Interference cancellation

1. A method implemented in an access point (AP) having antennas used in a wireless communications system including two first client devices each of which has M antennas and two second client devices each of which has N antennas, where M and N are even, the method comprising:

performing interference alignment (IA) in common vector spaces; and delivering M+N streams, wherein the two first client devices comprise a first uplink (UL) client device and a second UL client device and the two second client devices comprise a first downlink (DL) client device and a second DL client device, where M and N satisfy M≦N, wherein the delivering comprises:

receiving N/2 streams from each of the first and second UL client devices; and transmitting M/2 streams to each of the first and second DL client devices;

letting matrix A=[h 1 , . . . , h M , g 1 , . . . g N-M ] where H 12 =[h 1 , . . . , h M ] is a channel from the second UL client device to the first DL client device and H 11 =[g 1 , . . . , g M ] is a channel from the first UL client device to the first DL client device;

finding vectors w k that are in an intersection of images of transmit vector spaces at the first DL client device according to the following equation:

w

k

=

∑

i

=

1

M

⁢

⁢

∝

1

k

⁢

h

i

=

g

N

-

M

+

k

-

∑

i

=

1

N

-

M

⁢

⁢

β

1

k

⁢

g

i

generating full rank matrix C=[w 1 , . . . , w 2M-N ]; and

determining common vector spaces C 1 and C 2 as an inverse image of full rank matrix C in vector spaces of the first uplink (UL) client device and the second UL client device, respectively.

2. In a wireless communications system including a first uplink (UL) client device and a second UL client device each of which has M antennas, a first downlink (DL) client device and a second DL client device each of which has N antennas, and an access point (AP) having N antennas, where M and N are even and M and N satisfy M≦N, a method implemented in the first DL client device, the method comprising:

receiving M/2 streams from the AP, wherein interference alignment (IA) is performed in common vector spaces, and wherein M+N streams are delivered,

wherein the AP receives N/2 streams from each of the first and second UL client devices and transmits M/2 streams to each of the first and second DL client devices,

wherein the AP lets matrix A=[h 1 , . . . , h M , g 1 , . . . g N-M ] where H 12 =[h 1 , . . . , h M ] is a channel from the second UL client device to the first DL client device and H 11 =[g 1 , . . . , g M ] is a channel from the first UL client device to the first DL client device, finds vectors w k that are in an intersection of images of transmit vector spaces at the first DL client device according to the following equation:

w

k

=

∑

i

=

1

M

⁢

⁢

∝

1

k

⁢

h

i

=

g

N

-

M

+

k

-

∑

i

=

1

N

-

M

⁢

⁢

β

1

k

⁢

g

i

generates full rank matrix C=[w 1 , . . . , w 2M-N ], and determines common vector spaces C 1 and C 2 as an inverse image of full rank matrix C in vector spaces of the first uplink (UL) client device and the second UL client device, respectively.

3. In a wireless communications system including a first uplink (UL) client device and a second UL client device each of which has M antennas, a first downlink (DL) client device and a second DL client device each of which has N antennas, and an access point (AP) having N antennas, where M and N are even and M and N satisfy M≦N, a method implemented in the first UL client device, the method comprising:

transmitting N/2 streams to the AP, wherein interference alignment (IA) is performed in common vector spaces, and wherein M+N streams are delivered,

wherein the AP receives N/2 streams from each of the first and second UL client devices and transmits M/2 streams to each of the first and second DL client devices,

wherein the AP lets matrix A=[h 1 , . . . , h M , g 1 , . . . g N-M ] where H 12 =[h 1 , . . . , h M ] is a channel from the second UL client device to the first DL client device and H 11 =[g 1 , . . . , g M ] is a channel from the first UL client device to the first DL client device, finds vectors w k that are in an intersection of images of transmit vector spaces at the first DL client device according to the following equation:

w

k

=

∑

i

=

1

M

⁢

⁢

∝

1

k

⁢

h

i

=

g

N

-

M

+

k

-

∑

i

=

1

N

-

M

⁢

⁢

β

1

k

⁢

g

i

generates full rank matrix C=[w 1 , . . . , w 2M-N ], and determines common vector spaces C 1 and C 2 as an inverse image of full rank matrix C in vector spaces of the first uplink (UL) client device and the second UL client device, respectively.

4. A method implemented in a wireless communications system including two first client devices each of which has M antennas, two second client devices each of which has N antennas, and an access point (AP) having N antennas, where M and N are even, the method comprising:

performing interference alignment (IA) in common vector spaces; and delivering M+N streams,

wherein the two first client devices comprise a first uplink (UL) client device and a second UL client device and the two second client devices comprise a first downlink (DL) client device and a second DL client device, where M and N satisfy M≦N, wherein the delivering comprises:

transmitting N/2 streams from each of the first and second UL client devices to the AP; and transmitting M/2 streams from the AP to each of the first and second DL client devices,

letting matrix A=[h 1 , . . . , h M , g 1 , . . . g N-M ] where H 12 =[h 1 , . . . , h M ] is a channel from the second UL client device to the first DL client device and H 11 =[g 1 , . . . , g M ] is a channel from the first UL client device to the first DL client device; finding vectors w k that are in an intersection of images of transmit vector spaces at the first DL client device according to the following equation:

w

k

=

∑

i

=

1

M

⁢

⁢

∝

1

k

⁢

h

i

=

g

N

-

M

+

k

-

∑

i

=

1

N

-

M

⁢

⁢

β

1

k

⁢

g

i

generating full rank matrix C=[w 1 , . . . , w 2M-N ]; and determining common vector spaces C 1 and C 2 as an inverse image of full rank matrix C in vector spaces of the first uplink (UL) client device and the second UL client device, respectively.