Capacity of Multi-Channel Wireless Networks: Impact of Number of Channels and Interfaces Pradeep Kyasanur Nitin H. Vaidya Presented by Chen, Chun-cheng University of Illinois at Urbana-Champaign

Multi-hop Wireless Networks Wireless is popular in local area networks Possible use in multi-hop networks as well Mesh networks Ad hoc networks

Need for more capacity Per-node capacity decreases with increased node density Effect of shared wireless medium New applications require higher throughput Streaming video, games Use more spectrum

Multiple channels Typically, available frequency spectrum is split into multiple channels Large number of channels may be available 26 MHz 100 MHz 200 MHz 150 MHz 2.45 GHz 915 MHz 5.25 GHz 5.8 GHz 3 channels 8 channels 4 channels 250 MHz 500 MHz 1000 MHz 61.25 GHz 24.125 GHz 122.5 GHz

Multiple Interfaces Radio interfaces typically support one channel We assume a half-duplex transceiver Nodes may be equipped with multiple interfaces Common case may be small number of interfaces Number of interfaces per node expected to be smaller than number of channels

Example configuration IEEE 802.11 has multiple channels 12 in IEEE 802.11a Devices can be equipped with multiple interfaces Fewer interfaces than channels Soekris net4521 device

Interface and Channel Model 1 m m interfaces per node c identical channels are available Total bandwidth W, per channel bandwidth W/c 1 c W

Related Work [Gupta&Kumar] have studied the capacity of single channel networks Applicable to multi-channel networks when c = m 1 OR m c = m

How does the network capacity scale with large number of channels? Capacity Problem Denser network  Lower capacity 1 c m How does the network capacity scale with large number of channels?

Contributions Established tight bounds In arbitrary and random networks Shown capacity depends on ratio of c to m Derived insights from constructions Capacity-optimal routing and scheduling strategies Other work has developed practical protocols

Arbitrary network Nodes can be located anywhere on the torus Traffic patterns can be arbitrarily chosen Measure of capacity – bit-meters/sec maximize total bit-meters/sec

Interference constraint Interference among simultaneous transmissions Must have minimum distance between transmitters Limits number of simultaneous transmissions [Gupta & Kumar]: r(1+ ) r A B C D  is a guard parameter

Interface constraint Throughput is limited by number of interfaces Fewer interface & more channels  lower node throughput can be supported Maximum node throughput = m * W/c 1 m n nodes in the neighborhood  total throughput <= n* m * W/c

Arbitrary network – Region 1 Capacity constrained by interference

Arbitrary network – Region 2 Capacity constrained by interfaces

Random network [Gupta&Kumar] n nodes in the network Nodes placed uniformly at random on the torus Each node sets up a flow to a randomly chosen destination Measure of capacity – minimum of flow throughputs

Random Network Capacity Capacity limited by a set of constraints The constraints result in different capacity region s

Connectivity constraint Flows can be scheduled only when path between source-destination is connected This establishes the minimum transmission range [Gupta & Kumar]: Not connected Connected A D

Interference constraint Interference among simultaneous transmissions Must have minimum distance between transmitters Limits number of simultaneous transmissions [Gupta & Kumar]: r(1+ ) r A B C D  is a guard parameter

Destination bottleneck constraint Destinations randomly chosen  single node may be destination of multiple flows Per-flow throughput limited by total number of incoming flows & node throughput Lemma 3. The maximum number of fows for which a node in the network is a destination, D(n), is w.h.p. If node throughput, T <= m*W/c Per-flow throughput <= T/f f incoming flows D We have n nodes  capacity in

Random network – Region 1 Capacity constrained by connectivity + interference No dependence on m and c

Random network – Region 2 Capacity constrained by interfaces + interference

Random network – Region 3 Capacity constrained by destination bottleneck

Achieving capacity lower bound (LB) Single construction applicable for all regions Start with: Node locations, source-destination pairs A B C D Consider two source-destination pairs AB, CD

LB Step 1: Partition into cells Divide torus into square cells of area a(n) Lemma 4. If a(n) > , then each cell has nodes per cell, with high probability. A B C D

LB Step 2: Routing Route through cells on the straight line joining source and destination A B C D E F

LB Step 2: Routing Balance route assignment within each cell Not required in single channel networks A B C D E F Loses throughput Optimal strategy

LB Step 3: Flow Scheduling Goal: Ensure node is not scheduled to receive or send simultaneously Half-duplex transceiver constraint Build a routing graph D D F F E G B E G A A B 1) Vertices are nodes in the network 2) One edge for every hop C C

LB Step 3: Flow Scheduling A E G C D F B Edge color graph Divide every second into multiple hop slots Number of slots = Number of edge colors of routing graph Schedule each hop in some slot One second interval EG, FD AE, GB, CF

LB Step 4: Node Scheduling Goal: Ensure transmissions from a node do not interfere with other nodes Build an interference graph D D F F E G E G A B A B C C 1) Vertices are nodes in the network 2) One edge between each pair of interfering nodes

LB Step 4: Node scheduling Each hop slot uses a node schedule Four node colors are needed D D Vertex color graph F F E G E G A B A B C C One second interval EG, FD AE, GB, CF G E A, B, D C, F Channel 1 Channel 2

Derivation of lower bound Lemma 5. The maximum number of source-destination lines that intersect any cell is From lemma 4, each cell has nodes  each node has flows  can be colored with edge colors  divide 1sec into each of sec From lemma 4, each cell has nodes  each node has interfering nodes can be colored with  divide each edge color slot into mini-slots each of sec In each mini-slot bits can be transmitted  remove ceiling func., we have bits can be transmitted  

Derivation of lower bound Recall and capacity is Use the above three condition to derive the lower bound to be the same as the upper bound.

Conclusion Studied the capacity of multi-channel networks with varying number of interfaces Single interface per node often suffices Up to log(n) channels, 1 interface is sufficient

Future Work Impact of switching delay has to be better studied Is switching required at all? Capacity under other switching constraints – switch among only a subset of channels Analyze capacity of deterministic networks Other papers in this session look at this question

Arbitrary Network: Upper bound Interference constraints [Gupta&Kumar]: Each pair of simultaneous receivers must have minimum separation Separation depends on transmission radius Bounds the number of simultaneous transmissions Interface constraint: Only m interfaces available n nodes, each node transmits at rate W/c bits/sec