Ayman Elnashar

Supervisors:

Prof. Dr. Hamdy El-Mikati Prof. Dr. Said El-Noubi

ECMS (MobiNil)

Mansoura University Alexandria University

30 April 2005

Agenda

Introduction Numerically Robust Multiuser Receivers Quadratically Constrained Robust MUD Robust Adaptive Beamforming Thesis Contributions & Publications

MAP GSM Core

384kpbs-2Mbps

UMTS TD-SCDMA 3GPP CWTS

Up to 14 Mbps/cell

HSDPA

136+

ANSI-136

136 HS IS-95B 64 kbps

CDMA200 1x 307 kbps

EDGE

GPRS i-mode DoCoMo

115 kbps

38

4 kb

ps

GSM TDMA IS-54

CdmaOne IS-95A

PDC

Cellular Standards Evolution Introduction

1980

1995

1999

2001

2002

2002 2003 UWC-136

Japan Europe Americas

TACS NMT/TACS/Other AMPS Traffic is Almost Voice (1st G)

Data 9.6-14.4 Kbps (2nd G)

2004

2005

2006

(2.5 G)

CDMA20001x-EV-DO CDMA20001x-EV-DV

CDMA20003x

ANSI-41 Core

3GPP2 1.4Mpbs 2.4Mbps

3G &

Bey

ond

Multiple Access Techniques

Traffic channels: different users are assigned unique code and transmitted over the entire frequency band, for example, WCDMA and CDMA2000

Traffic channels: different frequency bands are allocated to different users,for example, AMPS and TACS

Traffic channels: different time slots are allocated to different users, for example, DAMPS and GSM

Power

Power

Power

FDMA

TDMA

FDD-CDMA Introduction

TDD-CDMA

Traffic channels: different users are assigned unique code and time slot, for example, TD-SCDMA

Codes

DS/CDMA Systems

In CDMA, users are multiplexed by distinct codes rather than by orthogonal frequency bands, as in FDMA, or by orthogonal time slots, as in TDMA

Introduction

Motivations Limitations

Multiple access interference (MAI) Capacity is interference-limited instead of BW-limited Near/Far Effect: Received power from users near to BS is higher than that of far away users.

We Need tight power control

Admitting asynchronous multiple access

Robustness to frequency selective fading

Multipath combining

Efficient bandwidth utilization

DS-CDMA System Model Introduction

, ,0

( ) ( )jm

j j j m j j mm

t a tα ϕ δ=

= −∑g

( ) ( ) ( )j j jm

n m n m∞

=−∞

= −∑h c .g

( ) ( ). ( )j j j jl

n l n lL τ∞

=−∞

= − −∑u S h

1( ) ( ) ( )

K

jj

n n n=

= +∑x u w Chip rate sampling synchronized to user j

1C

( )tϕ

Channel 1

Channel k Channel noise

Chip Pulse Shaping Filter

Chip Pulse Shaping Filter

Chip Matched Filter

1( )nS

( )j nS

jC

( )cT tϕ −

( )w n

( )ny FIR Linear Filter f

1u

ju

( )nx

Multipath Channel User 1

Data

User k

Data

Signature Sequence

Receiver Filter

Tx

Rx

0 1 2 3 4 5 6 7 8 9 10-0.2

0

0.2

0.4

0.6

0.8

1

1.2

time t (channel length = 10chips)

root

-rai

sed

cosi

ne c

hip

puls

e

Raised Cosine Pulse Shaping Filter

Single user Detection

MF user 1

MF user k

Sync 1 11

Sync k

Sync j 11

MF Bank

Hard

Decision MF user j

( )x n

1y

ˆ jy

ˆky

( )j tc

0

1 (.)bT

bT ∫

1y

jy

ky

Received Signal

Introduction

Multiuser Detection

Multiuser detection considers signals from all users which lead us to joint detection Reduces multiple access interference and hence

leads to capacity increase Alleviates the near/far problem Power Control can be used but not necessary

MUD can be implemented in the base station (BS) or

mobile station (MS), or both

Transmission for the Downlink MS is synchronous and equal-power MUD algorithm is simpler for synchronous CDMA

In case of Uplink the Transmission is Asynchronous

which is more complex and need robust algorithms

Introduction

MUD Techniques

Multiuser Receivers

Optimal MLSE Suboptimal

Linear

Zero- Forcing MMSE

Direct MMSE

Adaptive MMSE

LMS Algorithms

RLS Algorithms DD-MMSE

Blind MMSE

MOE Approach

CMA Approach

Subspace Approach

Polynomial Expansion

Non-linear

Multistage Decision -feedback

Successive interference cancellation

Neural Network

Introduction

Linear Multiuser Receivers

The linear detector output is a linear combination of the received chip sampled signals:

( ) ( ) ( )Hn n n=y f x

{ }( )1 1ˆ ( ) sgn Re ( )n n=s y

{ } { }22( ) ( )H HE n E n= = xxy f x f R f

{ }( ) ( ) ( )Hxx n E n n=R x x

Introduction

Linear receivers are of great significance due to ease of practical implementation

In BPSK the bit decision is made according to:

The detector output energy is given by:

The received signal autocorrelation matrix is given by:

Agenda

Introduction Numerically Robust Multiuser Detection Quadratically Constraint Robust MUD Robust Adaptive Beamforming Thesis Contributions & Publications

IQRD-RLS Algorithm Numerically Robust MUD

• The QR decomposition transforms the RLS problem into a problem that uses only transformed data values by Cholesky factorization of the least-squares data matrix

• This algorithm exhibits a high degree of parallelism, and can be mapped to triangular systolic arrays for efficient parallel implementation.

