On the Capacity of Distributed Antenna Systems Lin Dai

Transcription

1 On the apacity of Distributed Antenna Systems Lin Dai ity University of Hong Kong JWIT 03

2 ellular Networs () Base Station (BS) Growing demand for high data rate Multiple antennas at the BS side JWIT 03

3 ellular Networs () 3 o-located BS antennas Distributed BS antennas Implementation cost Lower Sum rate Higher? JWIT 03

4 A little bit of History of Distributed Antenna Systems (DAS) 4 Originally proposed to cover the dead spots for indoor wireless communication systems [Saleh&etc 987]. 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. JWIT 03

5 Single-user SIMO hannel 5 Single user with a single antenna. L> BS antennas. Uplin (user->bs). (a) o-located BS Antennas (b) Distributed BS Antennas Received signal: y gs z s (0, P) : Transmitted signal L z : Gaussian noise z (0, N ), i,..., L. i 0 g=γh L γ hannel gain : : Large-scale fading / i Log ( di, i ), i,..., L. L h : Small-scale fading h (0,), i,..., L. i JWIT 03

6 Single-user SIMO hannel 6 Single user with a single antenna. L> BS antennas. Uplin (user->bs). (a) o-located BS Antennas (b) Distributed BS Antennas Ergodic capacity without channel state information at the transmitter side (SIT): o g log P N 0 Ergodic capacity with SIT: w E h P g max Eh log P: E h [ P] P N 0 Function of large-scale fading vector JWIT 03

7 o-located Antennas versus Distributed Antennas With co-located BS antennas: Ergodic apacity without SIT: 7 o h L h is the average received SNR: E log P γ / N 0 With distributed BS antennas: Distinct large-scale fading gains to different BS antennas. Ergodic apacity without SIT: D o E log g h Normalized channel gain: g=β h β γ γ JWIT 03

8 8 apacity of DAS For given large-scale fading vector : [Heliot&etc ]: Ergodic capacity without SIT o o o 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. [Atas&etc 06]: Uplin ergodic sum capacity without SIT o o o K users, each equipped with N co-located antennas. BS antennas are grouped into L clusters. Each cluster has N l co-located antennas. Asymptotic result as N goes to infinity and and l are fixed. Implicit function of (need to solve fixed-point equations) omputational complexity increases with L and K. JWIT 03

9 apacity of DAS With random large-scale fading vector : 9 Average ergodic capacity (i.e., averaged over ) Single user Without SIT [Roh&Paulraj 0], [Zhang&Dai 04]: The user has identical access distances to all the BS antennas. i Log (, ), i,..., L. [Zhuang&Dai 03]: BS antennas are uniformly distributed over a circular area and the user is located at the center. / i i, i,..., L. [hoi&andrews 07], [Wang&etc 08], [Feng&etc 09], [Lee&ect ]: BS antennas are regularly placed in a circular cell and the user has a random location. / i Log ( di, i ), i,..., L. High computational complexity! JWIT 03

10 Questions to be Answered 0 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: ) capacity comparison and ) transmission power comparison for given average received SNR. What is the effect of SIT on the comparison result? JWIT 03

11 Part I. System Model and Preliminary Analysis [] L. Dai, A omparative Study on Uplin Sum apacity with o-located and Distributed Antennas, IEEE J. Sel. Areas ommun., 0. JWIT 03

12 Assumptions K users uniformly distributed within a circular cell. Each has a single antenna. L BS antennas. Uplin (user->bs). Random BS antenna layout! *: user o: BS antenna (a) o-located Antennas (A) (b) Distributed Antennas (DA) JWIT 03

13 Uplin Ergodic Sum apacity 3 Received signal: K y g s z Uplin power control: P, γ P0,..., K. s (0, P) L z g = γ γ h h L L : Transmitted signal : Gaussian noise z (0, N ), i,..., L. i : hannel gain : Large-scale fading / i, di,, i,..., L. : Small-scale fading hi, (0,), i,..., L. 0 Ergodic capacity without SIT K sum _ o =EH logdet IL P gg N0 =EH log det I P K 0 L gg N0 Ergodic capacity with SIT K sum _ w= max EH logdetil P gg P: E H [ P] P N,..., K 0 = max EH log det I P : E [ P H ] P0,..., K K L P gg N0 JWIT 03

14 More about Normalized hannel Gain 4 Normalized channel gain vector: With A: With DA: o β L g L i, j,, i j.. g =β h With a large L, it is very liely that user is close to some BS antenna : g h l, * if L. l * β e l * L h : Small-scale fading γ L β : Normalized γ Large-scale fading β. The channel becomes deterministic with a large number of BS antennas L! hannel fluctuations are preserved even with a large L! e l * if l l 0 otherwise JWIT 03

15 More about Normalized hannel Gain 5 Theorem. For n=,,, min β : β β n ( )! E n L h g, n L ( L)! n max E h g!, : n β which is achieved when which is achieved when β L β e *. l. L hannel fluctuations are minimized when β L maximized when β e *. l hannel fluctuations are undesirable when SIT is absent, desirable when SIT is available. L, JWIT 03

16 Single-user apacity () 6 Without SIT log ( ) 0 _ o _ w β e * l D* _ o D* _ w -- Fading _ o/ AWGN always hurts if SIT is absent! _ o/ AWGN quicly approaches as L grows. D* _ o _ o (average received SNR) 0 P0 / N0 (db) With SIT (when 0 is small) _ w / AWGN at low 0 -- Exploit fading D* _ w _ w JWIT 03

