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Smart Antenna: Principle, Design, and Application

Outline

? Introduction ? Basic concept of smart antenna ? Optimum criteria, adaptive algorithm, and system implementation for smart antenna ? Application

J.-A. Tsai, NTU 2003

15-2

What is smart antenna?

A smart antenna system combines multiple standard antenna elements with a signal-processing capability to optimize its radiation and/or reception pattern automatically in response to the signal environment. J.-A. Tsai, NTU 2003 15-3

Basic Principle of Smart Antenna

JAMMER Intercell Interference

Base Station

J.-A. Tsai, NTU 2003

15-4

Smart Antenna(SA)[3]

?

Two types of smart antennas can be identified ) Switched-beam ) Adaptive array (Adaptive beamforming)

J.-A. Tsai, NTU 2003

?ê??¨?·?:I

EEE Magaz ine

15-5

Smart Antenna

?

Performance comparison

Switched-beam

J.-A. Tsai, NTU 2003

?ê??¨?·?:I

EEEMagaz ine

15-6

Application of SA to Mobile Radio Environment(1/2)

Base Station

Downlink

scatters

Uplink

Mobile Station

J.-A. Tsai, NTU 2003

15-7

Application of Smart Antenna to Mobile Radio Environment (2/2)

Smart Antenna is primarily used for Interference Suppression in a mobile radio (cellular) environment.

J.-A. Tsai, NTU 2003

15-8

Benefits of Smart Antennas
Intercell Interference

Multipath
Base Station

Multipath

Uplink JAMMER

Downlink Mobile

Signal Fading

JAMMER

) Co-channel (jamming)and adjacent channel interference reduction ) Multiple access interference reduction for capacity improvement ) Robustness against multipath, fading, and noise to improve coverage and range ) Reduced power consumption for the handset ) Enhanced location estimates J.-A. Tsai, NTU 2003 15-9

System Model

Uniform linear array
Array Broadside

? i 2 d Reference Element 1

N

d

sin

?

? a(θ ) = ?1 e ? ?
J.-A. Tsai, NTU 2003

? d ? ? j?2π sinθ ? ? λ ?

... e

? d ? ? j?2π ( N ?1)sinθ ? ? λ ?

? ? ? ?

Array response vector

Pl Inci an de e W nt av e
T

W Pl a av n e eF ro nt

15-10

System Model (3)

x1 (t )

w1* (t )
* w2 (t )

x 2 (t )

Beamformer output y (t )
120 150

90

1 .5 1

60 30

interferer

0 .5

x M (t )
K

* wM (t )

180

0

x (t ) = ∑ si (t ) a (θ i ) + n (t )
i =1

210 240 300

330

desired signal

270

y (t ) = w H (t ) x (t )
J.-A. Tsai, NTU 2003 15-11

Optimization Criterion[4]

Pilot-Based Beamforming ? Maximum likelihood (ML) ? Maximum signal-to-noise ratio (known as beam-steering) ? Maximum signal-to-interference plus noise ratio (MSINR) ? Minimum mean square error (MMSE) ? Minimum variance distortionless response (MVDR)

J.-A. Tsai, NTU 2003

15-12

Optimization Criterion

Direction Finding (DF) based Beamforming ? Traditional DF techniques
)MUSIC (Multiple Signal Classification) )ESPRIT ( Estimation of Subspace Parameters via Rotational Invariance Tech. ) )WSF(Weighted Subspace Fitting)

? Requires the number of signals to be lower than the number of antenna elements

J.-A. Tsai, NTU 2003

15-13

MMSE Beamforming

(i ) = R xx r xd ? MMSE (Wiener) Solution: wMSE

?1

r xd = E [ x (t )d (t ) ]

d (t) is the desired signal

R xx is the Received Signal Covariance Matrix

? Requires pilot symbols or training sequence ? MMSE with the help of pilot symbols leads to Pilot Symbol Assisted (PSA) beamforming ? Popular PSA techniques
) Least Mean Squared (LMS) adaptive algorithm ) Direct Matrix Inversion (DMI) ) Recursive Least Square (RLS) adaptive algorithm
J.-A. Tsai, NTU 2003 15-14

Sample Matrix Inversion (SMI) algorithm

Estimate of the received signal covariance matrix:
? = 1 R xx N
H x n x ( ) ( n) ∑ n =0 N ?1

SMI also known as DMI (Direct Matrix Inversion):
? ( n ) = R ?1 ( n ? 1) ? R xx xx
?1