• Unfortunately, the QRD-RLS algorithm suffers from major drawback, namely, back-substitution which is a costly operation to be performed in array structure

The IQRD method is the promising one due to:

1. Pipelined implementation on VLSI

2. Good numerical stability 3. No back-substitution.

RLS Algorithm QRD-RLS Algorithm

IQR

D-R

LS

In the conventional RLS algorithm, the calculation of the Kalman gain requires matrix inversion of the autocovariance matrix of the received signal. If the data matrix is in ill-conditioned, the conventional RLS algorithm will rapidly become impossible.

IQRD-RLS Algorithm ( ) ( )H

xx n n=R R R ( 1) ( )( )H n nn

λ

− −=

R xaQR Decomposition ( 1)

( )( )

( )0

HH

HT

nn

nn

λ

−− −

=

RR

Pj

( ) 0( )

1 ( )n

nb n

=

aPIQRD Updating

1

Systolic Array Implementation Internal Cell

( 1)iij−

ix

ix ( )iij

( )ia n ( )ia n

( ) ( )iP n ( ) ( )iP n

Boundary Cell

( 1) ( )ib n−

( ) ( )ib n

( )ia n( ) ( )iP n

A rotation matrix , which successively annihilates the elements of intermediate vector against into a related Kalman gain value using a sequence of Givens rotations.

( )nP( )na ( 1)H n λ− −R ( )b n

Numerically Robust MUD

Received vector

Detector Parameters

0T

• The MOE linear detector can be obtained by minimizing the output energy of the receiver subject to certain number of constraints.

• The Closed-form solution of the above constrained optimization problem can be obtained using Lagrange method as follows:

Minimum Output Energy

( ) 11 11 1 1

Hopt xx xx

−− −=f R C C R C g

1 =C f gUnder constraints min Hxxf

f R fDetector vector

Covariance matrix

Channel vector

Signature vector matrix

Numerically Robust MUD

MOE Implementation Using IQRD-RLS

max/ min max/ min1max ( ) ( )H H n n

=gf R R f max/ min 1 1( )nβ=fΔ υ

( ) ( 1) ( ) ( )Hn n n nλ= − +Ψ Ψ d d1

1

( 1) ( )( )1 ( ) ( 1 ( )H

n nnn n n

λ

λ

−

−

−=

− −

Π πdπ Π )π

11 max/ min 1

max ( )H n−

== =

gυ g g Π g

{ } 11 1

1 1 1( ) ( ) ( ) ( )H H Hf n n n n−− −

= R R C C R R C g1

1( ) ( ) ( )Hn n n−

= Δ R R C

1( ) ( )Hn n=Π C Δ 1( ) ( ) ( )n n n−=fΔ Π g 1( ) ( 1) ( ) ( )Hn n n nλ−= − −Δ Δ j π 1( ) ( )Hn n=π C j

1( ) ( 1) ( ) ( )Hn n n nλ−= − −Π Π π π2 1 1

1 11

( 1) ( ) ( ) ( 1)( ) ( 1)1 ( ) ( 1) ( )

H

Hn n n nn n

n n nλλ

λ

− −− −

−

− −= − +

− −Π π π ΠΠ Π

π Π π

Detector Estimation

Channel Estimation

Any orthogonal subspace tracking algorithm can be employed for tracking the principle component of the.

• orthogonal projection approximation subspace tracking (OPASTd)

• normalized orthogonal OJA (NOOJA).

Subspace Tracking

Numerically Robust MUD

Subspace Tracking (new)

( ) 111 11

max H Hxx

−−

=gg C R C g

1( , ) ( 1) ( ) ( 1) ( 1)(1 ( 1) ( 1))2

H Hn n n n n n nζ ζ= − − + − − − −Ψ g g Π g g g

Cost Function

( ) ( 1) ( , )n n µ ζ= − − ∇gg gΨ g

Channel Update

21( , ) ( , ) 2 ( 1) ( 1) ( ) ( ) ( 1) ( ) ( ) ( )H H H

n n n n n n n n n nζ ζ µ µ−= + − − ∑ − − ∑ ∑g g gΨ g Ψ g g Π Π

Step-Size Estimation

( 1) ( ) ( )( )

( ) ( ) ( )

