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On the Capacity of Distributed Antenna Systems

On the Capacity of Distributed Antenna Systems. Lin Dai. City University of Hong Kong. Cellular Networks (1). Base Station (BS). Growing demand for high data rate. Multiple antennas at the BS side. Cellular Networks (2). Co-located BS antennas. Distributed BS antennas.

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On the Capacity of Distributed Antenna Systems

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  1. 1 On the Capacity of Distributed Antenna Systems Lin Dai City University of Hong Kong

  2. 2 Cellular Networks (1) Base Station (BS) Growing demand for high data rate Multiple antennas at the BS side

  3. 3 Cellular Networks (2) • Co-located BS antennas • Distributed BS antennas Implementation cost Lower Sum rate Higher?

  4. 4 A little bit of History of Distributed Antenna Systems (DAS) • Originally proposed to cover the dead spots for indoor wireless communication systems [Saleh&etc’1987]. • Implemented in cellular systems to improve cell coverage. • Recently included into the 4G LTE standard. • Multiple-input-multiple-output (MIMO) theory has motivated a series of information-theoretic studies on DAS.

  5. 5 Single-user SIMO Channel • Single user with a single antenna. • L>1 BS antennas. • Uplink (user->BS). (a) Co-located BS Antennas (b) Distributed BS Antennas • Received signal: : Transmitted signal : Gaussian noise • Channel gain : : Large-scale fading : Small-scale fading

  6. 6 Single-user SIMO Channel • Single user with a single antenna. • L>1 BS antennas. • Uplink (user->BS). (a) Co-located BS Antennas (b) Distributed BS Antennas • Ergodic capacity without channel state information at the transmitter side (CSIT): Function of large-scale fading vector g • Ergodic capacity with CSIT:

  7. 7 Co-located Antennas versus Distributed Antennas • With co-located BS antennas: • Ergodic Capacity without CSIT: m is the average received SNR: • With distributed BS antennas: • Distinct large-scale fading gains to different BS antennas. • Ergodic Capacity without CSIT: Normalized channel gain:

  8. 8 Capacity of DAS • For given large-scale fading vector g: • [Heliot&etc’11]: Ergodic capacity without CSIT • A single user equipped with N co-located antennas. • BS antennas are grouped into L clusters. Each cluster has M co-located antennas. • Asymptotic result as M and N go to infinity and M/N is fixed. • [Aktas&etc’06]: Uplink ergodic sum capacity without CSIT • K users, each equipped with Nbk co-located antennas. • BS antennas are grouped into L clusters. Each cluster has Nll co-located antennas. • Asymptotic result as N goes to infinity and bk and ll are fixed. • Implicit function of g (need to solve fixed-point equations) • Computational complexity increases with L and K.

  9. 9 Capacity of DAS • With random large-scale fading vector g: Average ergodic capacity (i.e., averaged over g) • Single user • Without CSIT • [Roh&Paulraj’02], [Zhang&Dai’04]: The user has identical access distances to all the BS antennas. • [Zhuang&Dai’03]: BS antennas are uniformly distributed over a circular area and the user is located at the center. • [Choi&Andrews’07], [Wang&etc’08], [Feng&etc’09], [Lee&ect’12]: BS antennas are regularly placed in a circular cell and the user has a random location. High computational complexity!

  10. 10 Questions to be Answered • How to characterize the sum capacity of DAS when there are a large number of BS antennas and users? • Large-system analysis using random matrix theory. • Bounds are desirable. • How to conduct a fair comparison with the co-located case? • K randomly distributed users with a fixed total transmission power. • Decouple the comparison into two parts: 1) capacity comparison and 2) transmission power comparison for given average received SNR. • What is the effect of CSIT on the comparison result?

  11. 11 Part I. System Model and Preliminary Analysis [1] L. Dai, “A Comparative Study on Uplink Sum Capacity with Co-located and Distributed Antennas,” IEEE J. Sel. Areas Commun., 2011.

  12. 12 Assumptions • K users uniformly distributed within a circular cell. Each has a single antenna. • L BS antennas. • Uplink (user->BS). Random BS antenna layout! *: user o: BS antenna (b) Distributed Antennas (DA) (a) Co-located Antennas (CA)

  13. 13 Uplink Ergodic Sum Capacity : Transmitted signal • Received signal: : Gaussian noise : Channel gain : Large-scale fading • Uplink power control: : Small-scale fading Ergodic capacity without CSIT Ergodic capacity with CSIT

  14. 14 More about Normalized Channel Gain : Small-scale fading • Normalized channel gain vector: : Normalized Large-scale fading • With CA: The channel becomes deterministic with a large number of BS antennas L! • With DA: • With a large L, it is very likely that user k is close to some BS antenna : Channel fluctuations are preserved even with a large L!

