Interference-Free Transmission for X channels - Interference Cancellation Using Space-Time Processing and Precoding Design - page 81

Receiver 1 Receiver 2

1
11

D

1
24

D

cccc , , ,

s sss , , , 11 12 13 14

21 22 23 24

D

1
12

1
23

D

Time slot 1

ssss , , ,

cccc , , ,

11 12 13 14

21 22 23 24

cccc , , ,

cccc , , ,

s sss , , ,

11 12 13 14

ssss , , ,

21 22 23 24

21 22 23 24

11 12 13 14

1
21

D

D

1
13

D

1
14

1
22

D

1 1 1 1 1 1

DDDDDD , ,

DDDDDDDDDD

1 1

,

1 1

,

1 1

,

1 1

,

1 1

11 13 11 14 11 12 24 21 24 22 24 23 23 21 23 22

2
11

D

D

2
24

cccc , , ,

ssss , , ,

11 12 13 14 21 22 23 24

D

2
23

2
12

D

ssss , , ,

cccc , , ,

Time slot 2

11 12 13 14

21 22 23 24

ssss , , , s sss , , ,

cccc , , ,

cccc , , ,

21 22 23 24

11 12 13 14

11 12 13 14

21 22 23 24

2
14

2
22

D D

D

2
21

2
13

D

2 2 2 2 2 2

DDDDDDDDDD

2 2

,

2 2

,

2 2

,

2 2

,

2 2

DDDDDD , ,

24 21 24 22 23 24

11 13 11 14 11 12 12 13 12 14

3
23

D

3
12

ssss , , , D

cccc , , , 11 12 13 14

21 22 23 24

D

3
11

D

3
24

cccc , , ,

ssss , , ,

Time slot 3

11 12 13 14

21 22 23 24

cccc , , ,

cccc , , ,

ssss , , ,

11 12 13 14

21 22 23 24

ssss , , , 21 22 23 24

11 12 13 14

3
13

D

3
14

3
21

D D

D

3
22

3 3 3 3 3 3

3 3 3 3 3 3 3 3 3 3

DDDDDD , ,

DDDDDDDDDD , , , , 23 21 23 22 23 24

12 14 12 13 12 11 11 14 11 13

4
12

4
23

D D

ssss , , ,

cccc , , ,

D

4
24

D

4
11

11 12 13 14

21 22 23 24

cccc , , , s sss , , ,

Time slot 4

11 12 13 14 21 22 23 24

ssss , , ,

ssss , , ,

cccc , , ,

11 12 13 14

21 22 23 24

cccc , , ,

21 22 23 24

11 12 13 14

D

4
14

D

4
22

4
13

4
21

D D

DDDDDD

4 4

,

4 4

,

4 4

DDDDDDDDDD

4 4

,

4 4

,

4 4

,

4 4

,

4 4

12 13 12 14 11 12 23 21 23 22 23 24 24 21 24 22

Fig. 5.4 Illustration of our precoding scheme at 4 time slots

V H 1 H 1 U † H 1 , V H 2 H 2 U † H 2 ,

H 1 = H 2 =

V G 1 G 1 U † V G 2 G 2 U †

G 1 =

G 1 ,

G 2 = (5.49)

G 2

where U H 1 ( denote the eigenvectors corresponding to

the largest eigenvalues of H 1 , H 2 , G 1 , G 2 , respectively. Also we use x 1

1 ) , U H 2 ( 1 ) , U G 1 ( 1 ) , U G 2 ( 1 )

x 2 to denote
that vector x 1 has the same direction as vector x 2 . As shown in Fig. 5.4 , our precoder
design procedure can be summarized as follows:
1. At time slot 1, design precoder A 1 . Design precoder B 1 to make D 11 U H 1 ( 1 )

D 11 . Design precoder A 2 to make D 13 ⊥ to make D 12 ⊥ D 11 , D 13 ⊥ D 12 , D 23 ⊥ D 21 ,