H

opt H

n n nn

n n nα

µη

− ∑=∑ ∑ +

g

g g

gΠΠ

Optimum Step-Size

2 ( ) 2 ( )a n b n cζ ζ− + ( 1)opta nµ= −

1 ( 1) ( 1) ( ) ( 1)Hoptb n n n nµ= + − − −gΠ g

2( 1) ( 1) ( ) ( 1) 2 ( 1) ( ) ( 1)H Hoptc n n n n n n nµ= − − − + − −gΠ g g Π g

2

( ) b b acna

ζ − ± −=

Lagrange Multiplier

( ) ( ) ( 1) ( ) ( 1)n n n n nζ∑ = − − −g Π g gGradient Vector

Numerically Robust MUD

Channel Vector Estimation Techniques

max/ min 1 1( )nβ=fΔ υ( ) 111 11 1

max maxH H Hxx xx

−−

= ==

g gf R f g C R C gMax/min Approach

1

1 1 1 1( ) ( ) .H Hxxn n γ−= −φ C R C C C ( ) ( ) ( )IMOE n n n=fΔ g Improved Cost

2( ) ( )fxx xx Nn n ασ= −R R I 1

1 11min ( )H H

xx−

==

gg g C R C g ( ) ( ) ( )MMOE n n n=fΔ gModified Cost

11 1

ˆ1 1

ˆ ˆˆ minˆ ˆ

H Hxx

H H

−

=g

g C R C ggg C C g

ˆ( ) ( ) ( )Capon n n n=fΔ gCapon Method

21 11

min ( )H Hxx−

==

gg g C R C g ( ) ( ) ( )POR n n n=fΔ g Power Method (POR)

{ }{ }11max min . . . .H H H

xxf f s t f s t f f ρ=

= ≤fg

R C g ( ) 1max/ min 1 max/ min

ˆxx Iν −= +f R C g

New Robust Multiuser detection technique

Numerically Robust MUD

Simulation Results (1)

0 100 200 300 400 500 600 700 800 900 10001

2

3

4

5

6

7

8

9

Iteration (n)

Out

put S

INR

(dB

)

MOE-IQRD w. Optimal channelMOE-IQRD w. Lagrange (MC)MOE-IQRD w. NOOja (PC)MOE-IQRD w. Lagrange (PC)MOE-IQRD w. OPASTd (PC)

SINR Comparison of Subspace Tracking Algorithms

Numerically Robust MUD

Simulation Results (2)

0 100 200 300 400 500 600 700 800 900 10000

1

2

3

4

5

6

7

8

9

10

snapshot index

Out

put S

INR

(dB

)

MOE-RLSMOE-RLS w. VLMOE-IQRD w. max/min methodMOE-IQRD w. Improved cost functionMOE-IQRD w. Modified cost functionMOE-IQRD w. Capon methodMOE-IQRD w. POR methodMOE-IQRD w. max/min and VL

Comparison between Output SINR for MOE-IQRD based detectors

Numerically Robust MUD

Complexity Analysis

3371 MOE-IQRD w. max/min and VL

2556 MOE-IQRD w. Capon

4046 MOE-IQRD w. POR

4356 MOE-IQRD w. modified

1356 MOE-IQRD w. Improved

1356 MOE-IQRD w. max/min

2079 - MOE-RLS w. VL

1596 - - MOE-RLS

Special case

Total complexity

Weight vector

Channel vector /VL technique

Intermediate matrix update

Kalman gain

Detector

2a aN N+

2a aN N+

6 fN

6 fN

6 fN

6 fN

6 fN

6 fN

2 2a a f aN N N N+ +

2 2a a f aN N N N+ +

22 f g gN N N+

22 f g gN N N+

2 2 2f g f f gN N N N N+ +

2f g f gN N N N+

22 2 2g g f gN N N N+ +

22 f g gN N N+2 4g gN N+

22 3f fN N+

3 22 2g g gN N N+ +

2 4g gN N+

2 4g gN N+

2 4g gN N+

2 4g gN N+

2 2a aN N+

f gN N

f gN N

f gN N

f gN N

f gN N

f gN N

22 3a a f aN N N N+ +

23 5a a f aN N N N+ +

23 2

4 6f g g

g f

N N NN N

+

+ +23 2

4 6f g g

g f

N N NN N

+

+ +2 2

2

3

4 6f g f f g

g g f

N N N N N

N N N

+ +

+ + +2

2

2

4 6f g f g

g g f

N N N N

N N N

+

+ + +3 23 4

4 6g f g g

g f

N N N NN N+ +

+ +

2 23 2 2

4 9f g g f

g f

N N N NN N

+ +

+ +

31, 10f gN N= =

Numerically Robust MUD

VL Techniques Comparison

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05

100.7

100.8

QI Constrained Value

Out

put S

INR

Ave

rage

(dB

)

0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24

100.4

100.5

100.6

QI Constrained Value

Out

put S

INR

Ave

rage

(dB

)

MOE-IQRD w. max/min and VL

MOE-RLS w. VL

MOE-IQRD w. max/min

MOE-RLS

Variable Loading Technique Comparison

Numerically Robust MUD

Agenda

Introduction Numerically Robust Multiuser Receivers Quadratically Constrained Robust MUD Robust Adaptive Beamforming Thesis Contributions & Publications

