Adaptive Opportunistic Beamforming in Ricean Fading Channels - Adaptive Signal Processing in Wireless Communications - page 186

N

∑ 1

( ) +

 ht

+ ( )

() = a exp jn θφ ( ) t Bt ( ), (7.15)

k k k k

n =

where

K
NK

a =

k

, (7.16)

k

( 1 + )

k

N

1

∑

( ) .

Bt () = bt ()exp( ) jn φ t (7.17)

k nk

NK ( 1 + )

k

n = 1

It is easy to show that B k ( t ) ~ C N (0,σ 2 ), where σ 2 = 1/(1 + K k ).
Let H k ( t ) denote the magnitude of ˜ k ( t ):

N

∑



Ht ht () = () = a exp( jn ( θφ + ( ))) t + Bt () . (7.18)

k k k k k

n = 1

Each user measures only H k ( t ) and then determines the data rate R k ( t ) at which the
data can be reliably transmitted from the base station to the user with a predetermined
SNR threshold. The determined rates R k ( t ) for all the users are fed back to the base sta-
tion. The requested rate R k ( t ) can be expressed as R k ( t ) = f ( H k ( t )), where f (·) is a non-
decreasing function, which can be assumed to be known at the base station. Hence, the
values of H k ( t ) are also assumed to be known at the base station in this section.
On the right-hand side of (7.18), the first term

∑

N

( )

+ ( )

a exp jn θφ ( ) t

k k

n = 1

is related to the LOS component and the second term B k ( t ) to the diffused component.
Let G k ( t ) denote the magnitude of the LOS component:

N

def

∑ θφ
1

( )

+ ( ) Gt () = a exp jn ( ). t (7.19)

k k k

n =

Then one can easily see that G k ( t ) is maximized with ϕ( t ) = -θ k and the maximum
value is a k . Motivated by this observation, the following adaptive opportunistic
beamforming algorithm is proposed to improve the performance [17]: