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. Network of Unknowns Queue Topology Interference 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. In This Thesis Unknowns in channel and source Channel Source 1 2 q1q1 q2q2 S1S1 S2S2 D h

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

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

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

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 Rx only knows the channel Finite block length –Multiplexing gain » throughput –Diversity order » reliability Reliability and Throughput can not be improved at the same time [Zheng and Tse 03]

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

16. Quantized Parameter Equal power on transmit antennas – i, eigenvalues of HH y are enough to know for outage –There are only m of them –Even more simplify, use only one Assume ordered eigenvalues – 1 > 2 >  > m Transmitter X Receiver Y H

17. Feedback and Power Allocation Allocate Power level s. t. –No outage –Average power constraint But the first interval –For i <  0, we are in outage H + X W Y Q( i ) 0 11 22 44 33 1 2 53 4

18. Sketch of Optimum Mapping, Q nonlinear equations Local behavior of F i (x) at x ! 0 linear equations recursive solution Approximation Quantizer, Q Throughput-Reliability curve 0 11 22 44 33

19. Mux-Div Tradeoff

20. Quantized Power and Rate Control Threshold  L For i >  L –Variable Codebook Gives mux gain For i <  L –Constant Codebook Gives div order Decouple mux and div

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

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. Network of Users So far –Only one user –Knowledge used in power/rate control More than one user The resources need to be divided 1 2 q1q1 q2q2 S1S1 S2S2 D

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. Which Eigenvalue Though? Take i to be quantized –Power guarantees channel 1,…,i –Let r i = ,  2 [0,1] –r j >r i 8 j<i Total mux gain –r > i  r 2 [0, i ] Can be done reverse –For given r, choose i= d r e mm XY i,R i

30. Quantized Parameter Transmitter X Receiver Y NtNt NrNr mm XY Equivalent channel –m parallel channel m Equal power on transmit antennas – i are enough to know –There are only m of them Assume ordered eigenvalues – 1 > 2 >  > m H