wireless transmission of short packets

Transcription

1 wireless transmission of short packets Petar Popovski Aalborg University, Denmark AAU, June 2016 P. Popovski (Aalborg Uni) short packets AAU, Jun / 19

2 short data packets gaining in importance with various M2M (Machine-to-Machine) and Internet of Things applications low latency packet transmission among vehicles small data chunks reported from sensors P. Popovski (Aalborg Uni) short packets AAU, Jun / 19

3 short data packets gaining in importance with various M2M (Machine-to-Machine) and Internet of Things applications low latency packet transmission among vehicles small data chunks reported from sensors short packets urge information theory and networking to talk to each other asymptotic information-theoretic results not applicable for short lengths low latency with reliability guarantees requires analysis of communication in a transient regime P. Popovski (Aalborg Uni) short packets AAU, Jun / 19

4 short data packets metadata data metadata (control information) becomes comparable in size with the data heuristic design of metadata and then complex coding for data does not work anymore metadata contains preamble, user address, error checking, protocol parameters, etc. important in multiuser systems with dynamic traffic P. Popovski (Aalborg Uni) short packets AAU, Jun / 19

5 options for sending metadata and data M D M D long packet short packet, separated data and metadata frequency frequency frequency M D M D M+D time frame-based transmission time low-latency packet with frequency diversity and joint metadata/data coding time short packet with joint metadata/data coding P. Popovski (Aalborg Uni) short packets AAU, Jun / 19

6 finite blocklength analysis an approximation of the maximal coding rate: (Polyanskiy, Poor, and Verdú, 2010): ( ) V log n R (n, ɛ) = C n Q 1 (ɛ) + O n C: Shannon capacity; V : channel dispersion; n: blocklength, ɛ: desired probability of error; Q 1 ( ) the inverse Q-function. P. Popovski (Aalborg Uni) short packets AAU, Jun / 19

7 finite blocklength analysis capacity 1.0 converse bound rate, R achievability bound normal approximation blocklength, n choosing the block size suggests that at small values of n the transmission is more efficient as the data block size increases. P. Popovski (Aalborg Uni) short packets AAU, Jun / 19

8 finite blocklength: how it affects the two-way channel node 1 should send data and receive ACK from node 2 within n = n 1 + n 2 channel uses n 1 n 2 example: ( 1 ɛ (k 1, n 1 ) )( 1 ɛ (k 2, n 2 ) ) > requires n = 203, out of which n 1 = 132 channel uses are for sending the data packet; n 2 = 71 channel uses are for sending the ACK. P. Popovski (Aalborg Uni) short packets AAU, Jun / 19

9 finite blocklength: how it affects the multiple access channel M devices sent in the uplink ALOHA frame with n channel uses, collisions destructive, K slots one slot has n K = n K channel uses given data size D, how to choose n K so as to maximize the probability of successful transmission? P S = M K ( 1 1 ) M 1 (1 ɛ (D, n K ) ) K P. Popovski (Aalborg Uni) short packets AAU, Jun / 19

10 finite blocklength in a broadcast channel the framing dogma of wireless cellular systems frame header with pointers to the data packets control information encoded messages we consider a downlink broadcast channel with individual short packet for each user P. Popovski (Aalborg Uni) short packets AAU, Jun / 19

11 finite blocklength in a broadcast channel the framing dogma of wireless cellular systems frame header with pointers to the data packets control information encoded messages we consider a downlink broadcast channel with individual short packet for each user tradeoff combining individual packets into a larger block leads to efficient coding, but the user spends energy on decoding data she does not need. P. Popovski (Aalborg Uni) short packets AAU, Jun / 19

12 system model one transmitter and K receivers. AWGN channel, with the output of the k th user at time t X t is the channel input, Z k,t N (0, 1) is the noise, γ is the SNR of user k. Y k,t γx t + Z k,t P. Popovski (Aalborg Uni) short packets AAU, Jun / 19

