September 19-20, 2005© SEIL Progress Summary “Dawn” MURI Review Anthony Ephremides University of Maryland Santa Cruz, CA September 12, 2006

© HyNet OUTLINE Over-Riding Theme: Layer Integration & Theoretical Foundations –Physical layer incorporation into MAC and beyond 1)Capture 2)Alternative Access/Receiver Comparison 3)Multicast Stability/Capacity 4)Tandem Network Stability/Capacity Network Coding

© HyNet (1)On Capture (with J. Wieselthier & G. Nguyen) Essence: –Bridging The Gap Of Networking And Communication-Information-Theoretic Approach To Multiple Access via the SINR Tool –Correcting Previous Analyses For Capture Probability Derivation

© HyNet Random-Access System Collision channel –no capture General Multiple-Access channel –all users “succeed” In-between: Reception in the presence of interference –SINR-based model One or more users can be successful Receiver

© HyNet Capture Probability Capture probability: –C n = Pr{at least one transmission is successful | n simultaneous transmissions} Expected number of successful packets in a slot: –S n = E{number of successful packets | n simultaneous transmissions} Multi-Packet reception capability –Depends on detector Receiver

© HyNet SINR-based Capture Model A packet from user j is successful if and only if b = 0: Perfect capture single detector: largest always successful multiple detectors: all are successful b = ∞: No capture (collision channel) when 2 or more transmit, none are successful P(j) = Power at receiving node from user j b = Threshold that depends on many system parameters (increasing function of rate) Receiver j

© HyNet Earlier Work (Zorzi & Rao, JSAC 1994) t = test user P n (r 0 ) = Pr{SINR(t) > b | r t = r 0 } h(r 0 ) = pdf of r 0 (distance of user to base station)  ( * ) is not valid for b < 1  Implicitly assumes only one signal can satisfy SINR Example: Propagation loss factor  = 4 Fading and shadowing are present *which exceeds 1 when (*)(*)

© HyNet Extend Model to Accommodate All Values of b Observations More than one user can satisfy SINR > b when b < 1  Interesting case C n = Pr{one or more users satisfy SINR condition} = Pr{largest signal satisfies SINR condition} Let user M be the one with the largest signal *Thus, C n = Pr{SINR(M) > b} Since all users are equally likely to be the largest *C n = n Pr{SINR(1) > b, M = 1}

© HyNet Analytical Evaluation of Capture Probability C n = n Pr{SINR(1) > b, M = 1} = Pr{SINR(M) > b} *where M is the user with largest received power Example: *For In general, where F P is the common cdf of the received power levels (which are i.i.d.)

© HyNet Simulation is Needed to Evaluate C n Users uniformly distributed in disk of radius  = 1 –No fading or shadowing: any propagation model can be accommodated Results for b > 1 are same as those obtained by others The model is not realistic!  Valid only in far-field region  Received power approaches ∞ as r approaches 0

© HyNet More-Realistic Physical Model Assume users are uniformly distributed in a circular region of radius  = 10. No fading. Curves for C n are drastically different from those for  Previously described performance is not correct  Overestimates received power when transmitter is close to receiver  = 2  = 4  = 2 instead of

© HyNet Multi-Packet Reception All packets for which SINR > b are successful –Not only the largest S n = n Pr{SINR(1) > b}  = 10

© HyNet A Network with Two Destinations Users uniformly distributed throughout union of 2 circles of radius  One destination receiver in each circle –Separated by distance d Traffic distribution –Each packet has a specific destination (receiver) Does not add to throughput when decoded at “wrong” receiver Adds to interference at both receivers –In intersection of 2 circles Packet is equally likely to be intended for D 1 or D 2 –In rest of region Packet is intended for closer destination

© HyNet C n for Two-Destination Network d = 20 (circles just touching) d = 15 (circles overlap)  = 10 n 1 = n 2 = n (i.e., same number of packets for each destination)  Results demonstrate impact of “broader interference” effect resulting from overlapping user populations

© HyNet (2) Alternative Access- Receiver Comparison (joint work with Jie (Rockey Luo) Essence: –Comparison of Scheduled and Simultaneous (Parallel) Multiple Access Strategies –Two Low-Complexity Schedules: TDMA PMAS –Spectral Efficiency vs. Energy Cost comparison –PMAS Dominates if Multiple Antennas are Available at the Receiver

© HyNet Three Channel Sharing Schemes Optimal (complex) Parallel transmission, Multiuser decoding. TDMA (simple) Sequential transmission PMAS (simple) Parallel transmission, Single user decoding. Joint Decoding R sum =log[1+  i P i /N 0 ] SNR i =P i /(N 0 +  j  i P j ) Single user Decoding Gaussian noise of power N 0 P i is the transmit power of user i. All channels have unit gain.

© HyNet Spectral Efficiency Comparison approximately half spectral efficiency 10 transmitters, time-invariant channel, channel gains randomly generated, transmitters know channel states 10 transmitters, time-variant channel, independent Rayleigh fading, transmitters do not know channel states approximately half spectral efficiency Comparing the three schemes: Optimal, TDMA and PMAS

© HyNet Comparison on System Slopes 10 transmitters, time-variant channel, Rayleigh fading, CDI at the transmitter K: number of transmitters M: number of receive antennas We can exploit space resource at the receiver!

