Wireless Networks with Limited Feedback : PHY and MAC Layer Analysis

1. Wireless Networks with Limited Feedback: PHY and MAC Layer Analysis PhD Proposal Ahmad Khoshnevis Rice University

2. Wireless Networks • Higher throughput • TAP: 400 Mbps • WiMax • 4G

3.  Queue Network of Unknowns Interference Topology Channel Battery

4. Why Unknowns Matter? • Physical layer example • Channel varies with time • If current condition known • Adapt and achieve higher throughput • Catch • We don’t care about the channel (unknown) • Only care about sending data • Time varying in nature • Periodic measurements • Spend resources for non-data • Should you measure unknowns ? If yes, how accurately ?

5. q2 S1 l1 D q1 l2 h S2 In This Thesis • Unknowns in channel and source • Channel • Source

6. Outline • Analysis of Physical Layer with Feedback • Background and related works • Feedback design • Throughput-reliability tradeoff • Proposed work: Managing Unknowns at Medium Access Layer • Background and related works • Road-map • Contribution summary

7. W(t) X(t) Y(t) + H(t) PHY: System Model

8. PHY Objective • Maximize throughput • Ergodic capacity • Minimize packet loss • Outage probability • Intuitively • Two metrics are against each other

9. Tx Rx H(t) PHY Unknown: Channel (H) • No one measures • Out of fashion • Receiver (Rx) measures • Transmitter and Receiver measures (Tx+Rx)

10. PHY: Limiting Performance Shannon, Goldsmith & Varaiya. Telatar, Jayaweera & Poor, Caire et. al. • Outage • Large gain with Tx knowledge • Greater rate of decay (slope) • Ergodic capacity • Some gain • Same rate of increase (slope)

11. PHY: Div-Mux Tradeoff [Zheng and Tse 03] • Rx only knows the channel • Finite block length • Multiplexing gain »throughput • Diversity order »reliability • Reliability and Throughputcan not be improved at the same time

12. Summary and Question • System Tx+Rx outperforms Rx only • Perfect channel knowledge requires infinite  capacity in feedback If only few bits were available for feedback, then What would be the impact on performance? How would the mux-div be affected?

13. Related Work: Finite Feedback • Beamforming • Narula et. al., 99, quantized beamforming • Mukkavilli et. al., Love and Heath, 03 • Power Control • Bhashyam et. al. 02, One bit feedback design, outage • Ligdas and Farvardin 00, Lloyd-Max quantizer, bit error rate • Yates et. al. 03, Lloyd-Max, power and rate, ergodic capacity • My work • Design and analysis of a low complexity channel quantizer • Multiple antenna system • Outage as metric • Analysis of diversity-multiplexing tradeoff

14. Outline • Analysis of Physical Layer with Feedback • Background and related works • Feedback design • Throughput-reliability tradeoff • Proposed work: Collision Channel with Feedback • Background and related works • Road-map • Contribution summary

15. W X Y + H Q(H) Limited Feedback Design • B bits of feedback • L= 2B • For a multiple antenna system • In Tap: m=4, n=4 • H is in 2*4*4 = 32 dimensional space

16. Transmitter X Receiver Y H Quantized Parameter • Equal power on transmit antennas • li , • eigenvalues of HHy • are enough to know for outage • There are only m of them • Even more simplify, use only one • Assume ordered eigenvalues • l1>l2>L>lm

17. W 1 3 5 2 4 X Y + H 0 g1 g3 g4 g2 Q(li) Feedback and Power Allocation • Allocate Power level s. t. • No outage • Average power constraint • But the first interval • For li<g0, we are in outage

18. linear equations recursive solution nonlinear equations Approximation Local behavior of Fli(x) at x!0 Quantizer, Q Throughput-Reliability curve 0 g1 g3 g4 g2 Sketch of Optimum Mapping, Q

19. Mux-Div Tradeoff

20. Quantized Power and Rate Control • Threshold gL • For li>gL • Variable Codebook • Gives mux gain • For li<gL • Constant Codebook • Gives div order • Decouple mux and div

21. Rx only nonzero Mux-Div: Quantized Power/Rate Control

22. Outline • Analysis of Physical Layer with Feedback • Unknown: Channel • Even a ‘little’ knowledge has a ‘lot’ of gain • Proposed work: Collision Channel with Feedback • Background and related works • Road-map • Contribution summary

23. q2 S1 l1 D q1 l2 S2 Network of Users • So far • Only one user • Knowledge used in power/rate control • More than one user • The resources need to be divided

24. Unknowns: Managing Queue State • Queues have time-varying state • Might be empty sometimes • In effect, # of active nodes is time varying • Design for Max # of user is conservative • Underutilized network for many traffic • “Active” management of queue states = Medium Access Protocols

25. Class of MAC Protocols • CDMA • TDMA • Round-Robin • Adaptive Scheduling • Random Access • Abramson 70, ‘The ALOHA System’, only random access w/o CA • Tobagi and Kleinrock 75, CSMA/CA, out-of-band busy tone • Karn 90, MACA, control handshake (RTS/CTS) • All of the above consume resources • Price paid for managing unknowns

26. Major Question What is the minimum price for unknown queue-state information ? • NOTE • Unknowns themselves not of interest, data is • How much overhead you HAVE to pay to send on this channel with unknowns (queue states) ?

27. Proposed Approach • Considered queuing theoretic [ISIT 2005] • Abandon it • Not scalable for more then 2 users • Does not provide intuition • Inspired by information theory • Rate of information in unknowns • In a finite delay system, transmitted packet conveys two information • Information contained in the packet • Timing information • Quantify timing information as a function of delay (=distortion) • Rate-distortion over collision channel

28. Summary • Managing unknowns • Physical layer • MAC layer • There is a lot of gain in knowing even a ‘little’ • Showed at PHY • Under investigation at MAC layer

29. li,Ri X Y m m Which Eigenvalue Though? • Take li to be quantized • Power guarantees channel 1,…,i • Let ri = a, a2[0,1] • rj>ri8j<i • Total mux gain • r > i a • r 2 [0 , i ] • Can be done reverse • For given r, choose i=dre

30. Transmitter X Receiver Y X Y Nr Nt m m Quantized Parameter H lm • Equal power on transmit antennas • li are enough to know • There are only m of them • Assume ordered eigenvalues • l1>l2>L>lm • Equivalent channel • m parallel channel