13 system model one transmitter and K receivers. AWGN channel, with the output of the k th user at time t X t is the channel input, Z k,t N (0, 1) is the noise, γ is the SNR of user k. Y k,t γx t + Z k,t the user k is active and receives a message M k with probability 1 q message size is D k distributed as { q if d = 0 P D (d) = if d {α,, αs} 1 q S P. Popovski (Aalborg Uni) short packets AAU, Jun / 19

14 system model T is the total transmission time computed by the sender. encoding: X t f t (M 1,, M K ) for t {1,, T } and X t = 0 for t {T + 1, } P. Popovski (Aalborg Uni) short packets AAU, Jun / 19

15 system model T is the total transmission time computed by the sender. encoding: X t f t (M 1,, M K ) for t {1,, T } and X t = 0 for t {T + 1, } decoding: ON-OFF function g k,t : (R {e}) t 1 {0, 1} { Yk,t, g auxiliary decoding sequence Ȳk,t k,t (Ȳ t 1 k ) = 1 e, otherwise stopping time T k min { n 1 : t > n, g k,t (Ȳ t 1 k ) = 0 }. decoding function h k,t (Ȳ t k ) attempts to recover the message M k. in a conventional frame each user knows g k,t and T k in advance. P. Popovski (Aalborg Uni) short packets AAU, Jun / 19

16 performance indicators transmission efficiency requires minimization of E[T ]. power consumption of the k th user: P k E [ Tk i=1 { } ] 1 g k,i (Ȳ i 1 k ) = 1 due to symmetry, E[P 1 ] = E[P k ] for each k. reliability requirement: [ ] P h k,tk (Ȳ T k k ) M k D k > 0 ɛ the function used to determine the required number of channel uses N(k, ɛ) min{n 0 : nr (n, ɛ) k} P. Popovski (Aalborg Uni) short packets AAU, Jun / 19

17 asymptotic lower bounds [ E[T ] 1 K ] C E D k = k=1 Kα(1 q)(s + 1) 2C E[P 1 ] 1 C E[D k] = α(1 q)(s + 1) 2C P. Popovski (Aalborg Uni) short packets AAU, Jun / 19

18 design of a new frame/protocol the information that the protocol needs to convey which users are active and have to receive messages; the message size D k of the active user; the message itself M k for each active user. P. Popovski (Aalborg Uni) short packets AAU, Jun / 19

19 design of a new frame/protocol users grouped in B = K/W user groups, max W users per group; user activity, message sizes and messages conveyed in user groups (UGs; B 1 pointers with reliability ɛ 1 ; control information of the second layer with reliability ɛ 2 ; the actual messages with reliability ɛ 3. ptr 2 ptr 3 ptr 4 UG 1 UG 2 UG 3 UG 4 message sizes messages with messages with P. Popovski (Aalborg Uni) short packets AAU, Jun / 19

20 expected transmission time and power min min ɛ [0,1] 3 : (V,W ) K S+1 3 k=1 (1 ɛ k) 1 ɛ (V,W,ɛ) T variable (V,W,ɛ) + β P variable. the inner optimization problem is convex P. Popovski (Aalborg Uni) short packets AAU, Jun / 19

21 numerical results Average power [ch. uses] Protocol (no opt.) Protocol Genie-aided protocol Lower bound Average frame duration [ch. uses] K = 16, P = 1, q = 0.5, α = 100, S = 1, and ɛ = 10 4 P. Popovski (Aalborg Uni) short packets AAU, Jun / 19

22 numerical results Average power [ch. uses] Protocol (no opt.) Protocol Genie-aided protocol Lower bound Average frame duration [ch. uses] 10 4 K = 16, P = 1, q = 0.5, α = 1000, S = 1, and ɛ = 10 4 P. Popovski (Aalborg Uni) short packets AAU, Jun / 19

23 conclusions and outlook short packets challenge the conventional wisdom used in wireless protocols. we have illustrated the new tradeoffs that appear in various multi-user channels and went in details with the broadcast channel. we have shown a latency-power tradeoff in broadcast channel with short packets. P. Popovski (Aalborg Uni) short packets AAU, Jun / 19