Optimizing Pulse Shaping Filter for DOCSIS Systems

Abstract

This paper proposes a cost efficient nearly linear phase approximation to an square root raised cosine (SRRC) pulse shaping filter that satisfies the out-of-band spectral constraints of DOCSIS down-stream channels. A nearly linear phase filter structure is converted to an SRRC filter using a weighted and sampled least-squares criterion to fit the magnitude and phase responses. To ensure stability, the search for optimum coefficients is constrained using the Steigliz–McBride (SM) and Gauss–Newton (GN) methods, which unfortunately also eliminates sets of stable coefficients, one of which could be and probably is the optimum. To expand the sets of coefficients that produce stable filters in the SM and GN methods, the transfer function is parameterized in a special way. The effectiveness of the proposed filter is verified and compared with other approaches.