Interference-Free Transmission for X channels - Interference Cancellation Using Space-Time Processing and Precoding Design - page 86

c 21 D 23

c 11 D 11

c 12

c 22

c 23

c 13

Receiver 1 Receiver 2

c 24

c 14

s 24

c 14

c 24

s 23

s 24

c 23

s 14

s 22

s 14 c 13

s 23 c 22

s 21

s 22 c 21

s 13 s 13

D 13 c 12

s 21

s 12

D 14 D 24

s 12

c 11

D 12 s 11

s 11

D 21

D 22

Fig. 5.6 Orthogonal structure when there are 3 receive antennas

G 1 B 2 ( H 1 A 2 (

1 ) = ω 1 ) (5.58)

G 2 B 2 ( † H 2 A 1 (

1 ) 1 ) = 0 (5.59)

G 2 B 2 ( † H 2 A 2 (

1 ) 1 ) = 0 (5.60)

1

B 2 (

2

|| 1 ) ||

F =

(5.61)

1 1 1

2 2 2

2 ( 1 + (β

21 )

+ (β

22 )

+ (β

23 )

)

Note that ( 5.58 ) contains three equations since it includes 3 1 vectors. Therefore, we

need to satisfy 6 equations. One of the unknowns is the parameter

×

. Thus, we need
at least 5 transmit antennas since each transmit antenna will lead to one unknown
parameter in the precoder matrix. To summarize, when M

ω

= ≥

3, we need N 5.

= ≥

Now we provide the complete precoder design procedure for M 3 and N 5:

1. At time slot 1, design precoder A 1 to make D 11 . Design precoder B 1 to

U H 1 ( 1 )

D 21 . Design precoder A 2 make D 12 ⊥ D 11 , D 22 || to make D 13 ⊥ D 11 , D 13 ⊥ D 12 ,

D 21 . Design precoder B 2 D 23 ⊥ to make D 14 || D 13 , D 24 ⊥ D 21 , D 24 ⊥ D 23 .

2. At time slot 2, design precoder B 1 . Design precoder A 1

to make D 12 U G 1 ( 1 )

D 22 . Design precoder B 2 to make D 14 ⊥

to make D 11 ⊥ D 12 , D 21 || D 11 , D 14 ⊥ D 12 ,

D 21 . Design precoder A 2

D 24 ⊥ to make D 13 || D 14 , D 23 ⊥ D 21 , D 23 ⊥ D 24 .

3. At time slot 3, design precoder A 2 . Design precoder B 2 to make D 23 U H 2 ( 1 )

D 13 . Design precoder A 1 to make D 11 ⊥ to make D 24 ⊥ D 23 , D 14 || D 13 , D 21 ⊥ D 23 ,

D 24 . Design precoder B 1

D 21 ⊥ to make D 12 ⊥ D 13 , D 12 ⊥ D 11 , D 22 || D 21 .

4. At time slot 4, design precoder B 2 to make D 24 . Design precoder A 2 to U G 2 ( 1 )

D 14 . Design precoder B 1 make D 23 ⊥ D 24 , D 13 ⊥ to make D 12 ⊥ D 13 , D 22 ⊥ D 24 ,

D 23 . Design precoder A 1 D 22 ⊥ to make D 11 ⊥ D 12 , D 11 ⊥ D 13 , D 21 || D 22 .

4, we can also align all the interference
along the same direction and use Scheme II to achieve our goal. However, we will

Here we need to point out that when M ≥