Multiuser Detection in CDMA A. Chockalingam Assistant Professor Indian Institute of Science, Bangalore-12 [email protected] achockal

Multiuser Detection in CDMA

A. ChockalingamAssistant Professor

Indian Institute of Science, Bangalore-12

[email protected]

http://ece.iisc.ernet.in/~achockal

Dr. A. Chockalingam Dept of ECE, IISc, Bangalore 2

Outline

Near-Far Effect in CDMANear-Far Effect in CDMA CDMA System ModelCDMA System Model Conventional MF DetectorConventional MF Detector Optimum Multiuser DetectorOptimum Multiuser Detector Sub-optimum Multiuser DetectorsSub-optimum Multiuser Detectors

– Linear DetectorsLinear Detectors» MMSE, DecorrelatorMMSE, Decorrelator

– Nonlinear DetectorsNonlinear Detectors» Subtractive Interference cancellers (SIC, PIC)Subtractive Interference cancellers (SIC, PIC)» Decision Feedback DetectorsDecision Feedback Detectors


DS-CDMA

Efficient means of sharing a given RF spectrum by different users

User data is spread by a PN code before transmission

Base station Rx distinguishes different users based on different PN codes assigned to them

All CDMA users simultaneously can occupy the entire spectrum

» So system is Interference limited


DS-SS

DS-SS signal is obtained by multiplying the information bits with a wideband PN signal

InformationBits

PN Signal

Carrier Modulation

InformationBits

PN Signalt

t

Tb

TcTb = N Tc

N : Processing Gain


Processing Gain

Ratio of RF BW (W) to information rate (R)

(e.g., In IS-95A, W = 1.25 MHz, R = 9.6 Kbps

i.e., )

System Capacity (K) proportional to

(voice activity gain) (sectorization gain)

(other cell interference loss)

(typically required)

R

WGp

dBX

XGp 21133

106.9

1025.13

6

pG

fob

Avp

GIE

GGGK

)/(

67.2vG

4.2AG

6.1fG

dBIE ob 6/


Near-Far Effect in DS-CDMA

Assume users in the system. Let be the average Rx power of each signal. Model interference from users as AWGN. SNR at the desired user is

Let one user is near to BS establishes a strongerLet one user is near to BS establishes a stronger Rx signal equal to Rx signal equal to

SNR then becomes SNR then becomes

When is large, SNR degrades drastically. When is large, SNR degrades drastically. To maintain same SNR, has to be reduced To maintain same SNR, has to be reduced i.e., loss in capacity.i.e., loss in capacity.

K

cs

sb

TPKN

TP

I

E

)1(00

sP1K

,saP 1a

cscs

sb

TPKTaPN

TP

I

E

)2(00

a2K


Near-Far Effect

Factors causing near-far effect (unequal Rx Signal powers from different users) in cellular CDMA– Distance loss

– Shadow loss

– Multipath fading (Most detrimental. Dynamic range of fade power variations: about 60 dB)

Two common approaches to combat near-far effect– Transmit Power Control– Near-far Resistant Multiuser DetectorsNear-far Resistant Multiuser Detectors


CDMA System Model

Data of User 1Data of User 1

Spreading Sequence Spreading Sequence of user 1of user 1

Chip shaping Chip shaping filterfilter 1


Spreading Sequence Spreading Sequence of user 2of user 2

Chip shaping Chip shaping filterfilter 2


Spreading Sequence Spreading Sequence of user Kof user K

Chip shaping Chip shaping filterfilter K

AWGNAWGN

ToToDemod/Demod/DetectorDetector

)(tr


Matched Filter Detector (MFD)

MFMFUser 1User 1

MF MF User 2User 2

MFMFUser KUser K

)(tr

nT

nT

nT

^

1 )(nb

^

2 )(nb

^

)(nbK

1r

2r

Kr

kj

kjkjjkkk nbEbEr

RnnE T 2][

nbRAr :R Correlation MatrixCorrelation Matrix

KEEEdiagA ,...,, 21


MFD Performance: Near-Far Scenario

E/b/No (dB)E/b/No (dB)

Bit Bit Error Rate Error Rate

0.4 0.4

0.1 0.1

NFR = 0 dBNFR = 0 dB




2-User system: 2-User system: PowerRx s User'Desired

PowerRx s User'gInterferinNFR

• Problem with MF Detector: Treats other user interference Problem with MF Detector: Treats other user interference (MAI) as merely noise(MAI) as merely noise• But MAI has a structure which can be exploited in the But MAI has a structure which can be exploited in the detection process detection process


Optimum Multiuser Detector

Jointly detect all users data bits

Optimum Multiuser Detector– Maximum Likelihood Sequence Detector

Selects the mostly likely sequences of data bits

given the observations

Needs knowledge of side information such as– received powers of all users– relative delays of all users– spreading sequences of all users



Optimum ML detector computes the likelihood fn

and selects

the sequence that minimizes The above function can be expressed in the form

where and

is the correlation matrix with elements

where

T K

kkkk dttcbEtrb

0

2

1

)()()(

Kkbk 1, )(b

BRBrBbrc TT ),(

TKrrrr ,...,, 21 TKK bEbEbEB ,...,, 2211

T

jiij dttctc0

)()()(



results in choices of the bits of the users

Thus Optimum Multiuser Detector is highly complex– complexity grows exponentially with number of userscomplexity grows exponentially with number of users– Impractical even for moderate number of usersImpractical even for moderate number of users

