On the apacity of Distributed Antenna Systems Lin Dai ity University of Hong Kong JWIT 03
ellular Networs () Base Station (BS) Growing demand for high data rate Multiple antennas at the BS side JWIT 03
ellular Networs () 3 o-located BS antennas Distributed BS antennas Implementation cost Lower Sum rate Higher? JWIT 03
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
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
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
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 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
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
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
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
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
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
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
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
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
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
8 Part II. Uplin Ergodic Sum apacity JWIT 03
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
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
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
Sum apacity without SIT () 75 70 65 60 55 50 45 40 35 A DA with B [ e,..., e ] * * l l K A Analytical (Eq. (3, 34)) Simulation DA Analytical (Eq. (3, 40)) Simulation 30 0 5 0 5 30 35 40 45 50 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.
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
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
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
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
7 Part III. Average Transmission Power per User JWIT 03
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?
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
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 0 0 5 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 0 0 5. Path-loss factor =4. JWIT 03
Sum apacity without SIT 3 0 For fixed K and D ( 0 0 5 L such that D ) 0 Llog ( K / L) sum _ o 0 L K log e 0 D sum _ o O( L) D 0 0 5 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
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 Than you! Any Questions? JWIT 03