Multi User Detection

7/28/2019 Multi User Detection

1/75

Dec. 06, 2004 Mohit Garg ISTE-STTP, TSEC First Prev Next Last Go ToFull Screen Quit

Multiuser Detection

Mohit Garg

([email protected])

Under the guidance ofProf. U. B. Desai

SPANN Lab

Department of Electrical EngineeringIIT-Bombay

Group Members: Prof. S. N. Merchant

Aditya Dua, Ritesh Sood, Prateek Dayal, Umesh Nimbhorkar
http://lastpage/http://lastpage/http://fullscreen/http://fullscreen/http://quit/http://quit/http://quit/http://fullscreen/http://lastpage/


2/75


Outline ...

Recapitulating CDMA

Standard single user detector Optimum multiuser detector Non-optimal multiuser detectors

An adaptive Minimum Probability of Error based multiuser detector pro-posed by our group


3/75


Code Division Multiple Access (CDMA)

All users transmit at the same time and across the entire frequency band

Users separated on the basis of their signature waveforms

sk(t) The signature waveforms may be Orthogonal

Non-orthogonal

Orthogonal CDMA does not give any capacity improvement over TDMA

or FDMA in a cellular system

No. of orthogonal signature waveforms is limited!

Non-orthogonal CDMA is therefore used
http://prevpage/http://prevpage/http://lastpage/http://lastpage/http://fullscreen/http://fullscreen/http://quit/http://quit/http://quit/http://fullscreen/http://lastpage/http://prevpage/


4/75


5/75


6/75Dec. 06, 2004 Mohit Garg ISTE-STTP, TSEC First Prev Next Last Go ToFull Screen Quit

The Single User Detector . . .

The simplest way: Apply a bank of matched filters, one for each user, to the

received signal

Demodulate all users independent of each other Consider the first time interval (i = 0) and the jth user,

r(t) = Ajbjsj(t) + Kk=1k=j

Akbk(i)sk(t)

+ n(t), 0 t < Tb= Signal + M AI + Noise

(6)

Multiple Access Interference (MAI) In-band interference unlike noise which is wideband

Cannot be rejected through a band-pass filter

Occurs in different forms in other systems also e.g. Multi-Carrier in-

terference in OFDM


7/75


8/75



Issues with the Single User Detector

+ Simple to implement

+ Does not require knowledge of the channel or the user amplitudes

Multiple Access Interference (MAI) Kk=1k=j

Akbk(i)kj

Gives non-zero probability of error even with zero noise due to MAI Near-Far Effect: Strong users overwhelm the weak ones. Thus stringent

power control is necessary

The single user detector forms the core of almost all CDMA handsets currently in use



Optimality of the Single User Detector

The matched filter is optimum only for AWGN interference The MAI term is not Gaussian in general

But can be approximated by a Gaussian random variable for large no.

of users Central Limit Theorem

Even if the MAI was Gaussian, the single user detector is still not optimum yj is not a sufficient statistic for bj

But [y1, . . . , yK]T is a sufficient statistic for [b1, . . . , bK]T

The single user detector would have been optimum Ifij = 0

i, j



Therefore,

Multiuser Detection!



Multiuser Detection

It is clear that the single user detector is not optimum

The optimum detector should take into account the information available inall yks to estimate the bit of a particular user This is known as Multiuser Detection and was proposed by Sergio Verdu in

early 1980s.

Any multiuser detector will utilise the information available in the MAI

term to demodulate the user and will not treat it like a noise term

Processing the interference term to extract useful information

Ideologically similar to utilising multipaths for diversity!
http://prevpage/http://prevpage/http://nextpage/http://nextpage/http://lastpage/http://lastpage/http://fullscreen/http://fullscreen/http://quit/http://quit/http://quit/http://fullscreen/http://lastpage/http://nextpage/http://prevpage/



Individually Optimum Multiuser Detector

Consider the simple 2-user case

r(t) = A1b1s1(t) + A2b2s2(t) + n(t), 0 t < Tb (10) The optimum estimate ofb1 will minimise the probability of error It is obtained by choosing b1 {1, +1} such that the aposteriori proba-

bility P(b1

|r(t), 0

t < Tb) is maximised.