MOE Implemented using PLIC structure

Adaptive Algorithm

+

-

Hqf

Haf

( )cy n( )y n

( )ay n

HB

( )x n

( ) 1

( )H H

a opt xx xx c

−=f B R B B R f

c a= −f f Bf

( ) 1

1 1 1H

c

−=f C C C g

( ) ( )mina

Hc a xx c a− −

ff Bf R f Bf

QC Robust MUD

Received vector

min Hxxf

f R f

Blocking Matrix

Reduced Rank Filter

Non-Adaptive Part

Optimal Detector

Robust MOE with QI constraint

( ) ( )mina

Ha a c a= − −c xxf

f f Bf R f Bf Under constraints 2Ha a β≤f f

( ) 1( ) 0a opt B Bλ −= +f R I p

HB = xxR B R BB B c=p P f H

B xx=P B R

ˆ( ) ( ) ( )a a an n nγ≈ −f f f

( ) ( )1 11 1 10 0( ) ( ) ( ) ( ) ( ) ( )a B B B B an I n n n I n nλ λ

− −− − −= + = +f R R p R f1( ) ( ) ( )a B Bn n n−=f R p

1ˆ ( ) ( ) ( )a B an n n−=f R f

{ }2Re 4

2

b b ac

aγ

− ± −=

Optimal Detector

Taylor Series

Lagrange Multiplier ˆ ˆ( ) ( )Ha aa n n= f f

{ }ˆ2Re ( ) ( )Ha ab n n= − f f

2( ) ( )Ha ac n n β= −f f

2Ha a β≤f f

RLS-based VL

QC Robust MUD

Robust MOE with QI constraint (RSD-VL)

( ) ( ) ( )20

12

H Hc a c a a asλ β= − − + −

af xxΨ f Bf R f Bf f fCost Function

( ) ( 1) ( )a n n nµ= − − ∇aa ff fDetector Update

0( ) ( ) ( ) ( 1) ( 1)H Hxx c xx an n n n nλ∇ = − + − + −

af aB R f B R Bf fGradient Vector

0( ) ( 1) ( ( ) ( 1) ( )) ( 1)a a an n n n n nµ µλ= − − − − − −B a Bf f R f p fRobust Detector

[ ]( ) ( 1) ( ) ( 1) ( )an n n n nµ= − − − −a B a Bf f R f pNon-Robust

( ) ( ) 20 0( ) ( 1) ( ) ( 1)

H

a an n n nµλ µλ β− − − − ≤a af f f fQI Constraint

{ }

2 2 20 0( 1) ( 1) 2 Re ( ) ( 1) ( ) ( ) 0

H HHa a a an n n n n nµ λ µ λ β− − − − + − =a af f f f f f

Quadratic Equation

Lagrange Multiplier 2

04

2b b ac

aλ − ± −

=

22 ( 1)a nµ= −af

{ }2 Re ( ) ( 1)H

aab n nµ= − −f f

2 2( )ac n β= −f

QC Robust MUD

Optimum Step-size of MOE-RSD w. VL

( ) ( ) ( )20

12

H Hc a c a a asλ β= − − + −

af xxΨ f Bf R f Bf f fCost Function

Updated Cost Function ( ) ( )( ) ( 1) ( ) ( ) ( 1) ( )a a a

Hn n n n n nµ µ= − + ∇ − + ∇xxf f fΨ f B R f B

[ ]( ) ( 1) ( ) ( 1) ( )an n n n nµ= − − − −a B a Bf f R f pNon-Robust Detector

2( ) ( 1) 2 ( ) ( ) ( 1) ( ) ( ) ( ) ( )a a a a a

HBn n n n n n n n nµ µ= − + ∇ − + ∇ ∇H

Bf f f f fΨ Ψ P f R

Quadratic Equation

( )2 ( ) ( 1) 2 ( ) ( ) ( ) ( )

( )a

a a a

H HB

nn n n n n n

nµ

µ

∂= ∇ − + ∇ ∇

∂f

Bf f f

ΨP f R

Differentiate zero

2( )

( )( ) ( ) ( )

a

a a

opt H

nn

n n n

αµ

σ

∇=∇ ∇ +

f

Bf fR

Optimum Step-Size

QC Robust MUD

Geometric Approach

O

The RLS-based VL technique The RSD-based VL technique

( )a nfE(SP)

ˆ ( )a nf

ˆ ( )a nf

( )a nf

DAF

ˆ ( )a nγ− f

ˆRe( ) ( )a nγ− f( ) ( )

afn nµ− ∇

( 1)n −af

( )a nf

20( ) ( ) ( 1)an n nµ λ− −f

( )a nf

10( ) ( ) ( 1)an n nµ λ− −f

C1A

C2

O

B

C

QC Robust MUD

Simulation Results (SINR)

0 100 200 300 400 500 600 700 800 900 10004

5

6

7

8

9

10

11

12

13

Iterations

Out

put S

INR

(dB

)

