Beamforming and Adaptive Antennae - Centre for Wireless ...

Tutorial ─ MIMO Communications with Applications to (B)3G and 4G Systems

Beamforming and Adaptive Antennae Markku Juntti and Juha Ylitalo

Contents 1. 2. 3. 3. 4. 5.

Introduction Beamforming Adaptive antennas Optimal antenna weights Adaptive antenna algorithms Summary References

MIMO Communications with Applications to (B)3G and 4G Systems ─ Beamforming & Adaptive Antennae

© J. Ylitalo & M. Juntti, University of Oulu, Dept. Electrical and Inform. Eng., Centre for Wireless Communications (CWC) 1

Beamforming: phased array

– small angular spread (macro cell) λ/2 ant. element separation --> correlated antennas --> Rxx ~diagonal

• "Fixed spatial filter"

0 Array Gain [dB]

• Beam steering = phasing the antenna array elements • Assumptions:

DOA = Direction of Arrival -5

DOA 1 = 0 deg. DOA 2 = 30 deg.

-10 -15 -20 -25 -30

-50 0 50 based on estimated DOA of desired Azimuth [deg] user – DOA tracking (slow vs. channel tracking) Butler Beams matrix 1-4 – fixed beams by e.g. Butler matrix feasible – interference suppressed by the beam pattern © J. Ylitalo & M. Juntti, University of Oulu, Dept. Electrical and MIMO Communications with Applications to (B)3G

–

and 4G Systems ─ Beamforming & Adaptive Antennae

Inform. Eng., Centre for Wireless Communications (CWC) 2

M=8

Beamforming: array response vector θ Uniform Linear Array : antenna M separated by (m-1)d from ref. antenna d= λ/2

d sinθ θ d

ant. M

Ref. antenna

• Array response vector: a(θ) = [1, e-j2πd sin(θ)/λ , e-j4πd sin(θ)/λ ... e-j2π(Μ−1)d sin(θ)/λ ]T = [1 e-jπ sin(θ) e-j2π sin(θ) ... e-jπ(Μ−1) sin(θ) ] when d=λ/2

T

; T denotes transpose



Beamforming: azimuth power spectrum θ

d sinθ ant. M

θ d

Ref. antenna

• Power spectrum as a function of azimuth angle θ : P(θ) = [a(θ)H x(θ)]2 = a(θ)H {x(θ)x(θ)H} a(θ)

P(θ) = a(θ)H Rxx a(θ) DOA resolution is limited by the array aperture: ∆θ ~ 96deg/M with ULA MIMO Communications with Applications to (B)3G and 4G Systems ─ Beamforming & Adaptive Antennae

H denotes here the complex conjugate transpose


Adaptive antennas " Optimal multi-channel filtering"

Ant 1 Ant 2

Ant M

Rxx

• Optimisation criteria - MMSE, ML, MV ...

• Optimal combining weights - typically in the form: α Rxx-1 h* ...

• Adaptive antenna algorithms

Criteria Algorithm Weights

- LMS, RLS, DMI, ...

Here we consider only optimal spatial combining algorithms: - Narrow-band assumption - Wide-band assumed only in 2D Rake receiver sense - Full-scale space-time equalisation will not be treated here MIMO Communications with Applications to (B)3G and 4G Systems ─ Beamforming & Adaptive Antennae


UE

Adaptive antenna algorithms: Introduction •

Two basic cases: - Beamforming with high correlated antennas - Diversity reception with low correlated antennas

•

Beamforming can utilise directional information

Diversity reception

w=Rxx

- optimum combining - each antenna weight has to be separately estimated - antenna weight proportional to SINR MIMO Communications with Applications to (B)3G and 4G Systems ─ Beamforming & Adaptive Antennae

Interfering UE

w=h*

- allows simple DoA based algorithms: only DOA needed to be estimated -optimal in Line-Of-Sight, AWGN case - DoA based algorithms apply also to transmission - allows also optimum combining algorithms

•

UEINT

Desired UE

Weight

-1 h*

Adaptation

+

© J. Ylitalo & M. Juntti, University of Oulu, Dept. Electrical and Inform. Eng., Centre for Wireless Communications (CWC) 6 Baseband processing

Optimisation criteria • Assumptions: - Signal and interference processes are uncorrelated --> different propagation paths - Signal and interference processes are stationary --> during estimation of weights - Signal and interference processes are additive --> linear radio channel

Performance of an adaptive algorithm depends on the statistical character of the desired and interfering signal in the temporal and spatial domain: - fading (temporal correlation) - correlation between antenna elements

"Optimum combining algorithms can suppress correlated interference at antenna array" MIMO Communications with Applications to (B)3G and 4G Systems ─ Beamforming & Adaptive Antennae

Idealised or perturbed propagation conditions?


