • Average long-term throughput per S-D pair can be kept constant even as the number of nodes per unit area n increases. • Per S-D throughput is not affected by the size of the nodes in the network.- Per S-D throughput of having just 1 pair of S-D nodes is the same as Per S-D throughput of having a 1000 nodes in the same amount the area. • Bad: • Trading per S-D throughput with the delay as what we saw in the motivation. • End-to-end delay could be order of minutes or hours. • Limited application: such as electronic mail, database synchronization between a mobile terminal and a central database

16. Exact Algorithms • Key Assumption: • The user moves independently around the network – might not be true as in the football game • The relay node is assumed to have infinite buffer size to hold all the different packets from different source nodes. –not true in reality. • Phase 1: • Scheduling of packet transmission from sources to relays(or final destination). • Phase 2: • Scheduling of packet transmission from relays(or the source) to final destinations. • The two phases are interleaved and every packet goes through at most two hops • Can view it as a big queue system composed of n nodes (including the source node itself) each with the serving capability of O(1/n), since there are total of n nodes, so the serving capability is O(1). How do the relay nodes get the source node packets? Since the Source node roams around (so do the relay nodes), so they will get the packet with equal probability chance (independent assumption made above).

20. Now Let’s Get Technical • Key Assumption Used To Derive Various Results: • 1. n nodes all lying in the open disk of unit area. • 2. Location of the ith user at time t is given by Xi(t) • 3. Assume the process {Xi(t)} is stationary and ergodic with stationary distribution uniform on the open unit disk. • 4. Trajectories of different users are independent and identically distributed • At time t, node i transmits data at rate R packets/sec to node j if • Pi(t) is the transmit power of node I • yij(t) be the channel gain from node it to node j, such that the received power at node j is Pi(t)yij

21. Continue… • Only consider large scale path loss characteristics in the fading channel model • where a is the familiar parameter n (a>=2) • B is the signal-to-interference ratio (SIR) required for successful transmission • No is the background noise • L is the processing gain of the system • For a narrow band L=1 • CDMA L>1 • Consider a scheduling and relay policy . Let be the number of source node i packets that destination d(i) received at time t under policy . Only consider long term throughput of which obviously depends on the size of the nodes n.

22. Comparison Table

23. Authors’ Own Critique • This Paper Is Based on Sender Centric Policy: • It is the senders that select the closest receiver to send to. Probability of capture (SIR>B) for single receiver decreases with increasing sender density in the sender-centric approach. • But Receiver Centric Policy is preferable in terms of signal to interference ratio for a single receiver. The signal from the selected sender is always the strongest and doesn’t depend on the sender density. Better when Ns>Nr.

25. Comment on the Graph • There exists an optimal sender density that maximizes the throughput. If sender density is too small, we do not exploit the potential for spatial channel reuse. If sender density is too large, the interference power becomes too dominant. The optimal sender density depends on the “a”. • For small a, channel gain is large, so interference should be large and far-reaching  Sender density should be small for maximum throughput. • For large a, channel gain is small, so interference should be small and more localized. Sender density should be large for maximum throughput.

26. Critique 1. Invalid assumption that user movements are independent of each other, not true all the time –football game. 2.     Infinite/large buffer size for the relay nodes – that is to say every node, since every node is part of the relay nodes. 3. Relay only once may not be enough, since the probability for an arbitrary node to be scheduled to receive a packet from a source node S is equal for all nodes and independent of S  Critique 3 is true when Critique 1 is true. 4. Does that mean per S-D pair still give O(1) throughput in long time average? Probably not, since you have to route more than once and multiple routing brings down the throughput. Or you can simply just wait, until the football game is over. 5. Only applicable to loose time delay constraint application such as Email --, so not applicable to real time application or practical in reality. 6. Delay is infinite for symmetric S-R and R-D phase, so giving absolute priority to R-D phase (commented by authors).

27. References • Matthias Grossglauser (AT&T Labs - Research), David Tse (University of California at Berkeley), “Mobility Increases the Capacity of Ad-hoc Wireles Networks”, IEEE Infocom, April, 2001 • http://nesl.ee.ucla.edu/pw/Infocom2001/Grossglauser01.pdf • David Tse (University of California at Berkeley), "Multiuser Diversity in Wireless Networks“, Wireless Communicaton Seminar at Standford University, April 16, 2001 http://degas.eecs.berkeley.edu/~dtse/pub.html