MOE-RLSMOE-RLS w. QCProposed

Output SINR with SNR = 30dB, 5 synchronous users, 31 Gold

Codes, and -10dB weaken user

0 100 200 300 400 500 600 700 800 900 10003

3.5

4

4.5

5

5.5

6

6.5

7

Iterations

Out

put S

INR

(dB

)

MOE-RLSMOE-RSDMOE-RLS w. QCProposed

Output SINR with SNR = 20dB, 5 synchronous users, 31 Gold

Codes, and -10dB weaken user

QC Robust MUD

Simulation Results (3)

0 100 200 300 400 500 600 700 800 900 10003.5

4

4.5

5

5.5

6

6.5

7

Iterations

Out

put S

INR

(dB

)

MOE-RSD, alpha = 0.01MOE-RSD, alpha = 0.1MOE-RSD, alpha = 0.9MOE-RSD w. QC, alpha = 0.01MOE-RSD w. QC, alpha = 0.1MOE-RSD w. QC, alpha = 0.9

MOE-RSD

MOE-RSD w. QC

Output SINR with SNR = 20dB, 5 synchronous users, 31 Gold Codes, and -10dB weaken user and variable step-size

QC Robust MUD

Robust CMA with QI Constraint

LCCMA1

LCCMA2

BSCMA

( )22

1min ( ) HJ E r − f

f f x

1H =C f g

( )22min ( ) ( )

a

Ha c aJ E r − −

ff f Bf x

2Ha a β≤f f

2Ha a β≤f fS.T. &

S.T.

( )1 2

0

1( ) ( ) ( ) 14

NH

a an

f j n jM

−

=

Ψ = − ∑ f Z f2( ) ( )H

a aj j β≤f f

1

( 1)( ) ( ) ( )

iMT

n i Mi n n

−

= −

= ∑Z z z

S.T.

( ){ }2

2min ( ) HJ E r−f

f f x 1H =C f g

{ } { }2 ( ) H H HJ E r E− +f f x f x x f 2 ( ) ( )H HJ n− +f f x f R f

min ( ) ( ) ( ) ( )( )a

H Ha c a c a c aJ R n− − + − −

ff f Bf x f Bf f Bf

2Ha a β≤f f

2Ha a β≤f fS.T. &

S.T.

QC Robust MUD

Simulation Results of Robust CMA

0 100 200 300 400 500 600 700 800 900 1000-10

-5

0

5

10

15

Iterations (n)

Out

put

SIN

R (

dB)

LCCMA1 w/t W.LCCMA1 w. W.LCCMA1 w. VLLCCMA2 w/t QILCCMA2 w. SPLCCMA2 w. VLLCCMA2 w. CG

Output SINR for Different LCCMA receivers with SNR = 30dB, 5 synchronous users, 31

Gold Codes, and -10dB weaken user

0 50 100 150 200 250-4

-3

-2

-1

0

1

2

3

4

5

Block Iteration (j)

Out

put

SIN

R (

dB)

BSCMA w. VLBCGCMA w. VLBGDCMA w. VLBSCMA BCGCMA BGDCMA

Output SINR for BSCMA receivers with SNR = 30dB, 5 synchronous users, 31 Gold Codes,

and -10dB weaken user

QC Robust MUD

Agenda

Introduction Numerically Robust Multiuser Receivers Quadratically Constrained Robust MUD Robust Adaptive Beamforming Thesis Contributions & Publications

LCMV Beamforming

Adaptive beamforming has been exploited in wireless communications, radar, sonar, speech processing, and other areas.

Recently, there has been a great effort to design robust adaptive beamforming techniques which improve robustness against mismatch and modeling errors and enhancing interference cancellation capability.

The mismatch may be caused by uncertainty in direction-of-arrival (DOA), imperfect array calibration, near-far effect, and other mismatch and modeling errors.

The so-called linearly constrained minimum variance (LCMV) beamformer, also known as Capon’s method, has bean a popular beamforming technique.

In LCMV beamforming method, the weights are chosen to minimize the array output power subject to side constraint (s) in the desired look direction (s).

This method assumes that the array manifold is accurately known, unfortunately, even small discrepancy between the presumed and the actual array manifold can substantially degrade its performance.

min Hxxw

w R w 0 0( ) 1H θ =w aS. T. 1

0 00 1

0 0 0 0

( )( ) ( )

xxH

xx

θθ θ

−

−=R aw

a R a

Robust Beamforming

Diagonal Loading Technique

Diagonal loading is a technique where the diagonal of the covariance matrix is augmented with a positive or negative constant prior to inversion

Diagonal loading technique has been a widespread approach to improve robustness against mismatch errors and random perturbations

Moreover, the performance of the signal detectors, which utilize the inverse of the data covariance matrix, experiences serious degradation when the sample support available for estimating the matrix is limited.

This problem can be overcome also by diagonally loading the data covariance matrix

Furthermore, it is well known that antenna sidelobes can be made small if the sample data correlation matrix is diagonally loaded before inversion is performed

Robust Beamforming

Robust Beamforming Design

The SOCP approach can be interpreted as a diagonal loading technique in which the optimal value of diagonal loading is computed based on the known upper bound on the norm of the signal steering vector mismatch

The SeDuMe optimization Matlab toolbox has been used to compute the weight vector of SCOP approach.

