Interference Cancellation for MAC Using Quantized Feedback - Interference Cancellation Using Space-Time Processing and Precoding Design - page 57

√ 2

√ 2
2

H

= U H H V H = U H H

√ 2
2

√ 2
2

(4.31)

−

where U H is a complex matrix and H , V H are all real matrices. Then we can multiply

both sides of Eq. ( 4.29 )by U †
H

as follows

⎛ ⎞ ⎛ ⎞

( v g )

†

( v g )

†

( v g )

†

y 1 v h v h

E s U †

c 1

⎝ v g | ⎠ = ⎝ v g | v g | ⎠

| | |

U †
H

v g )

†
| v g |

H

†
| v g |

v g )

v h − ( v g )

†
| v g |

c 2

( (

y 2 v h

⎛
⎝

⎞
⎠ .

v g )

†

(

n 1

v g | |

U †
H

+ (4.32)

v g )

†

(

n 2

v g |

|

⎛ ⎞ ⎛ ⎞

( v g )

†
| v g |

( v g )

†
| v g |

( v g )

†
| v g |

n 1 v h v h

⎝ ⎠ ⎝ ⎠

In the above equation, U †
H

is still white noise and U †
H ( v g )

†
| v g |

( v g )

†
| v g |

− ( v g )

†
| v g |

n 2 v h v h

is real matrix. So if QAM is used, then we have

⎧
⎨

⎛ ⎞ ⎫

⎬

⎛ ⎞

†
| v g |

v g )

†
| v g |

v g )

†
| v g |

v g ) ( ( (

y 1 v h v h

E s U †

⎝ ⎠ ⎝ ⎠

U †
H

Real =

v g )

†

H

v g )

†

v h − ( v g )

†

⎩

(

⎭

(

y 2 v h

v g | v g | v g | | | |

⎧
⎨

⎛ ⎞ ⎫

⎬

v g )

†

(

Real

n 1

c 1

⎝ v g | ⎠

|

U †
H

· + Real (4.33)

v g )

c 2

†

⎩

(

⎭

n 2

v g | |

⎧
⎨

⎛ ⎞ ⎫

⎬

⎛ ⎞

( v g )

†

( v g )

†

( v g )

†

y 1 v h v h

E s U †

⎝ v g | ⎠ ⎝ v g | v g | ⎠

| | |

U †
H

=

Imag

†
| v g |

v g )

H

†
| v g |

v g )

v h − ( v g )

†
| v g |

⎩

(

⎭

(

y 2 v h

⎧
⎨

⎫
⎬

⎛
⎝

⎞
⎠

v g )

†

(

Imag

n 1

c 1 v g |

|

U †
H

· + Imag (4.34)

v g )

†

c 2 ⎩

(

⎭

n 2

v g | |

Therefore, we can use the Maximum-Likelihood method to decode the real parts
and imaginary parts of c 1 , c 2 separately. For example, when we detect the real parts

of c 1 , c 2 ,wehave