Interference Cancellation and Detection for MAC with Two Users - Interference Cancellation Using Space-Time Processing and Precoding Design - page 19

respectively. We follow the steps in Sect. 2.1 to design the precoders.
Step 1 : Deriving the equivalent channel equations:
At time slot i , the signal model can be written as

E s HA i C E s GB i S

y i W i

= ( i ) + ( i ) +

E s H i C E s G i S

W i

= ( i ) + ( i ) + (2.80)

where H i and G i denote the equivalent channel matrices for Users 1 and 2 at time
slot i , respectively. Combining channel equations at the first N time slots, we have
⎛ ⎞

y 1
y 2
y 1
y 2
y 1
y 2

⎛ ⎞

− H 1 ) H 1 ) ··· H 1 − G 1 ) G 1 ) ··· G 1

⎝ ⎠

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

⎝ ⎠

H 2

) − H 2 ) ··· H 2 ) G 2 ) − G 2 ) ··· G 2

E s

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

=

. . . . . .

. . . . . .

H N

) H N ) ··· − H N ) G N ) G N ) ··· − G N ( 1 ( 2 ( N ( 1 ( 2 ( N )

⎛
⎝

⎞
⎠

c 1
c 2
c N
s 1
s 2
.
s N

⎛
⎝

⎞
⎠

n 1
n 2
n 1
n 2
n 1
n 2

× + (2.81)

Here we let

⎛
⎝

⎞
⎠

− H 1 ) H 1 ) ··· H 1 − G 1 ) G 1 ) ··· G 1

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

H 2

) − H 2

H 2 G 2

) − G 2

G 2

( 1 ( 2 ) ··· ( N ) ( 1 ( 2 ) ··· ( N )

H

= (2.82)

. . . . . .

. . . . . .

H N H N

) ··· − H N ) G N

G N

) ··· − G N

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

Step 2 : Creating the orthogonal structure of signal vectors:
Let

A i A i A i A i

( ) = ( ) = ( ) = ··· = ( )

1 2 3 N (2.83)

B i B i B i B i ( 1 ) = ( 2 ) = ( 3 ) = ··· = ( N ) (2.84)

Equations ( 2.83 ) and ( 2.84 ) will result in