Optimisation criteria, cont'd Optimisation of antenna combining weights based on • Maximum Signal-to-Interference-and-Noise criterion (SINR) • Least Mean Square criterion (LMS) --MMSE • Maximum Likelihood criterion (ML) • Minimum Variance criterion (MV) It is interesting to note that all these criteria lead to similar solution of optimal antenna array weight vector which can be described as:

wopt= α Rxx-1 h* in which α is a scalar scaling factor, wopt the optimal antenna weight vector Rxx-1 is the spatial correlation matrix and h represents the array response vector of the desired signal MIMO Communications with Applications to (B)3G and 4G Systems ─ Beamforming & Adaptive Antennae


MMSE criterion

Received signal x(t)= [x1(t) x2(t) … xM(t) ]T

- Widrow 1960

Ant 1 Ant 2

Ant M

Error signal: ε(t) = d(t) - w* x(t) Squared error: ε(t)2 = d(t)2 -2d(t)w*x(t) + w*x(t)x*(t)w

Criteria

Weight vector

Algorithm

w=[w1 … wM]T

Weights

Expected error value: E{ε(t)2} = d(t)2 -2w*rxd(t) + w*Rxxw

Σ -

Rxx = E { x x*} , is a MxM spatial correlation matrix

ε(t)

+

d(t)

rxd = E {d(t) x(t)}, is a Mx1 column vector (= h , ch.est.) MIMO Communications with Applications to (B)3G

d(t)2 =and signal power 4G Systems ─ Beamforming & Adaptive Antennae

error reference signal © J. Ylitalo & M. Juntti, University of Oulu, Dept. Electricalsignal and Inform. Eng., Centre for Wireless Communications (CWC) 9

MMSE ...

rxd

- selecting optimal w to minimise error: set gradient of E{ε(t)2} with respect to w to zero

Ant 1 Ant 2

Ant M

Rxx

∇w

{} = -2rxd(t) + 2Rxxw = 0

Thus optimal weight vector is obtained from:

Rxxwopt = rxd

and

Weight vector

Criteria Algorithm Weights

Σ

wopt = Rxx-1 rxd Above equation is known as Wiener-Hopf equation in matrix form. It is usually referred as optimum Wiener solution MIMO Communications with Applications to (B)3G and 4G Systems ─ Beamforming & Adaptive Antennae

w= Rxx-1 rxd

ε(t)

+

d(t)

error reference © J. Ylitalo & M. Juntti, Universitysignal of Oulu, Dept. Electrical andsignal Inform. Eng., Centre for Wireless Communications (CWC) 10

Optimal combining weights • MMSE (Wiener solution):

−1 * xx

wMMSE = R v

• Max SINR:

−1 * wSINR = α Rnn v

• Maximum Likelihood:

wML =

• Minimum

variance:

- Direction of desired signal known

S −1 * = R nn v * −1 1 + Sv Rnn v

1 −1 * R nn v * −1 v Rnnv

wMV

−1 Rnn 1 = * −1 1 Rnn1

Note:

S= signal power, v* = array response vector of the desired signal, Rnn= interference+noise covariance matrix, Rxx= total received here v = rxd signal (signal+interference+noise) covariance matrix, v=1University for of Oulu, Dept. Electrical and © J. Ylitalo & M. Juntti, MIMO Communications with Applications to (B)3G x(t) = s(t)v + n(t) and 4Gsignal Systemsweights ─ Beamforming & Adaptive Antennae Inform. Eng., Centre for Wireless Communications (CWC) 11 known in MV

Optimal combining weights Antennas

Linear matrix filter

Scalar processor sSINR

Rnn-1v*

sML , sMV 1/N

sMMSE S/(S+N)