Unfortunately, the computational burden of this software seems to be cumbersome which limits the practical implementation of this technique.

The SOCP-based method does not provide any closed-from solution, and does not have simple on-line implementations

In addition, this technique can be regarded as batch algorithm rather than adaptive scheme.

SOCP Approach min H

xxww R w 1 ( )H ε≥ ∀ ∈w c c A { }0( ) | ,e eε ε= = + ≤A c c a

min Hxxw

w R w 0 1H ε≥ +w a w { }0Im 0H =w a

S.T.

S.T. &

Robust Beamforming

0ˆmax min H

xxwaw R w 0 0ˆ ( ) 1H θ =w a 1

0 0 0 0ˆ ˆ( ( ) ) ( ( ) ) 1Hk k−− − ≤a a C a a

10 0ˆ

ˆ ˆmin ( ) ( ) ( )Hxxa

k k k−a R a 20 0ˆ ( )k ε− ≤a a 1 1

ε− =C I

11

0 0( )ˆ xx kλ

−− = +

Ra I a1

0 00 1

0 0 0 0

ˆ ( )ˆˆ ˆ( ) ( )

xxH

xx

θθ θ

−

−=R aw

a R a ( )

2

21

( )1

Mm

j m

zg λ ε

λγ=

=+

∑ Hxx =R UΓU0

H=z U a

S.T. &

S.T. where

Ellipsoidal

Constraint

Robust Beamforming Design (2)

3( )O M Eigendecomposition requires high computational burden of order The adaptive implementation updates both the covariance matrix and its

inverse to compute the diagonal loading value and the robust detector This technique is based on batch algorithm The rank of signal and noise may be uncertain or not exactly known and

need to be estimated in advance. The covariance matrix will be always diagonally loaded even without

mismatch.

Robust Beamforming

Proposed Formulation

ˆ ˆ( ) ( 1) ( ) ( )SDk k k kµ= − −0 0a a g1

( ) ( )( )( ) ( ) ( )

H

SD Hxx

k kkk k kαµ

σ−=+

g gg R g ( )1

0ˆ ˆ( ) ( ) ( 1) ( 1)xxk k k kλ−= − + − −0 0g R a a a

2 2 20 0 0 0( 1) ( 1) ( ) ( ) ( 1) ( 1) ( )H H

SD k k k k k k kµ ε ≤ − − − − − d d g g d d g

{ } { }0 0 0( 1) Re ( 1) , Im ( 1)T Tk k k − − − d d d

{ } { }( ) Re ( ) , Im ( )T Tk k k = g g g

( )21ˆ 0 0 0 0ˆ ˆ ˆ( ) ( ) ( ) ( ) ( )

2H

xxk k k k t kλ ε−Ψ = + − −a a R a a aCost Function

21 1 1 0b a c− ≥Step-Size Constraint

221 0 0ˆ( ) ( 1) 0SDa k kµ= − − >a a ( ) ( ){ }1 0 0 0 0ˆ( ) Re ( ) ( 1)H

SDb k k kµ= − − −a a a a

21 0 0( ) 0c k ε= − − >a a

21 1 1 1

1

( )b b a c

ka

λ± −

=Diagonal Loading Term

( )( )( ) ( )( )( )0 0 0 0 0 0 0 0ˆ ˆ( ) ( ) ( ) ( 1) ( ) ( ) ( ) ( 1)H

SD SDk k k k k k k kµ λ µ λ ε− − − − − − − − ≤a a a a a a a a

Spherical Constraint

( )( )10ˆ ˆ ˆ ˆ( ) ( 1) ( ) ( ) ( 1) ( ) ( 1)SD xxk k k k k k kµ λ−= − − − + − −0 0 0 0a a R a a a 1

0 0 0ˆ ˆ( ) ( 1) ( ) ( ) ( 1)SD xxk k k k kµ −= − − −a a R a

Steering Vector Update

Step-Size

Gradient Vector

Robust Beamforming

Geometric Approach

Q

A

B

C

O

D

( )0ˆ( ) ( ) ( 1)k k kµ λ − −a a

0 ( )ka

0ˆ ( )ka0ˆ ( 1)k +a

a

0 ( 1)k −d

0 ( )kd

0 ( )kd

1

2

ε

Geometric Representation for Robust Capon Beamforming with ellipsoidal constraint

Array direction Ar

ray

broa

dsid

e

Robust Beamforming

000 0ˆˆ

ˆ ˆmax min Hxxwa

w R w 0 0 0ˆ ˆ ( ) 1H θ =w a 20 0ˆ ( )k ε− ≤a a& & S.T.

