Multi-user CDMA Enhancing capacity of wireless cellular CDMA

Multi-user CDMA

Enhancing capacity of wireless cellular CDMA

Timo O. Korhonen, Helsinki University of Technology 2

Topics Today Dealing without multi-user reception:

asynchronous CDMA SNR power balance - near-far effect

Multi-user detection (MUD) classification and properties The conventional detector (non-MUD, denotations) Maximum likelihood sequence detection Linear detectors

Decorrelating detector Minimum mean-square error detector Polynomial expansion detector

Subtractive interference cancellation Serial and parallel cancellation techniques


The j:th user experiences the SNR:

signalvoltage ISI & noise voltage

2 2

2 2 2

2

, , ,

0

2

jj jjj

ij j ij ij j ji j i j i j

m mSNR

m n m m n n

E E E E

MAI channel noise

signal power for the j:th user

voltage at the I&D* at the decision instant

Asynchronous CDMA

i j

1

ˆ ( )U

j m jj ij ji

i j

m t m m n

ˆ ( )j mm t

( )jv t

( ) 2U Us t P

2 2( ) 2s t P

1 1( ) 2s t P

*Integrate and dump receiver

i j


Practical CDMA receiver

Hence, SNR upper bound for the j:th user is

01

c jj U

i effi

i j

L PSNR

P N B

1

U

ii

i j

P

2

2 2

2

, ,

0

2

jjj

ij ij j ji j i j

mSNR

m m n n

E E E

0 eff NN B P

/c j jL P WP R

0( )

mtu tLPF

local code

from channeldecision

phasing of sampling

2

0

2

0

( )

( )eff

V f dfB

V f df

f

NB

0S

2

020

Neff N

N

B SB B

B S

Effective BW is defined by:

for rectangular spectra:

( )V f


Perfect power control

Equal received powers for U users means that

Therefore the j:th user’s SNR equals

and the number of users is

where* (for BPSK)

Number of users is limited by channel AWGN level N0

processing gain Lc

received power Pr

1

1 11 c

o

U LSNR SNR

1max

1 0

1 1lim 1 1 c

cSNR

o

LU L

SNR SNR SNR

0 / 2SNR

Eb/No

(=SNR1/2)

10

2j j bc

eff N o

P PW ESNR L

B N P R N

00

( )( 1)

c j

eff j

L PSNR

N B U P

AWGN level decreases

maxU

*SNR1: received SNR without multiple access interference

1 ( 1)Uii i ji j

P P U P


Unequal received powers - the near-far -effect Assume all users apply the same power but their distance to the

receiving node is different. Hence the power from the i:th node is

where d is the distance, and is the propagation attenuation coefficient (= 2 for free space, in urban area = 3…5 )

Express the power ratio of the i:th and j:th user at the common reception point

Therefore, the SNR of the j:th user is

0 /i iP P d

jo i i j j i j

i

dP Pd P d P P

d

001

1

c j c jj jU

Uj

eff ieff ji

i ii j

i j

L P L PSNR SNR

dN B P N B Pd


The near-far effect in asynchronous CDMA Grouping the previous yields condition

Multiple-access interference (MAI) power should not be larger than what the receiver sensitivity can accommodate

Note the manifestation of near-far -effect because just one larger sum term on the left side of the equation voids it

Example: Assume that all but one transmitter have the same distance to the receiving node. The one transmitter has the distance d1=dj /2.5 and =3.68, SNR0=14, SNR1=25, Rb = 30 kb/s, Beff = 20 MHz, then

3.68

1

(2.5) 2U

j

i ii j

dU

d

3.68

0 1

3.68

0 1

1 1(2.5) 2

1 12 2.5 14

c

c

U LSNR SNR

U LSNR SNR

1 0 1

1 11

Uj

ci ii j

dL U

d SNR SNR

, (2 / ) /(1/ ) 2 / 2c BPSK c b b c b effL T T T T T B


By using the perfect power balance the number of users is

Hence the presence of a single user so near has dropped the number of users into almost 1/3 part of the maximum number

If this user comes closer than

all the other users will be rejected, e.g. they can not communicate in the system in the required SNR level. This illustrates the near-far effect

To minimize the near-far effect efficient power control is should be adaptively realized in asynchronous CDMA-systems

0 1

1 11 42

( ) ( )cU LSNR SNR

1 / 2.78jd d


Fighting against Multiple Access Interference

CDMA system can be realized by spreading codes having low cross -correlation as Gold codes (asynchronous usage) or Walsh codes (synchronous usage)

Multipath channel with large delay spread can destroy code cross-correlation properties a remedy: asynchronous systems with large code gain

assume other users to behave as Gaussian noise (as just analyzed!)