Similarly for user 2, i.e. we need to choose b2 such that P(b2|r(t), 0 t

||y||2y


48/75


Reducing Complexity Further . . .To further reduce the computational cost we consider:

MPOE Implementation using ISI Cancellation: Efficient MJPOE Minimizing the probability of error for each user separatelyMCPOE


49/75


Efficient MJPOEA proposed modification to the MJPOE algorithm proposed will now be dis-

cussed which

Reduces the computation allowing pre-computation of weights Weight computation is now done on channel variation timescales rather than

symbol timescales

Improves the BER performance Using the same signal model as before, the received signal at thepth antenna

can be written as

rp(i) = SpLAb(i 1) + SpRAb(i) + np

Demodulation


50/75


Demodulation

The receiver structure consists of a linear filter.

Augmented received vector r = [rT1 , . . . , rTP]

T (N P 1) Weights for the kth user, wk = [w

Tk1, . . . ,w

TkP]

T (N P 1) . Filter Output at the ith bit interval is

yk(i) = wH

kr(i)

=

Pp=1

wHkprp

=P

p=1 wHkpSpLAb(i 1) +P

p=1 wHkpSpRAb(i) + wHk n The Decision Rule is

bk = sgn[

(yk)]

Modification


51/75


Modification

E(

[yk]) =

[k]

= 0

Hence, a threshold of0 is not optimum Subtracting an estimate of this term from yk, we obtain the proposed deci-

sion statistic zk

zk = yk kwhere,

k =

P

p=1 wHkpSpLAb(i 1) Since, E([zk]) = 0, we get the proposed decision rule as

bk = sgn[(zk)]


52/75


Modification . . .

Some observations on the proposed demodulation scheme Does not involve any ISI term. Thus, we can pre-compute the weights

for MJPOE

(Cannot pre-compute for MCPOE since it requires training)

E([zk] ) = 0, which is the decision threshold. Thus, reduction inBER is expected

Simulation results support the claim


53/75


MCPOE: Conditional Probability of Error


54/75


MCPOE: Conditional Probability of Error

If bits +1 and -1 are equiprobable, the probability of error for the

k

th user,

conditioned on the transmitted bit vector b given by :

Pk|b =1

2P((yk) < 0|bk = 1) + 1

2P((yk) 0|bk = 1)

Density function ofyk conditioned on b given by:f(yk)|b(y|b) =

1

k

2exp

(y k)

2

22k

where:

k = k + Pp=1

wHkpSpRAb

k = wHk wk


55/75


Conditional Probability of Error . . .

Let k = k|1 when bk = 1 and k = k|1 when bk = 1

k|1 = k + Pp=1

wHkp Ki=1

i=k

Aibi

Mm=1

aim,pgimsiL(nim) + Ak

Mm=1

akm,pgkmskL(nkm)

k|1 =

k +

P

p=1wHkp

K

i=1i=k AibiM

m=1aim,pgimsiL(nim) Ak

M

m=1 akm,pgkmskL(nkm)


57/75


Figure 3: Schematic of the Space-Time MCPOE Adaptive Detector


58/75


MCPOE Adaptive Algorithm MCPOE : Minimum Conditional Probability of Error Minimizes probability of error for each user (conditioned on

transmitted bit vector) individually

Training sequence required for adaptation Gradient descent based adaptation of filter weights Ifw(i)k denotes the filter for detecting the kth user during the ith bit interval,

then :

w(i+1)k = w

(i)k Pk|bwk wk=w(i)k


60/75


MCPOE Adaptive Algorithm . . .

Define ukp = k|1wkp

and vkp = k|1wkp

uk = [uHk1, . . . ,uHkP]H and vk = [vHk1, . . . ,vHkP]H

ukp = SpLAb(i 1) +K

j=1j=k

Ajbj

M

m=1 ajm,pgjms(njm)jR + AkM

m=1akm,pgkms(nkm)kR vkp =

SpLAb(i 1) + Kj=1

j=k

Ajbj

Mm=1

ajm,pgjms(njm)jR Ak

Mm=1

akm,pgkms(nkm)kR

wk

k|1k

= wk2uk k|1wkwk3/2

wk

k|1

k

=

wk2vk k|1wkwk3/2


61/75


MCPOE Adaptive Algorithm . . .Blind Version

MCPOE requires a training sequence in adaptation mode We tried to make it blind by conditioning the probability of error

expression on the output of a matched filter rather than on the

training bits

Convergence rate not affected by the modification

Slight degradation in BER performance Similar modification works poorly for other training based adaptivedetectors such as LMS and RLS


