Interference Cancellation for MAC Using Quantized Feedback - Interference Cancellation Using Space-Time Processing and Precoding Design - page 61

V †

λ Υ 1
1

0

Υ 1 Υ 1 V †

Υ 1 = U

Υ 1 =

U

Υ 1 .

(4.45)

Υ 1

λ Υ 1
2

0

Then ( 4.44 ) becomes

Υ 1 Υ 1 V †

2

| HU

1 |

= | λ Υ 1

) +| λ Υ 1
2

2

h 11 |

2

h 21 |

2 2

h 12 |

2

h 22 |

2

| ( | +| | ( | +| )

Υ

v h |

2 1

| ≥

L L

(4.46)

where

h 11

h 12

HU

Υ 1 =

. (4.47)

h 21 h 22

Since the unitary matrix U does not change the distribution of H , each element

Υ 1

Υ 1 , i.e., h ij , is also a Gaussian distributed random variable with mean 0 and
variance 1. As a result, ( 4.43 ) can be written as

of HU

| H

P ( d → d )

exp

4 L

1 2

( | λ Υ 1
1

2

h 11 |

2

h 21 |

2

≤ − | cos θ

hg |

| ( | +| )

2

+| λ Υ 1
2

2

h 12 |

2

h 22 |

2

| ( | +| )) | γ 1 + γ 2 | . (4.48)

Further, we have

P ( d → d )

E exp

4 L ( |

1 2

( | λ Υ 1
1

2

h 11 |

2

h 21 |

2

≤ − cos θ

hg |

| ( | +| )

+| λ Υ 1
2

2

h 12 |

2

h 22 |

2 2

| ( | +| )) | γ 1 + γ 2 | )

E E exp

4 L ( |

( | λ Υ 1
1

1 2 2

h 11 |

2

h 21 |

2

= − cos θ

hg |

| ( | +| )

hg

+| λ Υ 1
2

2

h 12 |

2

h 22 |

2 2 1

| ( | +| )) | γ 1 + γ 2 | ) | θ

⎡ ⎤

1

⎣ ⎦

≤ E (4.49)

j = 1 [

| λ Υ 1
j

+ ( 8 L |

1 2 2 2 2

1 cos θ

hg |

| | γ 1 + γ 2 | ) ]

At high SNRs, one can neglect the one in the denominator and get

|·| γ 1 + γ 2 | ) − 4 E

8 L − 4

2

1

1 ( | λ Υ 1

P ( d → d ) ≤ . (4.50)

j

1 8

| cos θ

hg |

j =