Efficient and Robust Detection of GFSK Signals under Dispersive Channel, Modulation Index, and Carrier Frequency Offset
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Efficient and Robust Detection of GFSK Signals under Dispersive Channel, Modulation Index, and Carrier Frequency Offset Conditions Charles Tibenderana Communications Research Group, School of Electronics and Computer Science, University of Southampton, SO17 1BJ, UK Email: [email protected]
Stephan Weiss Communications Research Group, School of Electronics and Computer Science, University of Southampton, SO17 1BJ, UK Email: [email protected] Received 30 March 2004; Revised 5 October 2004 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. Keywords and phrases: Gaussian frequency shift keying, Bluetooth, constant modulus algorithm, carrier frequency offset correction, modulation index offset correction.
1.
INTRODUCTION
Gaussian frequency shift keying (GFSK) is a bandwidth preserving digital modulation technique, which has been used for low-cost transmission standards such as Bluetooth [1]. Relative low cost makes Bluetooth an attractive alternative to expensive high-data-rate wireless local area network (WLAN) services such as IEEE 802.11b. Therefore, in this contribution we aim at deriving GFSK receivers for high integrity data transfer, which can enable their use in inexpensive standards similar to Bluetooth more efficiently. Maximum likelihood detection of a sequence of GFSKmodulated bits can be achieved by a Viterbi receiver, which correlates the received signal over a bit period with all possible alternatives, before deploying the Viterbi algorithm to penalise illegitimate phase transitions in the filter outputs [2]. However, the use of a Viterbi detector is limited to coherent detection of signals where the modulation index (h) used in the modulation process is a rational number, thereby
ensuring a finite number of states. In addition, the Viterbi receiver is very vulnerable to inaccuracies in the modulation index, whereby it has been shown to be robust to variations of about |∆h
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