62/75


Figure 4: Schematic of the Blind MCPOE Adaptive Detector : Output of Matched filter Bank used as training bits


63/75


Simulation Results

Results for both synchronous and asynchronous multipath channels (with

multiple antennas)

BER performance compared with non-adaptive MMSE Convergence rates compared with training based LMS and RLS

Flat Rayleigh faded channel assumed for simulations


64/75

Dec. 06, 2004 Mohit Garg ISTE-STTP, TSEC First Prev Next Last Go ToFull Screen QuitFigure 5: Convergence curves for training based LMS and RLS (Multipath)


65/75

Dec. 06, 2004 Mohit Garg ISTE-STTP, TSEC First Prev Next Last Go ToFull Screen QuitFigure 6: Convergence Curves for MJPOE (Multipath)

100

Convergence Curves at 15dB Transmit SNR

Theoretical Probability of Error: MJPOE


66/75


0 50 100 15010

3

102

101

No. of Iterations

Prob.ofEr

ror(on

logscale)

Theoretical Probability of Error: MJPOETheoretical Probability of Error: Efficient MJOPE

Figure 7: Convergence performance comparison of MJPOE and Efficient MJPOE, K = 4, M = 3, N = 15, P = 4


67/75


Figure 8: Schematic of the Diversity Combining MCPOE Adaptive Detector


68/75


Figure 9: Convergence Curves for Training Based MCPOE (Multipath)


69/75


Figure 10: Comparison of MCPOE and Non-Adaptive MMSE (Multipath)


70/75


Figure 11: BER performance comparison of MJPOE, MCPOE and MMSE

100 Prob. of Error Vs. SNR

Simulated Recursive Least Squares (RLS)


71/75


0 2 4 6 8 10 1210

4

103

102

101

Transmit SignaltoNoise Ratio (SNR) (in dB)

Prob.ofEr

ror(on

logscale)

Simulated Recursive Least Squares (RLS)Theoretical Prob. of Error: MJPOETheoretical Prob. of Error: Efficient MJPOESimulated Prob. of Error: Efficient MJPOE

Figure 12: BER performance comparison of MJPOE and Efficient MJPOE, K = 4, M = 3, N = 15, P = 4


72/75


Figure 13: Effect of number of antennas on performance of MJPOE, for a fixed number of multipaths


73/75


Conclusion

+ MPOE based adaptive multiuser detection algorithms were proposed

+ Performance better than MMSE based approaches

+ Similar to the optimum multiuser detector without the overhead of expo-nential computation at each bit interval

High computational complexity

Work has been extended to OFDM-SDMA and MC-CDMA with encourag-ing results

References


74/75


Sergio Verdu, Multiuser Detection, Cambridge University Press, 1998.

Aditya Dua, U.B. Desai and R.K. Mallik, Minimum probability of error-based methods for adaptive multiuser detection in multipath DS-CDMA

channels, IEEE Transactions on Wireless Communications, May 2004.

R. Sood and U. B. Desai, Minimum probability of error demodulation for

multipath OFDM-SDMA systems, IEEE International Conference on Com-

munications, Jun. 2004.

P. M. Dayal, U. B. Desai and A. Mahanta, Minimum conditional probabil-ity of error detection for MC-CDMA, IEEE International Symposium on

Spread Spectrum Techniques and Applications, Aug. 30-Sept. 2 2004.

Mohit Garg, Umesh Nimbhorkar, U. B. Desai and S. N. Merchant, Efficientminimum probability of error demodulation for DS-CDMA systems, To ap-

pear in IEEE Wireless Communications and Networking Conference, Mar.

2005.

Prof. U. B. Desai

[email protected]

SPANN Lab

Dept. of Electrical Engineering


75/75


p g g

Indian Institute of Technology - Bombay

Mumbai 400076

Mohit Garg

[email protected]

Dept. of Electrical Engineering

Indian Institute of Technology - Bombay

Mumbai 400076

Documents

Multi User Detection