17 7 Single-user apacity () log ( ) AWGN 0 DA with β e * l Without SIT A higher capacity is achieved in the A case thans to better diversity gains. DA with β e * l With SIT A higher capacity is achieved in the DA case thans to better waterfilling gains. The average received SNR 0 0dB. JWIT 03

18 8 Part II. Uplin Ergodic Sum apacity JWIT 03

19 Uplin Ergodic Sum apacity without SIT 9 Sum capacity without SIT: K 0 sum _ o =EH logdet IL g g EH logdet IL 0GG N0 Sum capacity per antenna (with K>L): { } l P E log det I GG L L E H log 0 l L l L_ o H L 0 GG where denotes the eigenvalues of. G=B H B β β [,..., K ] H [ h,..., h ] K JWIT 03

20 More about Normalized hannel Gain 0 Theorem. As K, L and K / L, E [ ], H and when B L K L. 0 when B [ e *,..., e * ]. H 0. with E [ ], l l K With A: B L f x x x x as K, L and K / L. ( ) (( ) )( ( ) ) [Marceno&Pastur 967]. L K With DA and B [ e *,..., e * ]: l l K D* ( x ) ( x ) f ( x) e 0!( )! as K, L and K / L. JWIT 03

21 Sum apacity without SIT () log ( ) 0 L _ o D* L _ o D* L_ o L_ o Gap diminishes when 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) 0 P0 / N0 (db) JWIT 03

22 Sum apacity without SIT () A DA with B [ e,..., e ] * * l l K A Analytical (Eq. (3, 34)) Simulation DA Analytical (Eq. (3, 40)) Simulation Number of BS Antennas L A higher capacity is achieved in the A case thans to better diversity gains. The average received SNR 0 0dB. The number of users K=00. JWIT 03 D* sum _ o serves as an asymptotic lower-bound D sum _ o to.

23 Uplin Ergodic Sum apacity with SIT 3 Sum capacity with SIT: K sum_ w= max EH logdet IL P gg P : E [ P H ] P0 N,..., K 0 P P γ With A: The optimal power allocation policy: P * N 0 * g IL P j jg jg j g where is a constant chosen to meet the power constraint E P H P0, =,, K. [Yu&etc 004] With DA and The optimal power allocation policy: N arg max h P * i * 0 i * * 0 i i, h i i, i=,,l, where is a constant chosen to meet the sum power constraint K E P KP. H 0 B [ e,..., e ]: * * l l K JWIT 03

24 Signal-to-Interference Ratio (SIR) 4 (a) A (b) DA with B [ e,..., e ] * * l l K The received SNR 0 0dB. The number of users K=00. The number of BS antennas L=0. JWIT 03

25 Sum apacity () 5 B [ e,..., e ] * * l l K Without SIT D* sum _ o sum _ o L log ( ) sum K L 0 (average received SNR) 0 P0 / N0 (db) The number of users K=00. B [ e,..., e ] * * l l K sum _ o Gap between and (i.e., due to a decreasing K/L). With SIT D* sum _ o is enlarged as L grows D* sum _ o sum _ o even at high SNR (i.e., thans to better multiuser diversity gains) JWIT 03

26 Sum apacity () 6 DA with B [ e,..., e ] * * l l K A Without SIT A higher capacity is achieved in the A case thans to better diversity gains. With SIT A higher capacity is achieved in the DA case thans to better waterfilling gains and multiuser diversity gains. The average received SNR 0 0dB. The number of users K=00. JWIT 03

27 7 Part III. Average Transmission Power per User JWIT 03

28 Average Transmission Power per User 8 P0 Transmission power of user : P,,..., K. γ Average transmission power per user: K K P K P0 f ( x ) dx 0 γ x With A: o Users are uniformly distributed in the circular cell. BS antennas are co-located at cell center. With DA: o Both users and BS antennas are uniformly distributed in the circular cell. γ f L x ( x) R P0 R L What is the distribution of γ JWIT 03?

29 Minimum Access Distance 9 With DA, each user has different access distances to different BS antennas. Let () () ( L) d d d denote the order statistics obtained by arranging the access distances d,,, d L,. L () γ dl, d for L>. l An upper-bound for average transmission power per user with DA: R ( ) R y D DU P0 ( ) () f y f x y dxdy 0 0 d x f ( y) y R f L f () ( x y) L( F d, ( )), ( ) d l x y f d x y l x R 0 x R y ( x y) x arccos R y x R y R xy dl, x y R JWIT 03

30 Average Transmission Power per User 30 A: OL Average Transmission Power Per User L L DU L P P P P L 0 D 0 P0 D DU / DA: OL (path-loss factor >) For given received SNR, a lower total transmission power is required in the DA case thans to the reduction of minimum access distance. D With =4, if P P L D Path-loss factor =4. JWIT 03

31 Sum apacity without SIT 3 0 For fixed K and D ( L such that D ) 0 Llog ( K / L) sum _ o 0 L K log e 0 D sum _ o O( L) D L. The number of users K=00. 0 Given the total transmission power, a higher capacity is achieved in the DA case. Gains increase as the number of BS antennas grows. JWIT 03

32 3 onclusions A comparative study on the uplin ergodic sum capacity with colocated and distributed BS antennas is presented by using largesystem analysis. A higher sum capacity is achieved in the DA case. Gains increase with the number of BS antennas L. Gains come from ) reduced minimum access distance of each user; and ) enhanced channel fluctuations which enable better multiuser diversity gains and waterfilling gains when SIT 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 thans to better power efficiency. Without cell cooperation: lower inter-cell interference with DA? JWIT 03

33 33 Than you! Any Questions? JWIT 03