0 0ˆ ˆH τ≤w w

Joint Constraint Approach

00 0ˆ

ˆ ˆmax Hxxa

w R w1

LH

xx i i i ni=

= + ∑Rρ s s R

0

20 0 0 0ˆ

1

ˆ ˆ ˆ ˆmaxL

H H Hi i i

iσ

=

+

∑awρ s s w w w

( )( )

10

0 10 0

ˆ ( )ˆ ˆ( ) ( )

xxH

xx

kk k

υ

υ

−

−

+=

+

R I aw

a R I a

( ) ( )( ) ( )

1 10

0 1 10 0( )

xx xx xxH

xx xx xxkυ λ

λ λ

− −

− −

+ +=

+ +

R I R R I aw

a R I R R I a

( ) 10

0 10 0

ˆ ( )ˆ ˆ( ) ( )

xxH

xx

kk kυ −

−

+=

R I aw

a R a

( ) 11 10

0 10 0

ˆ ( )ˆ ˆ( ) ( )

xx xxH

xx

kk k

υ−− −

−

+=

I R R aw

a R a

( )1 10

0 10 0

ˆ ( )ˆ ˆ( ) ( )

xx xxH

xx

kk k

υ − −

−

−≈

I R R aw

a R a

10 0ˆxx

−=w R w0 0 0ˆ υ≈ −w w w

11

0 0( )ˆ xx kλ

−− = +

Ra I a

Robust Beamforming

Simulation Scenario

Presumed DOA

Actual DOA Jammer 1 Direction

2λ

0.03π

2ϕ

1ϕMismatch angle

Jammer 2 direction

Robust Beamforming

1w

1w1w1w

1w

∑

Array Output

Control algorithm

Adaptive processor

Signal processor

Beamformer

Simulation Results (SINR)

0 100 200 300 400 500 600 700 800 900 10000

5

10

15

20

25

Iterations (n)

SIN

R (d

B)

Standared CaponRobust Capon (Batch)Robust Capon (SS)Robust (SOCP)Proposed1Proposed2

Output SINR versus snapshot for SNR =40 dB, two 10dB interference, 0.3pi mismatch angle

0 100 200 300 400 500 600 700 800 900 1000-20

-15

-10

-5

0

5

10

15

Iterations (n)

SIN

R (d

B)

Standared CaponRobust Capon (Batch)Robust Capon (SS)Robust (SOCP)Proposed1Proposed2

Output SINR versus snapshot for SNR =20 dB, two 10dB interference, 0.3pi mismatch angle

Robust Beamforming

Simulation Results (Beampatterns)

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2-60

-50

-40

-30

-20

-10

0

Standared CaponRobust Capon (Batch)Robust Capon (SS)Robust (SOCP)Proposed

Angle (radian)steady state beampatterns for versus snapshot for SNR

=40 dB, two 10dB interference, 0.3pi mismatch angle

Robust Beamforming

Simulation Results (Moving Interference)

0 100 200 300 400 500 600 700 800 900 10000

5

10

15

20

25

Iterations (n)

SIN

R (d

B)

Standared CaponRobust Capon (Batch)Robust Capon (SS)Robust (SOCP)Proposed

Output SINR versus snapshot for SNR =20 dB, two moving 10dB interference, 0.3pi

mismatch angle

0 100 200 300 400 500 600 700 800 900 10000

2

4

6

8

10

12

14

16

18

20

Iterations (n)

SINR

(dB)

Standared CaponRobust Capon (Batch)Robust Capon (SS)Robust (SOCP)Proposed

Output SINR versus snapshot for SNR =20 dB, two coherent moving 10dB interference, 0.3pi mismatch angle

Robust Beamforming

Agenda

Introduction Numerically Robust Multiuser Receivers Quadratically Constraint Robust MUD Robust Adaptive Beamforming Thesis Contributions & Publications

Contributions Summary (1)

• A general DS/CDMA system model which account for asynchronism, multipath propagation, near-far effect, signature mismatch, and inter-symbol-interference (ISI) is developed.

• MUD survey and performance comparison for existing techniques is performed anchored in the proposed model.

• A fast subspace tracking algorithm is Developed and deployed for channel estimation with MOE detector.

• A generalized frame work for building IQRD-based multiuser receivers is offered.

• Based on the above proposed frame work, comparative analyses between the recently proposed channel estimation techniques, subspace tracking and the proposed techniques is conducted.

• A combined subspace approach and a quadratic constraint is proposed to produce robust and optimum multiuser receiver.

• The systolic array implementation is exploited to facilitate real-time implementation of the proposed IQRD-based receivers.

Contributions &Publications

Contributions Summery (2)

• A new VL technique is devised in this thesis and integrated into a recursive steepest descent (RSD) algorithm rather than the RLS algorithms to produce robust MOE detector with low-computational complexity. This VL is exploited to fulfill the quadratic constraint on the detector norm to improve the performance of the multiuser receiver against modeling and mismatch errors.

• Additionally, an optimum step-size closed-form expression for the proposed RSD algorithm is derived.

• The proposed VL technique has been integrated also into the LCCMA algorithms and the BSCMA algorithm to produce robust constant modulus based receivers for sample-by-sample and block-adaptive, respectively.

• We have proposed a low-complexity recursive implementation for the robust Capon beamforming algorithm which incorporating ellipsoidal constraint on the steering vector using the proposed RSD algorithm and the recursive conjugate gradient (RCG) algorithm.

