Interference-Free Transmission for X channels - Interference Cancellation Using Space-Time Processing and Precoding Design - page 85

Receiver 1 Receiver 2

D

1
11

D

1
23

cccc , , ,

cccc , , ,

11 12 13 14

21 22 23 24

1
12

1
24

1 D D

2

3 4

Time slot 1

ssss , , ,

s sss , , , 11 12 13 14

21 22 23 24

cccc , , ,

cccc , , ,

ssss , , ,

11 12 13 14

ssss , , ,

21 22 23 24

21 22 23 24

11 12 13 14

D

1
21

3 4

1 2

D

1
13

D

1
14

1
22

D

DDDDDDDDDD 1

1 1

,

1 1

,

1 1

,

1 1

,

1 1

DDDDDDDDDD

1

,

1 1

,

1 1

,

1 1

,

1 1

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

2
11

D

2
23

D

cccc , , ,

cccc , , ,

21 22 23 24

11 12 13 14 2

24

D

D

2
12

2 1 4

3

s sss , , , ssss , , ,

Time slot 2

11 12 13 14 21 22 23 24

cccc , , ,

cccc , , ,

ssss , , ,

ssss , , ,

11 12 13 14

21 22 23 24

11 12 13 14

21 22 23 24

2
13

2
21

D 4 3 D 2 1

D

2
14

D

2
22

2 2 2 2 2 2 2 2 2 2

DDDDDDDDDD

2 2

,

2 2

,

2 2

,

2 2

,

2 2

DDDDDDDDDD , , , ,

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

3
23

D

3
11

D

cccc , , , cccc , , ,

11 12 13 14 21 22 23 24

3
24

3
12

D

D

3 4 1 2

ssss , , ,

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

1 2 D

3
14

D

3
21

3 4

D

3
22

DDDDDDDDDD

3 3

,

3 3

,

3 3

,

3 3

,

3 3

DDDDDDDDDD

3 3

,

3 3

,

3 3

,

3 3

,

3 3

23 21 23 22 23 24 24 21 24 22

12 14 12 13 12 11 11 14 11 13

4
23

4
11

D

D

cccc , , ,

cccc , , ,

11 12 13 14

21 22 23 24

4
12

4
24

D D

4 3

2 1

ssss , , ,

Time slot 4 ssss , , ,

11 12 13 14

21 22 23 24

cccc , , , cccc , , ,

21 22 23 24 11 12 13 14

s sss , , , ssss , , ,

21 22 23 24 11 12 13 14

4
13

4
21

D 2 1

4
14

D 4 3

4
22

D D

DDDDDDDDDD 4

4 4

,

4 4

,

4 4

,

4 4

,

4 4 4 4 4 4 4 4 4 4 4

DDDDDDDDDD , , , , 12 13 12 14 11 12 11 13 11 14

24 21 24 22 24 23 23 21 23 22

Fig. 5.5 Illustration of our precoding scheme at 4 time slots. The number in the circle denotes the
design order in each time slot

satisfy less number of constraints. Therefore, in order to find the minimum number
of needed transmit antennas, we only need to calculate how many transmit antennas
are needed to send S 2 without interference.
Assume that we have already finished the precoder design for C 1 , C 2 , S 1 . Then
as shown in Fig. 5.5 , at Receiver 1, we have D 11 and D 12 which are useful signals
and D 13 which is interference. At receiver 2, we have D 23 which is useful signal
and D 21 and D 22 which are interference and along the same direction. Now we
design precoder B 2 for codeword S 2 .FromFig. 5.5 , we know that we need D 14 ||

D 13 ,

D 24 ⊥ D 21 , D 24 ⊥ D 23 , i.e.,