Multiplicative FIR Filtering Approach For Equalization of Bandlimited Channels
Charan Litchfield · SoutheastCon 2022 · 2022
This paper presents a computationally efficient equalizer for application in dispersive communication channels. While equalization is well understood in context of Finite Impulse Response (FIR) channel models the approach in this paper differs from conventional FIR forms offering greatly reduced multiply-add complexity (up to 50%) and improved round-off noise performance (∼ 15% for 6 bit precision and greater for lower resolutions). In this paper we show that the L − stage Multiplicative Finite Impulse Response (MFIR) approach with a single adder and multiplier can accurately approximate a real pole of an equalizer (with appropriate zero locations) to the same level of a standard FIR filter with N =2Ltaps. Typical dispersive channel models will invariably yield more than one real pole (or complex conjugate poles) and we investigate the application of approximating more than one pole. It is apparent, in order to keep complexity of the MFIR implementation below that of the well known Transversal FIR filter approach to equalization, that the number of poles, M, modelling an ideal equalizer must necessarily satisfy $M \leq \left\lfloor {\frac{N}{L}} \right\rfloor $ otherwise it is suggested to utilize a Transversal FIR filter structure due to similar levels of computational complexity.