Additional compensation of MAI yields further capacity (increases receiver sensitivity). This can be achieved by Code waveform design (BW-rate/trade-off) Power control (minimizes near-far effect) FEC- and ARQ-systems Diversity-systems: - Spatial - Frequency - Time multi-user detection


Note that there exists a strong parallelism between the problem of MAI and that of ISI:

Hence, a number of multi-user detectors have their equalizer counter parts as:

maximum likelihood zero-forcing minimum mean square decision feedback

General classification of multi-user detectors: linear subtractive

Asynchronous channel of K-users behaves the same way as a single user channel having ISI with *memory depth of K-1

MAI versus ISI (Inter-Symbolic Interference)

*This could be generated for instance by a multipathchannel having K-1 taps


Maximum-likelihood sequence detection Optimum multi-user detection applies maximum-likelihood

principle:

The ML principle has the optimum performance provided transmitted

symbols equal alike has large computational complexity - In exhaustive

search 2NK vectors to be considered! (K users, N bits) requires estimation of received amplitudes and phases

that takes still more computational power can be implemented by using Viterbi-decoder that is

‘practically optimum’ ML-detection scheme to reduce computational complexity by surviving path selections

We discuss first the conventional detector (by following the approach we already had to familiarize to denotations)

Considering the whole received sequence, find the estimate for the received sequence that has the minimum distance to the allowed sequences


Formulation: Received signal Assume

single path AWGN channel perfect carrier synchronization BPSK modulation

Received signal is therefore

where for K users

Note that there are Lc chips/bit (Lc : processing gain)

1( ) ( ) ( ) ( ) ( )

K

k k kk

r t A t g t d t n t

( )k

A t is the amplitude( )

kg t is the spreading code waveform

( )k

d t is the data modulation of the k:th user

( )n t is the AWGN with N0/2 PSD


Conventional detection (without MUD) for multiple access

The conventional DS receiver for K users consists of K matched filters or correlators:

Each user is detected without considering background noise (generated by the spreading codes of the other users) to be deterministic (Assumed to be genuine AWGN)

decision0( )

bTx t dx

1( )g t

decision0( )

bTx t dx

2( )g t

decision0( )

bTx t dx

( )Kg t

1d

2d

ˆKd

( )r t


Output for the K:th user without MUD Detection quality depends on code cross- and

autocorrelation

Hence we require a large autocorrelation and small crosscorrelation (small ISI)

The output for the K:th user consist of the signal, MAI and filtered Gaussian noise terms (as discussed earlier)

Received SNR of this was considered earlier in this lecture

,

1( ) ( )

b

i k i kTb

g t g t dtT

,

,

1,

0 1,i k

i k

i k

i k

1 ,

1( ) ( )

1( ) ( )

b

b

k kTb

Kik k k i k i i kTi k

b

k k k k k

y r t g t dtT

y A d A d n t g t dtT

y A d MAI z


Matrix notations to consider detection for multiple access

Assume a three user synchronous system with a matched filter receiver

that is expressed by the matrix-vector notation as

1 2,1 2 2 3,1 3 3 1

2 1,2 1 1 3,2 3 3 2

3 1

1

,3 1 1 2,3 2 2 3

1

2 2

3 3

A d

A

y A d A d z

y A d A d z

y A dd z

d

Ad A

1 2,1 3,1 1 1 1

2 1,2 3,2 2 2 2

3 1,3 2,3 3 3 3

1 0 0

1 0 0

1 0 0

y A d z

y A d z

y A d z

y RAd z

datanoisematched filter outputs

received amplitudescorrelations between each pair of codes


The data-term and the MAI-term Matrix R can be partitioned into two parts by setting

Note that hence Q contains off-diagonal elements or R (or the crosscorrelations)

and therefore MF outputs can be expressed as

Therefore the term Ad contains the decoupled data and QAd represents the MAI

Objective of all MUD schemes is to cancel out the MAI-term as effectively as possible (constraints to hardware/software complexity and computational efficiency)

y RAd z

R I Q

( ) y I Q Ad z d QAdA z

y RAd z with


Asynchronous and synchronous channel In synchronous detection decisions can be made bit-by-bit In asynchronous detection bits overlap and multi-user

detection is based on taking all the bits into account

The matrix R contains now partial correlations that exist between every pair of the NK code words (K users, N bits)

1

( ) ( ) ( ) ( ) ( )K

k k k kk

r t A t g t d t n t

4

3

6

5

2

1User 1

User 2

11bT 13 bT

4

3

6

5

2

1User 1

User 2

1 21bT 23 bT

asynchronous ch. synchronous ch.


Asynchronous channel correlation matrix In this example the correlation matrix extends to 6x6

dimension:

Note that the resulting matrix is sparse because most of the bits do not overlap

Sparse matrix - algorithms can be utilized to reduce computational difficulties (memory size & computational time)

y RAd z

2,1

1,2 3,2

2,3 4,3

3,4 5,4

4,5 6,5

5,6

1 0 0 0 0

1 0 0 0

0 1 0 0

0 0 1 0

0 0 0 1

0 0 0 0 1

R


Decorrelating detector The decorrelating detector applies the inverse of the

correlation matrix to suppress MAI

and the data estimate is therefore

We note that the decorrelating detector eliminates the MAI completely!

