Overview of MIMO Radio Channels

Transcription

1 Helsinki University of Tecnology S Postgraduate Course in Radio Communications Overview of MIMO Radio Cannels 18, May 2004 Suiyan Geng

2 Outline I. Introduction II. III. IV. Caracteristics of MIMO cannels MIMO cannel capacity Environments and simulation metods Cannel models Summary References V. Homework Page 2

3 I. Introduction (1/3) Multiple-Input Multiple-Output (MIMO) System: Transmitting (TX) and receiving (RX) ends equipped wit multiple antenna elements. Radio cannel: propagation medium between te TX and RX antennas. Page 3

4 I. Introduction (2/3) MIMO is critical tecnology for current and fortcoming cellular systems. Due to te potentials: Page 4

5 I. Introduction (3/3) MIMO cannel is two-dimensional (spatial and temporal), tey are often described independently. Development of MIMO cannel models are based on propagation environment, i.e., macro-, micro- or pico cell. Te simulation metods include statistical, measurement-based and ray-tracing. MIMO cannel is various and complex, we ll concentrate mainly on: Introduce te basic MIMO cannel concepts, try to compare tem wit conventional (SISO) cannels as possible. Investigate some empirical cannel models and teir applications. Page 5

6 II. MIMO cannel transfer function MIMO cannel transfer function H is a complex matrix. For narrowband of M and N antenna elements at TX and RX expressed as H = M M L M 1N L M M 1 L L MN t t Were is complex coefficient between i / j TX/RX antennas ij ij Cannel amplitude gains are usually Rayleig distributed variables. Page 6

7 II. Capacity of te radio cannel Te capacity of a communication system (Sannon s formula) as C = W log 2 1+ ( ) SNR In te ig capacity links (e.g. WLANs), limited by two problems Hig patloss (include in SNR) Interference of multipats (include in W) Te use of MIMO systems could resolve bot above-mentioned problems Provides greater gain. Cancel interference wit use of array processing tecniques. Page 7

8 II. MIMO cannel capacity Several cannel parameters influence on MIMO capacity. Capacity is lower wit increasing Ricean factor Lower capacity can be caused by iger cannel fading correlation Hig XPD enances te capacity Increased MIMO cannel capacity Page 8

9 II. MIMO cannel capacity Two capacity forms are often used to describe different properties of MIMO cannel. Ergodic (mean) capacity: 1. Maximal average information rate over te distribution of te cannel matrix elements, so it is significant wen every cannel used. 2. Used as a measure for te spectral efficiency, more representative for average trougput acievable on te cannel. Outage capacity: 1. Quantifies level of performance tat is guaranteed wit a certain level of reliability, e.g., define te probability tat capacity is less tan outage capacity as q, information rate guaranteed for 1-q cannel realizations. 2. Describe diversity advantage of te cannel. Page 9

10 II. MIMO cannel caracteristics Recall te conventional (SISO) cannel impulse response (IR) a N jφi () t ( t, τ ) a ( t) e δ ( τ τ ) jφ () t () t e = i=1 i i were is complex amplitude of te multipat components. i Cannel is described as time-variant. WSSUS assumption is often made for deriving te cannel parameters. No information about te angle-of-arrival (AOA) of eac multipat component. i Page 10

11 II. Caracteristics of MIMO cannel MIMO cannel IR can be expressed as N r i t, τ = ai t e a θi δ τ τ i r a θ i ( ) ( ) jφ () t ( ) ( ) ( ) i=1 were is te spatial response vector. Usually, it is a function of array geometry and AOA of te received signal. MIMO cannel IR is a summation of several multipat components, eac as its own amplitude, pase and AOA. In te model, information on space and time are described independently. Page 11

12 II. MIMO cannel classification MIMO cannel is classified as Low-rank: S < 1 t and S (narrow-band) B < ϕ ϕ 3 db 1 Hig-rank: St or Sϕ ϕ3db (wide-band ) B S and S are delay spread and angle spread, is receiver bandwidt, t ϕ 3dB ϕ r r denotes 3dB-beamwidt of te antenna array in azimut. For simplicity, directional dispersion is restricted only on azimut direction. B r Page 12

13 II. Cannel estimation metods Statistical metod Temporal and spatial properties are often generated independently, and AOA in te mobile station is uniformly distributed on π,π. Measurement-based [ ] Measurement is used to generate te time-variant directional distribution of cannel IRs τ,t,θ. ( ) Ray tracing metod Based on te geometric teory and reflection, diffraction and scattering models, owever, ig computational burden makes it difficult to use. Page 13