• Notations used above:

x(t) = s(t)v + n(t) Rxx = E{x(t) x*(t)} Rnn = E{n(t) n*(t)} Rss = E{s(t) s*(t)} s(t) = s(t)v Rxx = Rss +Rnn MIMO Communications with Applications to (B)3G and 4G Systems ─ Beamforming & Adaptive Antennae

Note: n(t) includes both interference and AWGN: n(t)=I(t)+N0 v is the array response vector corresponding to desired signal direction © J. Ylitalo & M. Juntti, University of Oulu, Dept. Electrical and Inform. Eng., Centre for Wireless Communications (CWC) 12

Adaptive antenna algorithms • Adaptive antenna algorithms solve the optimal antenna weights for (rapidly) changing radio channel state • Different criteria (MMSE, max SINR, ML, MV) lead to the same solution • Task is to estimate Rnn and rxd and find a simple and robust (direct or iterative) way to invert Rnn • Rnn characteristics have an important role in the adaptation • Typical adaptive antenna algorithms:


wopt= α Rnn-1 rxd*

For more details about matrix inversion, see S. Haykin: "Adaptive filter theory", Prentice Hall

- LMS - DMI - RLS


Example: DMI algorithm • Direct matrix inversion

wopt= Rxx-1 rxd*

only estimates of Rnn and rxd are known:

1 K ˆ E{Rxx} = Rxx = ∑ x(k ) x * (k ) K k =1 1 K E{rxd } = rˆxd = ∑ x(k )d * (k ) K k =1

•

−1 wˆ opt = Rˆ nn rˆxd

Thus we get

if Rnn can be estimated (α =1) or if only Rxx can be estimated MIMO Communications with Applications to (B)3G and 4G Systems ─ Beamforming & Adaptive Antennae

−1 wˆ opt = Rˆ xx rˆxd


DMI algorithm • Example: GSM burst 58 bit Data

26 bit ( d ) Training sequence

K 1 E{Rxx } = Rˆ xx = ∑ x(k ) x * (k ) K k =1

58 bit Data

1 K E{rxd } = rˆxd = ∑ x(k )d * (k ) K k =1

• Procedure – calculate E{Rxx} over the whole burst (K=148) – calculate E{rxd} over the known symbols (K=26)

−1 wˆ opt = Rˆ xx rˆxd

( actually E{rxd} = E{h}= estimate of the impulse response)

•

E{Rxx} and E{rxd} are calculated for each burst

•

E{Rxx} and E{rxd} can be averaged over several bursts snr K +2− M E { } ≅ • If rxd is known and Rnn can be estimated: snropt K +1 => K > 3M (roughly) MIMO Communications with Applications to (B)3G and 4G Systems ─ Beamforming & Adaptive Antennae

© J. Ylitalo & M. Juntti, University of Oulu, Dept. Electrical and K=no of independent samples, M= no Inform. Eng., Centre for Wireless Communications (CWC) 15

antennas

of

Summary

• Simple beamforming (beampointing) is simple and robust and applies well to FDD systems • Adaptive antenna algorithms can be applied to interference suppression • Adaptive antenna algorithms/ optimum combining is required for good MIMO performance: ”spacetime equalisation”



References • •

Monzingo and Miller, Introduction to Adaptive Arrays”, Wiley, 1980. Winters, J. ”Optimum Combining in Digital Mobile Radio with Cochannel Interference”, Selected Areas in Communications, IEEE Journal on ,Volume: 2 , Issue: 4 , Jul 1984, Pages:528 539

•

J. C. Liberti. and T. S. Rappaport, Smart Antennas for Wireless Communications: IS-95 and Third Generation CDMA Applications, Prentice Hall, Upper Saddle River, NJ, 1999.

•

Ylitalo, J.; Tiirola, E.; ” Performance evaluation of different antenna array approaches for 3G CDMA uplink”, Vehicular Technology Conference Proceedings, 2000. VTC 2000-Spring Tokyo. 2000 IEEE 51st ,Volume: 2 , 15-18 May 2000, Pages: 883 - 887 vol.2 MIMO Communications with Applications to (B)3G and 4G Systems ─ Beamforming & Adaptive Antennae
