A General Model of Wireless Interference

A General Model of Wireless Interference LiliQiu, Yin Zhang, Feng Wang, Mi Kyung Han University of Texas at Austin RatulMahajan Microsoft Research Presented by Guanfeng Liang CS598JH – Fall 07

Background of 802.11 • Two coordination functions • Distributed coordination functions: DCF • Point coordination functions: PCF • Two cases in DCF • Broadcast: CW=CWmin • Unicast: CW=min{(CWmin+1) 2k -1,CWmax}

Overview of the Model • Input: traffic demands and RF profile Rmn • Output: estimated sending/receiving rates • One-hop communication • Broadcast/unicast • Saturated/unsaturated

Assumption on Radio Behavior • Transmitter m • Channel is “clean” when the total received power is below βm • Receiver n • Signal strength is at least γn • SINR is at least δn • Thermal noise at n: Wn

Outline • Background • Broadcast Traffic • Unicast Traffic • Conclusion

Broadcast Sender Model • Assumption: • Exponential packet length • Transitions of nodes are independent • Markov chain • Si – set of nodes transmitting simultaniously • M – transition matrix

Construction of M Remainidle Si Sj Exit transmition Start transmition Remainactive

Construction of M (cont.)

Computing C(m|Si) • Each term is modeled as a lognormal r.v. • The sum is approximated by a lognormal r.v.

Computing the Throughput • Solve the stationary probability of M • Throughput

Handling Similar Packet Sizes • When packet sizes are similar, overlapping transmissions starts/ends at similar times. • Synchronization graph Gsyn(Si) • m, n is connected is C(m|{n})<0.1 and C(n|{m})<0.1 • Connected nodes in Gsyn(Si) form synchronization group G • For of Gsyn(Si), M(i,j)=0 if and • All nodes in G exit the transmission mode together with probability Tslot/Tμ

Handling Unsaturated Demands • Compute Q(m) iteratively • Given old value Qprev, derive M and compute • Update Q according to

Scalability Issue • 2N states and 22N state transitions • Prune states and transitions • Prune states if the number of edges in the corresponding synchronization graph is too large (>1) • Prune transitions if the transition probability is too low (<0.001)

Broadcast Receiver Model • Goodput - • Lmn – packet loss rate from m to n • Need to translate slot-level loss rates into packet loss rate Lmn • A low slot-level loss rate may result in a high packet loss rate

Broadcast Receiver Model • Three cases of packet losses • Low RSS • Collision with packets from the same synchronization group • Collision with packets from hidden terminals

Slot-Level Loss Probabilities • Slot-level loss rate due to low SINR • Collision within synchronization group • Collision with hidden terminals

Packet Loss probabilities • can be estimated with the packet loss rate when only a single user is transmitting • Assuming the background traffic is a ON/OFF process with fraction of time in ON period =

Unicast Sender Model • Computing • Average contention window under packet loss rate L • Expected number of transmissions

Unicast Sender Model (cont.) • Computing • Average overhead from m to n

Unicast Sender Model (cont.) • Computing • Traffic demand constraint • Computing throughput

Unicast Receiver Model • Data/ACK packet losses due to low RSS • Three cases of collision losses • C1: data collides with other data • C2: data collides with other ACKs (G) and data • C3: ACK (Gm) collides with other ACKs and data

Unicast Receiver Model (cont.) • C2 and C3 are mutually exclusive • A given G stops transmitting first in state i with probability • Combined loss rate of C2 and C3

Unicast Receiver Model (cont.) • Approximate Rack(m,n|Si) as a lognormal r.v. • - Probability of r sending m an ACK in state i

UnicastGoodput

Conclusion • Developed a general model of wireless interference in static networks • Estimating interference among an arbitrary number of senders • Modeling unicast transmissions • Modeling heterogeneous nodes with different traffic demands

Thank you!

A General Model of Wireless Interference