VTCSpring04presentation - Centre for Digital Signal...

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Unformatted text preview: Centre for Digital Signal Processing Research · Channel Shortening Filter Design Based on Polynomial Methods Cenk Toker 1 , Sangarapillai Lambotharan 1 , Jonathon A. Chambers 2 , Buyurman Baykal 3 1 Centre for Digital Signal Processing Research, King’s College London, UK 2 Cardiff School of Engineering, Cardiff University, Cardiff, UK 3 Dept. Elec. Eng., Middle East Technical University, Ankara, Turkey 18 May 2004 1/14 Centre for Digital Signal Processing Research 1 Introduction • Channel shortening is an important method to reduce the complexity of receiver structures. — In MLSD equalisers the complexity of the detector grows exponentially with the length of the channel, — In multicarrier based systems the length of the (cyclic) prefix is proportional to the channel length decreasing the throughput. • The basic idea is to compress the most of the energy of a wide-spread channel impulse response to a given limited length. • There are several criteria, we will use minimising the mean square error under the unit energy constraint. • Mostly FIR channel shortening filters are considered in the literature. • IIR channel shortening filter provides superior channel energy compression. • In spite of noise amplification, IIR filter outperforms its FIR counterpart in SINR performance. 18 May 2004 2/14 Centre for Digital Signal Processing Research 2 Notation, Definitions and Preliminary • Assume the polynomial of order nP ( q- 1 : backward shift operator (unit delay)) P ( q- 1 ) = p + p 1 q- 1 + · · · p np q- nP • Conjugate polynomial : (Conjugation and time reversal) P * ( q ) = p * + p * 1 q + · · · p * np q nP • Diophantine equation: ax + by = c — If t is a factor of a and b it must also be a factor of c , in order a solution exists a 1 tx + b 1 ty = c 1 t....
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VTCSpring04presentation - Centre for Digital Signal...

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