14 II. Cannel environments Macrocell Mobile station perspective Base station perspective Scatterers surrounding MS are about te same/iger eigt, implies arriving signal from all directions, i.e., AOA is uniformly distributed π,π. [ ] BS is deployed iger tan te surrounding scatterings, multipat components are restricted to a smaller angular region θ BW. Page 14

15 II. Cannel environments Microcell BS antenna is mounted at same eigt as surrounding objects, scattering process also appens in vicinity of BS. Implies AOA is larger tan in Macrocell environments. Large angle spreads and antenna element spacings result in lower signal correlation, provide an increased diversity gain. Picocell A property of many indoor cannels. Te most complicated environments. Experimental measurements sow tat te scaterers appear in cluster, wic means te multipat components arriving in group. Page 15

16 II. Statistical models Lee s model (Macrocell) Te discrete AOAs at mobile θ i R D sin 2π i N Te correlation of te signals between any two elements of te array ρ 1 0 cos N N 1 i= 0 ( d, θ, R, D) = exp[ j2πd ( θ + θ )] (scatterers evenly spaced on a circular ring) Level of correlation will determine performance of spatial diversity metods. 0 i Page 16

17 II. Statistical models Geometrically based elliptical model (Microcell) Scaterers are uniformly elliptically distributed, BS and mobile are te foci. A nice attribute is multipat signals arrive witin an absolute delay τ m, ignoring te larger delays (experience greater patloss). τ m Coice of will determine bot te delay spread and angle spread. Page 17

18 II. Statistical models Sale-Valenzuela s mode (Indoor) Time and angle are statistically independent. () t = α δ ( t τ ) i= 0 j= 0 ij T i () t = α δ ( θ Θ ω ) i= 0 j= 0 i, j correspond clusters and rays witin a cluster. are Rayleig distributed wit mean square value described ij by a double-exponential decay Θ is te mean angle, uniformly distributed [ π,π ]. ω is ray angle witin a i ij cluster modeled as a Laplacian distributed wit zero mean and standard deviation. i ij ij α ij ( Γ) ( τ γ ) 2 2 α ij = α 00 exp Ti exp σ f ( ω) 1 2ω = exp 2σ σ ij Page 18

19 II. Measurement-based models Extended Tapped- Delay- Line Model A wideband extension of traditional statistical tapped-delay-line model and includes AOA information W ( τ, t, θ ) a w ( t ) δ ( τ τ ) δ ( θ θ ) = w=1 W taps, eac wit time delay, complex amplitude and AOA. Te joint density functions of te model parameters sould be determined from measurements. w w Page 19

20 II. Measurement-based models Ricean K-factor Model expression: K ( antenna _ ) ( dis tan ce _ d ) In SISO, a ig K- factor (power ratio of LOS/ mean NLOS components) is desirable because te smaller fade margin needs to be allocated. In MIMO, ig-k cannel sow a lower MIMO capacity. Because iger K, more dominant H LOS, its effect is to drive up antenna correlation and overall effective rank down terefore sow low useable spatial degree of freedom. E.g., a (4,4) MIMO capacity wit K = 0 is almost always iger tan wit K = 10. From a network deployment perspective, use of MIMO does not/does substantially improve link trougput near BS/ far away from BS. Page 20

21 III. Summary Pysical layer is te bottleneck of wireless communication systems. MIMO system is being more and more interesting due to te potentials in wic. Te performance of radio systems igly depend on te accurate cannel information, wic provides te reliable estimates for te system design. It is important to know te knowledge of MIMO cannel. Basic MIMO cannel concepts, te empirical cannel models and teir applications are introduced and analysed. Page 21

22 IV. References [1] J. Ful et al., Unified cannel model for mobile radio systems wit smart antennas, IEE Proc. Vol. 145, No. 1 February [2] Ricard B. Ertel and Psulo Cardieri, Overview of spatial cannel models for antenna array communication systems, IEEE Personal Communications, Feb., [3] David Gesbert et al., From teory to practice: an overview of MIMO Space-Time coded wireless systems, IEEE Jounal on delected areas in communications, Vol. 21, No. 3, April [4] Arogyaswami Paulraj, Roit Nabar and Dananjay Gore, Introduction to Space-Time wireless communications, Cameridge University Press. Page 22

23 Homework 1. In ig capacity environments (e.g, WLANs), wat factors limit te capacity of communication system? Wy? wat cannel parameters influence on MIMO cannel capacity? Try to explain (more detailed explanation is preferred). Page 23