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 1.The channel changes very often within a single codeword. 2.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 N 0 : if E |d| -2 exists, 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 capacities IEEE 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. if E |d| -2 exists, C > 0 C = 0 for Rayleigh fading.

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

12. Path Loss | d i | 2 ~ |r i | -4 no shadowing no Rayleigh fading Signal Attenuation r1r1 r2r2 r3r3

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

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

15. Multiuser Diversity + Frequency Diversity Let each user have M parallel channels. 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. For Rayleigh fading, DL-capacity is positive if M > 1. Remark 1: Theorem 1 does not hold for a finite number of users, in general.

16. Multiuser Diversity + Frequency Diversity 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. d = max{|d 1 |; |d 2 |; ··· ; |d M |}

17. Path Loss |d i | 2 ~ |r i | -4 2 nd order frequency diversity no shadowing Signal Attenuation Rayleigh fading

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

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 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. Cellular systems are interference limited. You want to minimize interference into other cells instead of transmit power. 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. Large number of users makes interference symmetric. Reuse factor 2:

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

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

24. Takk for oppmerksomheten Tacka dig för uppmärksamhet Danke für die Aufmerksamkeit Grazie per attenzione شكرت أنت لإنتباه