A fast multi-level GFSK matched filter receiver

Near optimal reception of a multilevel Gaussian frequency shift keying symbol can be achieved using a matched filter bank (MFB) receiver, which will require M^(K+L-1) filters for M modulation levels, a K-symbol observation interval, and a Gaussian filter with an L-symbol support length. This is prohibitive for most applications for the large values of K necessary to ensure best performance. In this paper we present a recursive algorithm that eliminates redundancy in providing the matched filter outputs by use of a smaller set of 1-symbol long intermediate filters, followed by an iterative process to propagate phase gained over K successive single symbol stages. If exemplarily operated in a Bluetooth receiver, the computational cost can be reduced by two orders of magnitude. Additionally we demonstrate that the intermediate filter outputs provide a means to detect carrier frequency and modulation index offsets, which can be corrected by iteratively recomputing the coefficients of the intermediate filter bank.