However, channel noise is filtered by the inverse of correlation matrix - This results in noise enhancement!

Decorrelating detector is mathematically similar to zero forcing equalizer as applied to compensate ISI

1dec

L R

1

1

1

ˆ

( )dec

dec

RAd

d R y

R z

Ad R z Ad z

AA Q dd


Decorrelating detector properties summarized

PROS: Provides substantial performance improvement over

conventional detector under most conditions Does not need received amplitude estimation Has computational complexity substantially lower that the

ML detector (linear with respect of number of users) Corresponds ML detection when the energies of the users

are not know at the receiver Has probability of error independent of the signal energies

CONS: Noise enhancement High computational complexity in inverting matrix R


Polynomial expansion (PE) detector Many MUD techniques require inversion of R. This can be

obtained efficiently by PE

For finite length message a finite length PE series can synthesize R-1 exactly. However, in practice a truncated series must be used for continuous signaling

1

0

SNi

PE ii

w

L R R ˆPE PE yd L

Weightmultiplication

R

Weightmultiplication

R

y yR Weightmultiplication

2 yR

matchedfilterbank

( )r t

ˆPE PE yd L

y yR 2 yR

R

0w 1w 2w

0 10 1

0

ˆ ...S

S

S

NNi

PE i Ni

w y w y w y w y

d R R R R


Mathcad-example

1

0

SNi

ii

w

R R

iw2R

1 R

= series expansion of R-1 (to 2. degree)


Minimum mean-square error (MMSE) detector

Based on solving MMSE optimization problem with

that should be minimized This leads into the solution

One notes that under high SNR this solution is the same as decorrelating receiver

This multi-user technique is equal to MMSE linear equalizer used to combat ISI

PROS: Provides improved noise behavior with respect of decorrelating detector

CONS: Requires estimation of received amplitudes and

noise level Performance depends also on powers of

interfering users

2E[ ]d Ly

120

ˆ ( / 2)MMSE N d L y R A y


Successive interference cancellation (SIC)

1ˆ ( )bA t T 1 1( )bg t T

1( )ˆ bs t T( )br t T

MFuser 1 decision

bT

( )r t

1( )r t

1d

+

-

Each stage detects, regenerates and cancels out a user First the strongest user is cancelled because

it is easiest to synchronize and demodulate this gives the highest benefit for canceling out the

other users Note that the strongest user has therefore no use for this

MAI canceling scheme! PROS: Small HW requirements and large performance

improvement when compared to conventional detector CONS: Processing delay, signal reordered if their powers

changes, in low SNR:s performance suddenly drops

To

the

next

sta

ge

1d


Parallel interference cancellation (PIC)

spreader2

ˆ ( )bA t T

ˆ ( )K bA t T

1ˆ ( )bA t T 1

( )ii

s t

2

( )ii

s t

( )ii K

s t

-+

-

-

matchedfilterbank

decisions and

stage weights

( )br t T

1(1)d

2ˆ (1)d

ˆ (1)Kd

1(0)d

2ˆ (0)d

ˆ (0)Kd

amplitudeestimation

parallel summer

1( )ˆ bs t T

2 ( )ˆ bs t T

( )ˆK bs t T

With equal weights for all stages the data estimates for each stages are

Number of stages determined by required accuracy (Stage-by-stage decision-variance can be monitored)

ˆ ˆ( 1) ( )

ˆ( ( ))

m m

m

d y QAd

Ad QA d d z

y Ad QAd z

initialdata estimates

minimization tends to cancel MAI

( )

y I Q Ad z

d QAdA z


PIC properties

SIC performs better in non-power controlled channels PIC performs better in power balanced channels Using decorrelating detector as the first stage

improving first estimates improves total performance simplifies system analysis

Doing a partial MAI cancellation at each stage with the amount of cancellation increasing for each successive stage tentative decisions of the earlier stages are less

reliable - hence they should have a lower weight very large performance improvements have achieved

by this method probably the most promising suboptimal MUD

PIC

var

iati

ons


Benefits and limitations of multi-user detection

Significant capacity improvement - usually signals of the own cell are included

More efficient uplink spectrum utilization - hence for downlink a wider spectrum may be allocated

Reduced MAI and near-far effect - reduced precision requirements for power control

More efficient power utilization because near-far effect is reduced

If the neighboring cells are not included interference cancellation efficiency is greatly reduced

Interference cancellation is very difficult to implement in downlink reception where, however, larger capacity requirements exist (DL traffic tends to be larger)

PROS:

CONS:

Documents

Multi-user CDMA Enhancing capacity of wireless cellular CDMA