Need to know the received signal energies of all the users

},...,,{ 21 Kbbb K2K


Suboptimum Detectors

Prefer

– Better near-far resistance than Matched Filter DetectorBetter near-far resistance than Matched Filter Detector

– Lesser complexity (linear complexity) than OptimumLesser complexity (linear complexity) than Optimum DetectorDetector

Linear suboptimum detectors

– Decorrelating detectorDecorrelating detector

– MMSE detectorMMSE detector


Decorrelating Detector

1r

2r

Kr

Linear TransformationLinear Transformationand Detectorand Detector

rR 1sgn()

^

b

DecisionDecision

kk

kke

R

EQp

1

)(

)1( 2

)( kke

EQp

For the case of 2 usersFor the case of 2 users 2

1

1

1

xxR

andand



For the case of 2 users

and

– operation has completely eliminated MAI components at the output (.e., no NF effect)

– Noise got enhanced (variance increased by a factor of )

1

1

R

1

1

1

12

1

R

212

22

221

111

1

1

nnbE

nnbE

rR

rR 1

21

1



Alternate representation of Decorrelating detector

– By correlating the received signal with the modified signature waveforms, the MAI is tuned out (decorrelated)

– Hence the name decorrelating detector

)(tr)()( 21 tctc

T

0

^

1b

)()( 21 tctc

T

0

^

2b


MMSE Detector

1r

2r

Kr


rA 1sgn()

^

b

DecisionDecision

• Choose the linear transformation that minimizes the mean square error between the MF outputs and the transmitted data vector b


MMSE Detector

• Choose the linear transformation where is determined so as to minimize the mean square error (MSE)

• Optimum choice of that minimizes is

rAb 0

A

)]()[()( rAbrAbEbJ T

A )(bJ

120 IRA


MMSE Detector

1r

2r

Kr


sgn()^

b

DecisionDecision

rIR12

• When is small compared to the diagonal elements of MMSE performance approaches Decorrelating detector performance

• When is large becomes (i.e., AWGN becomes dominant)

2

R

2

0A I2


Adaptive MMSE

Several adaptation algorithms – LMS– RLS

Blind techniques

LinearLinearTransversalTransversal

FilterFilter

AdaptiveAdaptiveAlgorithmAlgorithm

Re()Re()

Estimate of theEstimate of thedata bitsdata bits

Training bitsTraining bits


Performance Measures

Bit Error Rate

Asymptotic efficiency: Ratio of SNRs with and without interference

represents loss due to multiuser interference

Asymptotic efficiency easy to compute than BER

k

kek

Lt

0


Performance Measures

dBE

E

1

2

k

0.0 0.0

1.0 1.0

-20.0 -20.0 -10.0 -10.0 10.0 10.0 0.0 0.0 20.0 20.0

MMSE MMSE

Optimum Detector Optimum Detector

DC DC

MF Detector MF Detector


Subtractive Interference Cancellation

Multistage interference Cancellation approaches

– Serial (or successive) Interference Canceller (SIC)

» sequentially recovers users (recover one user per stage)

» data estimate in each stage is used to regenerate the

interfering signal which is then subtracted from the original

received signal

» Detects and removes the strongest user first

– Parallel Interference Canceller (PIC)» Similar to SIC except that cancellations are done in parallel


SIC

MatchedMatchedFilterFilter

RemodulateRemodulate& Cancel& Cancel

MF MF DetectorDetector

)(tr

^

1b

2e meRemodulateRemodulate

& Cancel& Cancel

Stage-1Stage-1

^

mb

1me

Stage-mStage-m

MF MF DetectorDetector


m-th Stage in SIC

^

mbme

MFMFUser mUser m

MFMFUser KUser K

SelectSelectStrongestStrongest

User User

mc

^

mE

1me

MF DetectorMF Detector

Remodulate Remodulate & Cancel& Cancel


Performance of SIC

Good near-far resistance Most performance gain in achieved using just

2 to 3 stages High NFR can result in good performance!

– Provided accurate estimates of amptitude and timing are available

Sensitive to amplitude and timing estimation errors– increased loss in performance for amplitude estimation

errors > 20 % Some amount of power control may be required to compensate for the near-far resistance loss due to imperfect estimates and low NFR


PIC

)(tr

MFMFUser 1User 1

MFMFUser KUser K

)1(1r

)1(Kr

)1(

1

^

b

)1(^

Kb

K

ii

j

iii bE

11

)1(^

1

)(1

jr)(

1

^ j

b

K

Kii

j

iiKi bE1

)1(^

)( jKr

)(^ j

KbStage 1Stage 1

Stage jStage j


Performance of PICPerformance of PIC

Good near-far resistance

Similar performance observations as in SIC

Performance of PIC depends more heavily on the relative amplitude levels than on the cross-correlations of the user spreading codes

Hybrid SIC/PIC architectures


DFE Detector

MFMFUser 1User 1

MFMFUser KUser K

1T

KT

cT

cT

FFFFFF

FFFFFF

CentralizedCentralizedDecisionDecision

FeedbackFeedback

1

^

b

Kb^

• Feedback current data decisions of the stronger users as wellFeedback current data decisions of the stronger users as well• DFE multiuser detectors outperform linear adaptive receiversDFE multiuser detectors outperform linear adaptive receivers• Complexity, error propagation issuesComplexity, error propagation issues

Documents

Multiuser Detection in CDMA A. Chockalingam Assistant Professor Indian Institute of Science, Bangalore-12 [email protected] achockal