© HyNet Superiority of PMAS over TDMA General Results : PMAS is better than TDMA ! In low power regime, let # of terminals  ∞ R PMAS  R OPT / 2 R OPT, R PMAS  # receive antennas R TDMA  constant Multiantenna sampling creates a multi dimensional image. Nature helps separating signals (multiuser multiplex gain) Orthogonal channel sharing is inefficient in exploiting multiuser multiplex gain.

© HyNet Summary The dominance of TDMA is due to its simplicity. 1. Orthogonal channel sharing is inefficient in exploiting multiuser multiplex gain. Such inefficiency can be significant in the low power regime. 2. Overcoming this inefficiency with simple alternative is the key challenge. We showed that such alternative exists in low power regime multiple access systems. 3.

© HyNet (3) Multicast Stability/Capacity (joint work with B. Shrader and Y. Sagduyu) Essence: –Extension of Collision Channel Results –Stability Region Capacity Region –Simple Network coding Scheme Extends Stability Region to the Capacity Region

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© HyNet (4) Tandem Network Stability/Capacity (via Network coding) (joint work with Y. Sagduyu) Essence: –Joint Access/Network coding Broadcasting over Wireless Tandem Networks –Focus on Stable Throughput –Extensions (Cooperative/Competitive Strategies, Energy Optimization)

© HyNet Tandem network: Multiple sources. Error-free transmissions & Mostly broadcasting. Case 1: Assume continuously generated packet traffic, i.e. saturated packet queues. –With or without Network Coding, Find Maximum Throughput Region. Case 2: Allow packet queues to empty. –With or without Network Coding, Find Maximum Stable Throughput Region. Model and Objectives i,j : average rate (packets/s) i j

© HyNet Three separate queues at node i: Plain Routing: Network Coding: Tandem Wireless Network Model (Saturated Queues) Scheduled Access: Group 1: 1, 4, 7, …, Group 2: 2, 5, 8, …, Group 3: 3, 6, 9, … Activate node group m over disjoint fractions of time t m, m  {1,2,3}. Random Access: Node i transmits (new or collided) packets with fixed probability p i. (Crucial Point) 123 n -1 n 456 Q i 1 stores source packets node i generates. Q i 2 stores relay packets from right neighbor of node i Q i 3 stores relay packets from left neighbor of node i + or Qi1Qi2Qi3Qi1Qi2Qi3 Qi1Qi2Qi3Qi1Qi2Qi3 Qi3Qi3 Qi1Qi1 Qi2Qi2 (Linear combination)

© HyNet Achievable Throughput Region under Scheduled Access  i r and  i l : total rates of packets arriving at node i from right and left neighbors. i : throughput rate from node i to destinations M i. Throughput rates satisfy: Achievable throughput region A includes s.t.: For n = 3, achievable throughput region A is:

© HyNet Allow packet queues to empty. –Packet underflow possible: node can wait to perform Network Coding or proceed with Plain Routing. –Consider two dynamic strategies based on instantaneous queue contents: Strategy 1 : Every node attempts first to transmit relay packets and transmits a source packet only if both relay queues are empty. Strategy 2: Every node attempts first to transmit a source packet and transmits relay packets only if the source queue is empty. –Strategy 2 expands the stability region STR(S) to the boundary of TR(A). Stable Throughput Region under Scheduled Access

© HyNet Deriving the achievable and stable throughput regions A and S is difficult. –Throughput regions depend on the transmission schedules t. Consider alternative measures: Assume saturated queues (or non-saturated queues together with strategy 2.). Alternative Optimization Measures Minimum transmitted throughput “Sum”-delivered throughput Find best schedule t to maximize min or  over  A or  S.

© HyNet Throughput Optimization Results For broadcasting with M i = N – {i}, i  N :  min = 0 for optimal values of .  Network coding doubles .  No improvement in min, as n increases.  Objectives of maximizing min and  under broadcast communication cannot be achieved simultaneously.

© HyNet Extension to Random Access Assume saturated queues (otherwise, the problem involves interacting queues). –Nodes randomize between waiting or transmitting source packets or relay packets. –Source packet transmissions: A: Transmit new source packets at any time slot (no feedback - possible loss) B: Transmit source packets until they are received by both neighbors (feedback + repetition) C: Transmit linear combinations of source packets (feedback + coding) : Packet remains in queue Q i 1. Packet enters queue Q i 2. Packet enters queue Q i 3.

© HyNet Wrap-Up Four Inter-Related Sets of Contributions Physical Layer Role in MA Network coding in Wireless Multicast Environments Stable Throughput Region Focus

© HyNet Plans Convert Throughput Results (packets/s) to Spectral Efficiencies (bits/s) Scheduling versus Parallel Transmission (with or without Network Coding) Packet Erasure Channel Models to be Broadened Connect Delay Analysis to Back-Pressure Algorithm