Opportunistic Communications under Energy & Delay Constraints Narayan Mandayam (joint work with Henry Wang)
Opportunistic Communications Wireless Data on the Move Intermittent Connectivity Opportunities for transmission arise in time, frequency and space Examples of situations include: Wireless Access to the Internet Infostations Wireless LANs How to efficiently design opportunistic transmission strategies?
Opportunistic Communications: A Historical Perspective Janus, the Roman God 2 heads are better than 1 Brahma, the Indian God 4 heads are better than 1 Meteor Burst Channels Bounce radio waves off meteor showers
Outline File Transfer Problem: To transfer a file (fixed number of packets) through a wireless link under both energy and delay constraints A binary (on/off) power control scheme is used System Model & Assumptions Optimum Transmission Design Numerical Examples Extensions to Other Opportunistic Scenarios
System Model Communication Model A fixed size data file L (packets) Finite battery energy budget E (Joules) Time varying wireless channel Two performance metrics of the file transfer Probability of Success File Transfer Delay Objective : to find an optimal power control policy that maximizes the probability of success while under a certain delay constraint
Delay Constrained Scenarios No delay constraint There is no constraint on the time spent in transferring the file. Average delay constraint The average time spent in transferring the file has to be less than a requirement. Strict delay constraint The exact time spent in transferring the file has to be less then a requirement.
Finite State Markov Channel Model Slow fading: received SNR remains at a constant level for a constant packet duration t Partition SNR A into finite intervals, and model the channel as a K-state Markov chain. s ( k) : A [ A ( k), A ( k+ 1) ), k = 0,1, LK 1 State transitions occur only into neighboring (or same) states Transition probabilities depend on Doppler frequency
File Transfer System Model ARQ Scheme: Stop & Wait Instantaneous ACK/NAK and transmitter arranges for retransmission (if necessary).
Binary (on/off) Power Control Scheme Discrete time sequence t 0, t 1,, t N-1, where t i+1 - t i = t and N is communication window At each time instant t i we need to decide the transmit power P i for the slot [t i, t i+1 ) Binary power control scheme, i=0,1,,n-1 action 1: a i =1 P i =P action 0: a i =0 P i =0 System State: v=(s,e,l); s: channel state; e: residual energy l: the number of remaining packets in the buffer
Probability of Successful File Transfer Events E 1 & E 0 E 1 E 0 All L packets are successfully transmitted within energy budget E Joules. File transfer fails: there is neither enough energy left nor enough time to transmit the remaining packets. Communication ends if either E 1 or E 0 occurs Policy π =[a 0 a i a N-1 ], a i (v) {0, 1} Probability of successful file transfer: R(π ) = Prob{E 1 π}
Power Control under No Delay Constraints Under no delay constraints, the optimal policy is such that the transmitter chooses action 1 only on the best channel state; otherwise, the transmitter remains silent and waits (action 0). Wait Best Channel State
Power Control under Average Delay Constraints Problem: subject to max R( π ) π N avg ( π ) N D N avg (π): Average communication window size when applying policy π Optimal transmission policies can be derived via infinite horizon dynamic programming algorithms
S0: [-, 1.26dB), S1: [1.26dB, 4.59dB), S2: [4.59dB,6.72dB), S3: [6.72dB, 8.41dB), S4: [8.41dB,9.92dB), S5: [9.92dB, 11.42dB), S6:[11.42dB,13.18dB), S7: [13.18dB, ) Optimal (Stationary) Policy under Average Delay Constraints (N D =45) l=18 l=5
Maximum Probability of Success under Average Delay Constraints 1-R(π*) vs. N D R(π*) vs. f d
Power Control under Strict Delay Constraints Problem: subject max R( π ) π to N( π ) N D N(π): communication window size when applying policy π Optimal transmission policies can be derived via finite horizon dynamic programming algorithms
S0: [-, 1.26dB), S1: [1.26dB, 4.59dB), S2: [4.59dB,6.72dB), S3: [6.72dB, 8.41dB), S4: [8.41dB,9.92dB), S5: [9.92dB, 11.42dB), S6:[11.42dB,13.18dB), S7: [13.18dB, ) Optimal (Non-Stationary) Policy under Strict Delay Constraints (N D =100) Time i=0, l=18 Time i=90, l=5
Maximum Probability of Successful File Transfer R(π*) vs. f d 1-R(π*) for both delay constrained cases
Summary for average and strict delay constrained Scenarios The optimal policies are stationary under an average delay constraint The optimal policies are non-stationary under a strict delay constraint The optimal policies are threshold rules on channel states, residual energy and the number of remaining packets in the buffer Success probability of the file transfer increases as Doppler frequency increases
Extensions to Other Opportunistic Scenarios Energy and Delay Constrained Power Control over Fading Channels Information capacity considerations Maximize minimum sum of expected rates Energy Efficient Packet Scheduling over Fading Channels under Delay Constraints Policies depend on packet arrival processes and include residual buffer and channel state information Dynamic Power Control under Mobility Random walk model for time-varying channel characterization