• Additionally, a joint constraint approach is proposed to produce robust beamforming algorithm which is capable of providing robustness against steering vector mismatch and noise enhancement at low SNR.

• A comparative analysis is conducted between most recent beamforming algorithms as well as the proposed approaches in the presence of moving and coherent jamming.

Contributions &Publications

Publications List (updated on Oct. 2011) • Major Publications in Refereed Journals: • A. Elnashar, “On efficient implementation of robust adaptive beamforming based on worst-case

performance optimization” IET Signal Processing, Vol. 2, No. 4, pp. 381-393, Dec. 2008. • A. Elnashar, S. Elnoubi, and H. Elmikati “Performance Analysis of Blind Adaptive MOE Multiuser

Receivers using Inverse QRD-RLS Algorithm,” IEEE Trans. On Circuits and systems I, Vol. 55, No. 1, pp. 398-411, Feb. 2008.

• A. Elnashar, S. Elnoubi, and H. Elmikati “Further study on Robust Adaptive Beamforming with optimum diagonal loading,” IEEE Trans. on Antennas and Propagation, Vol. 54, No 12, pp. 3647-3658, Dec. 2006.

• A. Elnashar, S. Elnoubi, and H. Elmikati, “Low-Complexity Robust Adaptive Generalized Sidelobe Canceller Detector for DS/CDMA Systems,” International Journal of Adaptive Control and Signal Processing, vol. 23, no. 3, pp. 293-310,March 2008, John Wiley & Sons, Ltd.

• T. Samir, S. Elnoubi, and A. Elnashar, “Block-Shanno Minimum BER Beamforming,” IEEE transactions on Vehicular Technology, Vol. 57, No. 5, pp. 2981-2990, Sept. 2008.

• International Conferences: • T. Samir, S. Elnoubi, and A. Elnashar “Block-Shanno MBER algorithm in a spatial multiuser

MIMO/OFDM” in Proc. 14th European Wireless Conference EW2008, 22-25 June 2008. • T. Samir, S. Elnoubi, and A. Elnashar “Class of Minimum Bit Error Rate Algorithms,” in Proc. ICACT

2007, Korea, Feb. 2007, pp. 168-173. • T. Samir, S. Elnoubi, and A. Elnashar, “Block-Shanno Minimum BER Beamforming” in Proc. ISSPA

2007, UAE, Feb. 2007. • A. Elnashar, “Robust Adaptive Beamforming,” ACE2 Network of Excellence Workshop on Smart

Antennas, MIMO Systems and Related Technologies, Myconos, Greece, 8 June 2006.

Contributions &Publications

Publications List (Cont.)

• A. Elnashar, S. Elnoubi, and H. Elmikati, “Performance analysis of robust MOE detectors at low SNR based on the IQRD-RLS algorithm,” In Proc. IST Mobile and Wireless Communications Summit, Myconos, Greece, 4-8 June, 2006.

• A. Elnashar, S. Elnoubi, and H. Elmikati “Robust Adaptive Beamforming with Variable Diagonal Loading,” In Proc. Sixth International Conference on 3G and Beyond - 3G 2005, 07-09 November 2005, The IEE, Savoy Place, London, UK, pp. 489-493.

• A. Elnashar, S. Elnoubi, and H. Elmikati “A Robust Block-Shanno Adaptive Blind Multiuser Receiver for DS-CDMA Systems,” In Proc. IST Mobile & Wireless Communications Summit 2005, Dresden, Germany, 19-23 June, 2005.

• A. Elnashar, S. Elnoubi, and H. Elmikati “A Robust Linearly Constrained CMA for Adaptive Blind Multiuser Detection,” In Proc. IEEE WCNC 2005 conference, Vol. 1, pp. 233-238, New Orleans, LA, USA, 13-17 March, 2005,

• A. Elnashar, S. Elnoubi, and H. Elmikati “A Robust Quadratically Constrained Adaptive Blind Multiuser Receiver for DS/CDMA Systems,” IEEE International Symposium on Spread Spectrum Techniques and Applications (ISSSTA 2004), Sydney, Australia 30 Aug 2004 - 3 Sept 2004.

• A. Elnashar, S. Elnoubi, and H. Elmikati “A Novel Adaptive Blind Multiuser Receiver for DS/CDMA Based on combined Inverse QRD-RLS Algorithm and constrained Optimization Approach,” in Proc. ISPACS 2003, Awaji Island, Japan, pp. 423-428, December 7-10, 2003.

• A. Elnashar, S. Elnoubi, and H. Elmikati “Computationally Efficient Real-Time Blind Multiuser Detection for cellular DS/CDMA Based on Inverse QRD-RLS Algorithm and Subspace Tracking,” in Proc. MWSCAS 2003, Cairo, Egypt, December 28-31, 2003.

• A. Elnashar, S. Elnoubi, and H. Elmikati “Robust Adaptive Blind Multiuser Receiver for DS/CDMA Based on combined Inverse QRD-RLS Algorithm and MOE” in Proc. SOFTCOM 2003 conference, Croatia, pp. 512-515, Oct. 2003.

Contributions &Publications