  15. 15 More about Normalized Channel Gain • Theorem 1. For n=1,2,…, which is achieved when which is achieved when • Channel fluctuations are minimized when • maximized when • Channel fluctuations are undesirable when CSIT is absent, • desirable when CSIT is available.

  16. 16 Single-user Capacity (1) • Without CSIT • -- Fading always hurts if CSIT is absent! • quickly approaches 1 as L grows. • With CSIT (when m0 is small) • at low m0--“Exploit” fading (average received SNR)

  17. 17 Single-user Capacity (2) • Without CSIT DA with • A higher capacity is achieved in the CA case thanks to better diversity gains. • With CSIT • A higher capacity is achieved in the DA case thanks to better waterfilling gains. DA with The average received SNR .

  18. 18 Part II. Uplink Ergodic Sum Capacity

  19. 19 Uplink Ergodic Sum Capacity without CSIT • Sum capacity without CSIT: • Sum capacity per antenna (with K>L): where denotes the eigenvalues of .

  20. 20 More about Normalized Channel Gain • Theorem 2. As and and with when when • With DA and • With CA: as and as and [Marcenko&Pastur’1967]

  21. 21 Sum Capacity without CSIT (1) • Gap diminishes when u is large -- the capacity becomes insensitive to the antenna topology when the number of users is much larger than the number of BS antennas. (average received SNR)

  22. 22 Sum Capacity without CSIT (2) • A higher capacity is achieved in the CA case thanks to better diversity gains. CA DA with • serves as an asymptotic lower-bound to . The average received SNR The number of users K=100.

  23. 23 Uplink Ergodic Sum Capacity with CSIT • Sum capacity with CSIT: • With CA: • With DA and The optimal power allocation policy: The optimal power allocation policy: where z is a constant chosen to meet the power constraint , k=1,…, K. [Yu&etc’2004] i=1,…,L, where z is a constant chosen to meet the sum power constraint

  24. 24 Signal-to-Interference Ratio (SIR) (a) CA (b) DA with The received SNR The number of users K=100. The number of BS antennas L=10.

  25. 25 Sum Capacity (1) • Without CSIT • Gap between and is enlarged as L grows (i.e., due to a decreasing K/L). • With CSIT even at high SNR (i.e., thanks to better multiuser diversity gains) (average received SNR) The number of users K=100.

  26. 26 Sum Capacity (2) • Without CSIT DA with • A higher capacity is achieved in the CA case thanks to better diversity gains. CA • With CSIT • A higher capacity is achieved in the DA case thanks to better waterfilling gains and multiuser diversity gains. The average received SNR The number of users K=100.

  27. 27 Part III. Average Transmission Power per User

  28. 28 Average Transmission Power per User • Transmission power of user k: • Average transmission power per user: • With CA: • With DA: • Users are uniformly distributed in the circular cell. BS antennas are co-located at cell center. • Both users and BS antennas are uniformly distributed in the circular cell. What is the distribution of

  29. 29 Minimum Access Distance • With DA, each user has different access distances to different BS antennas. Let denote the order statistics obtained by arranging the access distances d1,k,…, dL,k. • for L>1. • An upper-bound for average transmission power per user with DA:

  30. 30 Average Transmission Power per User • CA: • DA: (path-loss factor a>2) For given received SNR, a lower total transmission power is required in the DA case thanks to the reduction of minimum access distance. • With a=4, if Path-loss factor a=4.

  31. 31 Sum Capacity without CSIT • For fixed K and ( such that ) Given the total transmission power, a higher capacity is achieved in the DA case. Gains increase as the number of BS antennas grows. The number of users K=100.

  32. 32 Conclusions • A comparative study on the uplink ergodic sum capacity with co-located and distributed BS antennas is presented by using large-system analysis. • A higher sum capacity is achieved in the DA case. Gains increase with the number of BS antennas L. • Gains come from 1) reduced minimum access distance of each user; and 2) enhanced channel fluctuations which enable better multiuser diversity gains and waterfilling gains when CSIT is available. • Implications to cellular systems: • With cell cooperation: capacity gains achieved by a DAS over a cellular system increase with the number of BS antennas per cell thanks to better power efficiency. • Without cell cooperation: lower inter-cell interference with DA?

  33. 33 Thank you! Any Questions?

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