Efficient and robust detection of GFSK signals under dispersive channel, modulation index, and carrier frequency offset conditions

Gaussian frequency shift keying is the modulation scheme specified for Bluetooth. Signal adversities typical in Bluetooth networks include AWGN, multipath propagation, carrier frequency, and modulation index offsets. In our effort to realise a robust but efficient Bluetooth receiver, we adopt a high-performance matched-filter-based detector, which is near optimal in AWGN, but requires a prohibitively costly filter bank for processing of K bits worth of the received signal. However, through filtering over a single bit period and performing phase propagation of intermediate results over successive single-bit stages, we eliminate redundancy involved in providing the matched filter outputs and reduce its complexity by up to 90% (for K = 9). The constant modulus signal characteristic and the potential for carrier frequency offsets make the constant modulus algorithm (CMA) suitable for channel equalisation, and we demonstrate its effectiveness in this paper. We also introduce a stochastic gradient-based algorithm for carrier frequency offset correction, and show that the relative rotation between successive intermediate filter outputs enables us to detect and correct offsets in modulation index.