Multi-User Receiver

서울대학교 이동통신연구실 이 광 복

Multi-User Receiver

• A Conventional receiver is designed for a AWGN channel, not a co-channel interference limited environment

• In a multiuser environment,

a conventional receiver is acceptable, if multiuser interference can be modeled as white Gaussian noise

- Energies of received signals are not dissimilar - Cross correlation of signature waveforms is low

Multi-User Receiver

Receiver Types

• Conventional receiver

• Multi-stage detection

• MMSE detection

• Optimum receiver

• Decorrelator

<Correlator type>

<Matched filter type>

Conventional Single User Receiver

  dt

) (t y

) (t

s (despreading sequence)

) ˆ( j b

Matched Filter

) (t

y bˆ( j)

matched f ilter coef f icients : despreading sequence

sync

Conventional Multi-User Receiver

Matched filter user 1

Sync 1

 

b j₁



 

b₂ j Matched 

filter user 2

Matched filter user K

Sync 2

Sync K

 j b_K









 )

(t y

• Asynch.

• Synch.

• Crosscorrelation is not zero

• IS-95 downlink, uplink

• power control

• Walsh sequence

Conventional Receiver : Issues

(Two user case)

) ( ) (

) ( )

( ) ( )

(t b₁ i s₁ t iT ₁ b₂ i s₂ t iT ₂ n t y

M

M i M

M

i

 





















  

) ( ) (

) ( )

( ) ( )

(t b₁ i s₁ t iT b₂ i s₂ t iT n t y

M

M i M

M

i

 



















 

) (t y

)

1(t s

dt t s t n dt

iT t s iT t s i b i

b₁( )^ ₂( )



₁( ^ ) ₂( ^ ) ^



( ) ₁( )

Multi-stage Receiver









) (t r

)

1(t r

)

1(t s

)

2(t r

)

2(t s )

1(t

b b₂(t)

)

3(t

 r







Multi-stage Receiver (Cont’d)

Matched Filter

User 1



Matched Filter

User 2



w1



w2













  



  



  



  



MMSE Receiver

~r i

b g

w~₁ r t

b g

?

^{b i$1}

b g

30^

45^

~ :s₂ 1 , 2

1 2

F HG I

KJ

~:s₁ 1, 2

3

 2

F HG I

KJ

w~₁

Find minimizing^w~1

E b i

L e

₁

b g b g

^ b i₁

j

² E b i

c

₁

b g

r ^T

b g

i w₁

h

²

NM O

QP

^{ }

$ ~ ~

No a priori knowledge required

Adaptive signal processing approach

ML receiver

Prob

c h

r d_i ^

F

^

b

r ^ d_i

g

HG I

1

KJ

2

1 2

2 2

2

 ^exp 

Choose “d_i” which maximizes prob(r|d_i) (Ex) 2users

Possible Tx Signals: (3,1), (3,-1), (-3,1), (-3,-3) Rx Signal Likely Tx signal

4 (3, 1) 2 (3, -1) -2 (-3, 1) -4 (-3,-1)

• Asynchronous two-user case

Find b₁(i) & b₂(i) for i=-M,…M which minimizes

 

²

   

²

1 M

k k k

k i M

r t b i s t iT  dt

 

    

 



 





• Synchronous two-user case

Choose b₁(i) & b₂(i) which minimizes

r t b i s t b i s t dt

iT i T

b g b g b g b g b g

c h

b g^  

z

^{1 1 1 2 2 2}

• Received signal for a two user case

  1  1  2   2   

M M

i M i M

r t b i s t iT b i s t iT n t

 





 



 

     

   

   

2

1 2 1

0

1 2

1 1 2 2

, : Spreading waveforms, 1

, : Symbol sequences

, , , , : received energy per bit

Tb

k

s t s t s t dt

b i b i

    



 



Decorrelating receiver

  ^{ }    

  ^{ }      

1

1 1

1

1 2 2 1

+ noise term

i T iT

i T iT

y i r t s t iT dt

b i b i s t iT s t iT dt





 

   



 

   

     

     

1 2

0

1 1 2

2 2 1

noise term noise term

T s t s t dt y i b i b i y i b i b i









  

  



iT

user 1

user 2 b i₁b g

b i₂b g

(i1)T

    

 

 

 

   

     

     

 

     

1 1

1

2 2 2

1 1

1

2 2 2

1 1

1 , , ,

1

b i n i

y i

y i b i n i

b i n i

H y i y i b i n i

y i b i n i

y i H b i n i









   

      

   

     

     

   

 

 

           

       

  

• Synchronous case

~ ~ ~ ~

~ ,

~ ~ ~

y i H b i n i n i

b i H y i

b g b g b g b g b g d b g b g i b g

  

 ^

0

0 ¹ Ignoring

z

Hb g0 ¹

c h^{ b i1}b g

b i₂b g

z

~

~

sgn ~

sgn ~ ~

H

b i y i

y i

y i y i

y i y i

b i H y i

0 1

1

1

1 1

1

1

1

1 1

0

1

12 2

12 12

12 2

12 12

1

2 12

2

1 12 2

12 1 2

1

d b g i

b g b g

b g b g b g

b g b g d i b g d b g i b g





 





L NM O

QP

 





L NM O

QP L

NMM O

QPP

^{ }



 

L NMM O

QPP



FH IK











 



