Adaptive Equalization for Wireless Channels - Adaptive Signal Processing in Wireless Communications - page 252

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FIgure 9.7 Diagram of the continual and staggered pilot tones (training) in the European
standard for Digital Video Broadcast. The column index k is the frequency or subcarrier index,
and the row index b is the block or symbol index. Shaded circles represent training data. The con-
tinual pilots are not regularly spaced in frequency; the full list is available in [49].

entire time-domain block contain training for any given frequency coefficient to be
considered known. In this case, a simple one-tap LMS or RLS adaptation rule can be
implemented for each FEQ coefficient. Similarly, one-tap DD-LMS and CMA rules can
be formed when training is not available. In vector form, the LMS, DD-LMS, and CMA
FEQ updates for an SCCP system are [50]

( )

    =     +         −    

µ  

*



d b + 1 d b y b F x b x b

LMS LMS

( )

   { } −    

    =     +    

µ  

* − 1

 

d b + 1 d b y b F Q F x b x b

DD DD

(9.18)

   ( )

    =     −    



*

d b + 1 d b µ y b  F e b

CMA CMA CMA


 


 

   ( )

*

   ( ) −    ( )     =

− 1



 

− 1

 

− 1

e b F x b Fx b γ Fx b ,

CMA

and the RLS FEQ update with forgetting factor ρ is

( )

   

    =     +        

1 iag  

*

r b ρ r b − y b y b

( )

   ( )

    =     +    

*

P b ρ P b − 1   y b F x b (9.19)

RLS     =        

d b

− rP 1

bb .

Due to the diagonal structure of r , the RLS update requires only marginally more com-
putations and converges much faster than LMS [50]; hence it is preferable of the two.