R xx ( n ? 1) x ( n ) x H ( n ) R xx ( n ? 1)
?1 ?1

1 + x H ( n ) R xx ( n ? 1) x ( n )
?1

J.-A. Tsai, NTU 2003

15-15

SMI Beam-forming
K Asynchronous Users

Transmitter

Transmitter

σ

σ

θK
2

σ
φ2

σ σ: angle
spread

φ3
3

R

θ1
φ1 1

R=0.5λ
J.-A. Tsai, NTU 2003

φ4

4

Receiver 4-element uniform circular array

15-16

SMI Beam Pattern

J.-A. Tsai, NTU 2003

15-17

SMI Beam Pattern

J.-A. Tsai, NTU 2003

15-18

Least Mean Square (LMS) algorithm[1]

1.Beamforming Output:
H ? y ( n) = w ( n) x( n)

2. Estimation error:

e( n ) = d ( n ) ? y ( n )
3. Weight adaptation:

? (n + 1) = w ? ( n ) + ? x( n)e* ( n) w
J.-A. Tsai, NTU 2003 15-19

MSNR Beamforming

? If the Interference is “white”, MSNR beamforming is optimum ? Often termed as the conventional beamforming
(i ) MSNR Weight: wSNR = ζ a (θ i )

? The optimal weight for MSNR is a scalar multiple of the Array Response Vector ? The weight vector tries to “co-phase” the signals at the output of the array

J.-A. Tsai, NTU 2003

15-20

MSNR based Eigen-Beamforming

? The optimal weight for MSNR is the principal eigenvector of the following Simple Eigenvalue problem (SE)
R ss wSNR = λ wSNR R ss is the desired signal covariance matrix

? Alternative option (since the desired signal is not available)
R xx wSNR = λ ′ wSNR

R xx is the received signal covariance matrix
J.-A. Tsai, NTU 2003 15-21

Solution to the SE

? There are different algorithms to solve the Simple Eigenvalue problem
)Power Method )Lagrange Multiplier Method

J.-A. Tsai, NTU 2003

15-22

Power Method

? The most common method to solve the SE ? Power method can be described by the following iterations:
w(k + 1) = R ss (k ) w( k ) w(k + 1) w(k + 1) = w(k + 1)
complexity

O( N 2 + N )

? Metric of computational complexity O(η N ) :η times N Complex Multiplications

J.-A. Tsai, NTU 2003

15-23

Lagrange Multiplier Method

? Treats the SE a constrained optimization problem

? Maximize

w H R ss w subject to the constraint

wH w = 1

? Functional based on Lagrange Multiplier:

J ( w ) = w H R ss w + γ (1 ? w H w )
? Iteration based on steepest ascent:

w( k + 1) = w( k ) +

1 ? ?(k ) 2
J ( w)
Computational Complexity

? : Step-size
? : Gradient vector of
2 O (2 N + 4.5 N ) J.-A. Tsai, NTU 2003

15-24

MSINR Beamforming[2]

? If the Interference is not “white”, MSINR beamforming is optimum ? Often termed as the optimum beamforming
(i ) = ζ R uu a (θ i ) MSINR Weight: wSNR ?1

R uu : is the interference & noise covariance matrix
? The Interference and Noise covariance matrix fine tunes the weight according to the spatial distribution of the interference and noise
J.-A. Tsai, NTU 2003 15-25

MSINR based Eigen-Beamforming

? The optimal weight for MSINR beamforming is the principal eigenvector of the following Generalized Eigenvalue problem (GE)

R ss wSINR = λ R uu wSINR
R ss is the desired signal covariance matrix

R uu is the interference & noise covariance matrix

Alternate approach

R xx wSINR = λ R uu wSINR
R xx is the received signal covariance matrix
J.-A. Tsai, NTU 2003 15-26

Algorithms to solve GE

? Generalized power method is the most common method to solve the GE

J.-A. Tsai, NTU 2003

15-27

Generalized Power Method to solve GE

? Generalized Power Method reduces the GE to a Simple Eigenvalue problem
R uu = R uu Ruu
?*/ 2 ?1/ 2
*/ 2 1/ 2

R uu w = ?
1/ 2

Ruu R ss Ruu Ruu w = λ Ruu w
1/ 2 1/ 2

R uu R ss R uu = ?

?*/ 2

?1/ 2

? ? = λ?

? Power Method can be employed to solve the SE

J.-A. Tsai, NTU 2003

15-28

Application of Smart Antenna(CDMA)[2]

? Conventional or 1-D RAKE receiver
- Diversity combining of temporally resolvable multipath components

? 2-D RAKE receiver
- Independent space-time processing
- Spatial optimum combining followed by temporal diversity combining 1-D RAKE Receiver 2-D RAKE Receiver
finger #1 Element #1

τ1
c ( t ? τ1 )
?


Element #2

finger #2

Beamformer w1* Beamformer w2*

finger #1

∫ RAKE Combiner
c? ( t ? τ 1 ) finger #2

RAKE combiner

τ2
c? ( t ? τ 2 )



decision


c? ( t ? τ 2 )

decision

Element #N

finger #L

τL


c? ( t ? τ L )

Beamformer wN*

finger #L


c? ( t ? τ L )

J.-A. Tsai, NTU 2003

15-29

Summary
? Smart antenna (beam-forming) can be used to suppress interference, thus enhance system capacity. ? Smart antenna (beam-forming) can be used to mitigate multipath channel fading, thus enhance the link quality and extend coverage. ? Smart antenna can be used to enhance location estimation for E911 service ? Smart antenna can be used to reduce power consumption for handheld unit. ?. Nothing comes free, cost remains significant issues for the implementation of smart antenna
J.-A. Tsai, NTU 2003 15-30

Reference
[1] S. Haykin” Adaptive Filter Theory”, Prentice Hall Publishing Company, 1996 [2] A.F. Naguib,” Adaptive Antenna for CDMA Wireless Network”, PhD Dissertation. Stanford University. [3] Winters, J.H.; Gans, M.J “The range increase of adaptive versus phased arrays in mobile radio systems.; Vehicular Technology, IEEE Transactions on , Volume: 48 Issue: 2 , Mar 1999 [4] Buehrer, R.M. and J.-A, Tsai “Intelligent Antenna –Uplink Wireless Communications” , Bell Lab Technical Journal, 1999 (99’ Best Paper Award)

J.-A. Tsai, NTU 2003

15-31

Home Work(1)
? MIMO Rayleigh Channel Capacity (Foschini and Gans[1])

? ? ? SNR ? ? C = log 2 det ? I nR + ? ?H ?H ? ? nT ? ? ?

? Capacity is treated as a random variable
2 ? C = log 2 1 + SNR ? H ? ? ?

This is the Shannon Capacity

Where SNR is signal-to-noise ratio (nT , nR) ( # of Tx. Ant., # of Rx. Ant.) H – Channel matrix of fade coefficients (Each element is a complex Gaussian random variable) J.-A. Tsai, NTU 2003 15-32

Home Work(2)
Space-Time Trellis Code
– Similar to Multiple Trellis-Coded Modulation (MTCM) – Maximum Likelihood Sequence Decoder – Coding & Diversity Gain

Space-Time Layered Code(BLAST)
– Coding and Decoding Performed in a Layer-by-Layer Fashion(V,C,D) – Need Channel Estimation Beamforming Algorithm (Nulling) – Prone to Error Propagation – Diversity Gain

Space-Time Block Code
– Space-Time Signal Processing (Alamouti Code) – Diversity Gain
J.-A. Tsai, NTU 2003 15-33

Home Work (3)
STB Encoder
S = [s1 s 2 ]

h1

Receiver ML
Y

t0 [s1 s 2 ] → ? s1 ? ? s2

t1 * ? ? s2 ? s1* ?

h2

? y1 ? ? h1 ? y1 = s1 h1 + s 2 h2 + n1 ? ? *? = ? * ? * * ? y 2 ? ? h2 ? y 2 = ? s 2 h1 + s1 h2 + n 2 Η Η = h1 + h2
H

(

2

2



?
2

Η

h2 ? ? h1* ? ?

? s1 ? ? n1 ? ? s ? + ?n* ? ? 2? ? 2? ? n1 ? ?n* ? ? 2?
15-34

J.-A. Tsai, NTU 2003

2 ? ? s y h1 + h2 ? 1? H ? 1? = Η ? *? = ? ?s ? 0 ? ?2 ? ? y2 ? ? ?

h1

2

? 2? + h2 ? ? 0

? s1 ? H + Η ?s ? ? 2?

Home Work (4)

Pilot-Based Beamforming ? Maximum likelihood (ML) ? Maximum signal-to-noise ratio (known as beam-steering) ? Maximum signal-to-interference plus noise ratio (MSINR) ? Minimum mean square error (MMSE) ? Minimum variance distortionless response (MVDR)

J.-A. Tsai, NTU 2003

15-35

Home Work (5)

(i ) = R xx r xd ? MMSE (Wiener) Solution: wMSE

?1

r xd = E [ x (t )d (t ) ]

d (t) is the desired signal

R xx is the Received Signal Covariance Matrix

? Requires pilot symbols or training sequence ? MMSE with the help of pilot symbols leads to Pilot Symbol Assisted (PSA) beamforming ? Popular PSA techniques
) Least Mean Squared (LMS) adaptive algorithm ) Direct Matrix Inversion (DMI) ) Recursive Least Square (RLS) adaptive algorithm
J.-A. Tsai, NTU 2003 15-36


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