Multiuser Diversity in Delay-Limited Cellular Systems

1. Multiuser Diversity in Delay-Limited Cellular Systems Ralf R. Müller ralf@iet.ntnu.no Department of Electronics & Telecommunications Norwegian University of Science & Technology, Trondheim Giuseppe Caire & Raymond Knopp {caire,knopp}@eurecom.fr Institut Eurècom Sophia-Antipolis, France

2. Disclaimer This is NOT a talk on fair scheduling of users. Here: • Fairness is not enough. • Each user has to get their message instantaneously with probability going to 1.

3. Ergodic vs. Delay-Limited Capacity • The channel changes very often within a single codeword. • The channel is constant within a single codeword. Two extreme cases of fading channels: Ergodic capacity Delay-Limited capacity

4. Delay-Limited Capacity for a Single User Let the fading d be known at both transmitter and receiver, AWGN channel with energy per symbol E and noise density N0: ifE |d|-2exists,C > 0 and f (d) = |d|-2. C = 0 for Rayleigh fading.

5. Delay-Limited Capacity for Many Users The result is given as a multi-dimensional optimization problem in Stephen V.Hanly, David N.C. Tse:Multiaccess fading channels. Part II: Delay-limited capacitiesIEEE Trans. Inform. Theory, vol. 44, no. 7, pp. 2816 - 2831, Nov. 1998.   Can we obtain a gain by multiuser diversity without any drawback in quality of service, e.g. no additional delay?

6. Gaussian Multiple-Access Channel without Fading

7. Dual Representation of GMAC without Fading

8. Transmit Power vs. Receive Power Rescaling of axis in power region

9. Transmit Power vs. Receive Power

10. GMAC with Fading Let the attenuations be random from codeword to codeword. ifE |d|-2exists,C > 0 C = 0 for Rayleigh fading.

11. Single User vs. Infinite Users Single User: Infinite Users: for all rates

12. Signal Attenuation Path Loss |di|2 ~ |ri|-4 no shadowingno Rayleigh fading r3 r1 r2

13. Delay-Limited Capacity for Path Loss spec. efficiency [bits/sec/Hz] inf. orth. users infinite users single user [dB]

14. There is a gain by multiuser diversity without any drawback in quality of service, ifE |d|-2exists. Without constraints to orthogonal separation of users, the gain is greater.

15. Multiuser Diversity + Frequency Diversity Let each user have M parallel channels. For Rayleigh fading, DL-capacity is positive if M > 1. • Theorem 1: • Subject to some technical conditions on the rates and the fading, each user uses only that channel of theirs which has the best propagation conditions, as the number of users approaches infinity. Remark 1: Theorem 1 does not hold for a finite number of users, in general.

16. Multiuser Diversity + Frequency Diversity d = max{|d1|; |d2|; ··· ; |dM|} • Corollary 1: • Subject to some technical conditions on the rates and the fading, frequency diversity only re-shapes the fading distribution, as the number of users approaches infinity.

17. Signal Attenuation Rayleigh fading Path Loss|di|2 ~ |ri| -4 2nd order frequency diversity no shadowing

18. Delay-Limited Capacity without Rayleigh fading with Rayleigh fading single user orthogonal limit spec. efficiency [bits/sec/Hz] channel capacity The mean fading changes as well. [dB]

19. Uplink vs. Downlink • Theorem 2: • Thanks to multiple-access broadcast duality on Gaussian channels, all results for multiple-access channels and transmit power, also hold for the Gaussian broadcast channel.

20. Cellular Systems Cellular systems are interference limited. You want to minimize interference into other cells instead of transmit power. • Corollary 2: • Subject to some technical conditions on the rates and the fading, minimizing interference power onto base stations of other cells instead of transmit power is equivalent to re-shaping the fading distribution as the number of users approaches infinity. Open question: Does MAC broadcast duality apply here?

21. Cellular Systems (cont’d) Consider a linear cellular system w.l.o.g. You want to minimize interference into other cells instead of transmit power. Reuse factor 2: Large number of users makes interference symmetric.

22. Delay-Limited Capacity of Cellular System reuse 2 Spectral effciency can be doubled. spec. efficiency [bits/sec/Hz] capacity reuse 3 reuse 4 reuse 2 reuse 3 reuse 4 single user path loss exponent

23. Coming Soon ... Hexagonal cells ... Rayleigh fading Just one more thing: path loss exponent 2: with

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