Cooperative HARQ with Poisson Interference and Opportunistic Routing

Transcription

1 Cooperative HARQ with Poisson Interference and Opportunistic Routing Amogh Rajanna & Mostafa Kaveh Department of Electrical and Computer Engineering University of Minnesota, Minneapolis, MN USA.

2 Outline Introduction HARQ Relay network System Model MAC protocol Transport Capacity Transport Capacity Approximation Numerical results : Capacity Optimization

3 HARQ Message b 0 b... b k Codeword c 0 c... c n/ c n/+... c n- c n Puncturing Block Block Block 3 ) Hybrid Automatic Retransmission request combines channel coding and retransmission protocols to combat degradations in wireless channels. ) HARQ aims to balance the tradeoff between efficiency (rate) and reliability (error probability). 3 3

4 HARQ Tx [] [] Rx ACK NACK ) Blocks are sent by transmitter (Tx) incrementally in response to receiver (Rx) requests ) Rx combines all the blocks it has received to decode the message Illustration: With mutual information, I, and transmission rate, R, message is decoded with st block i.e., I > R. Message is not decoded with st block, requires nd block as well, i.e., I +I > R. 4 4

5 Relay Network Users Relays Server Coverage: Connection to remote locations Capacity: High data rates Energy efficiency: Low power transmission for fixed coverage area 5 5

6 Relay Network Relay Selection: ) Opportunistic selection: Relay with best channel or most progress is selected. ) Nearest Neighbor selection: ) n s ) n d Transmission: ) Cooperative ) Non-cooperative n n s n s n d 6 n d n 6 6

7 Cooperative HARQ Cooperative HARQ: [] n n s nd n FEC x U = [U U U 3 code rate: R Hop U n s n d I =log(+sir ) Hop U n n d I =log(+sir ) 3 Hop U 3 n n n d I 3 =log(+sir 3 ) If I +I +I 3 R 'x' is n d 7

8 Transport Capacity R d C = per hop rate * density * distance (Bit meters /sec/unit area) Tradeoff between 3 terms[3]: per hop rate ==> density and distance Balance Tradeoff ==> Network design problem Optimal rate & density to maximize transport capacity 8

9 System Model Assumptions about mobile nodes Each mobile has a stationary flow of packets to be transported to random destination. Mobiles move according to the random waypoint model [4]. S-D assumptions: S-D distance is a random variable with finite mean. S-D pair has no sense of paths; network is in charge of sending packets via multiple hops. Nodes > -D homogeneous Poisson Point Process Φ={X i }, intensity λ /m. Typical S-D pair: origin Destination at a random distance along X-axis. 9

10 p-slotted ALOHA Slot Slot Slot 3 Slot 4 Slot 5... Slotted channel: Tx of a data packet Relay selection Every slot, a node Tx, w.p p Rx, w.p -p Φ Φ t Φ r In the st part of every slot, a node Φ t Transmits a data packet, either its own or of another source node. In the nd part, a distributed relay selection process selects a potential relay for the next hop communication[]. 0

11 Source Transmission ( Block Case) FEC Source node: 'b' information bits x > N symbol codeword U Codeword U is split into non-overlapping blocks {U i } of length L = N/. Source transmits the st code rate R = b/l. (Relays transmit the st or nd the same R) y R from n s 0 SIRy,0 = h y α h k y X k α

12 Progress Progress: Transmission distance per hop in the direction of destination. Opportunistic routing: Relay with most progress to destination is chosen. Progress in st hop D Total progress up to nd hop ( ) [ ( ) ( ( ))] t Φ R, p = I R Φ X cos θ, i, 0 i X i I = log ( + ) i, 0 SIR i,0 ( ) [ ( ) ( ( ))] t Φ R, p = I + I R Φ,X X θ X D n cos t, i, 0 i,x n X n st : relay n location i i

13 Capacity n n n 3 D D n d n s D D t Expected progress in nd hop D t ( Φ,R, p) = D ( Φ,R, p) D ( Φ,R, p) ( R, p) = [ D ( Φ,R, p) ] d ΕΦ Capacity is a spatial measure of Progress Rate Density C = R λp d ( R, p) depends on the distribution of extremal shot noise D and D t. No closed form expression possible 3

14 Capacity Approximation Approximation to expected progress based on decoding cells { } v R I +I R Σ = : I I η v, 0 v,η = v, 0 v,η = = log log ( d, 0) Average cell area ( + SIR ) v,0, ( ) + SIR v,η, 0 η Average location of st relay Ε [ ] ( ) Σ = P I + I R dv R Φ t v, 0 v,η 4

15 Capacity Approximation W, a square centered around ( 0,0) & η s.t W = [ ] Ε Σ 0 η ( W +d )/ Maximum progress Φ r (W + ) ~ Poisson, with parameter ~ d ( R, p) = W +d e c c + ( - p) W c= λ d 5

16 Capacity Optimization Exact capacity optimization R, p = arg Monte Carlo simulation max [ R λp d ( R, p) ] op R, p Approximate capacity optimization R, p = arg max Convex optimization problem ~ [ R λp d ( R, p) ] ap R, p 6

17 Numerical Results R op and R ap against α at λ =. 7

18 Numerical Results p op and p ap against α at λ =. 8

19 Numerical Results R op and R ap against λ at α = 3. 9

20 Numerical Results p op and p ap against λ at α = 3. 0

21 M-round HARQ Decoding cells I Σ v,η k = v R M : Iv,η R k k= 0 Expected area approximation M = log ( ) k +SIR, η = d 0 v,η, k k i i= Ε M M Φ t v,η k k= R 0 [ Σ ] =W = P I R dv M 0. η η M M M d i i= W + /

22 M round HARQ Maximum progress M M d i i= W + / Φ r ( + ) ( ) ( ) + W ~ Poisson c, c= λ - p W M M Total progress upto M th hop ~ d t M ( R, p) = W M + M i= d i e c c Progress in M th hop M ~ ~ d M ( ) ( ) R, p = d t R, p M i= d i Optimization max R, p ~ [ R λp d ( R, p) ] M

23 Summary For a network with Poisson interference and opportunistic routing, we solve the network design problem of choosing the optimal HARQ coding rate and Medium Access Probability (MAP) by optimizing the transport capacity. Optimization of the approximate expression for transport capacity, based on decoding cells, yields close to optimal HARQ coding rate and MAP. Optimal HARQ coding rate and MAP are independent of node density.. 3

24 Select References [] B. Zhao and M. Valenti, Practical relay networks: a generalization of hybrid- arq, Selected Areas in Communications, IEEE Journal on, vol. 3, no., pp. 7 8, Jan [] F. Baccelli, B. Blaszczyszyn, and P. Muhlethaler, An aloha protocol for multihop mobile wireless networks, Information Theory, IEEE Transactions on, vol. 5, no., pp , Feb [3] J. Blomer and N. Jindal, Opportunistic routing in ad hoc networks: How many relays should there be? what rate should nodes use? in Proc. of IEEE Global Commun. Conf., 00. [4] Johnson, D. B.; Maltz, D. A. (996). "Dynamic Source Routing in Ad Hoc Wireless Networks". Mobile Computing. The Kluwer International Series in Engineering and Computer Science 353. p