GMSK linearization and structured channel estimate for GSM signals

GMSK is a spectrum-efficient modulation scheme, and it is adopted as the modulation standard of GSM systems. However, because of its phase modulation, Gaussian filtering, and partial response signaling properties, GMSK is not a linear modulation. We present a linear approximation of GMSK signals at T/2 fractional spacing. The partial response channel with a memory length of 3 symbol periods, which is the pulse-shaping function inherent in the GMSK modulation, can be clearly identified in this linear approximation. Further more, we use this partial response channel information in the estimation of the wireless channel, which includes the physical propagation channel and the modulation pulse-shaping function. Conventional channel estimators, e.g., correlator or least-squares estimator approaches, do not exploit the information of the pulse-shaping function which is known and available. Our proposed structured channel estimate is more accurate since we incorporate the knowledge of the channel structure in the estimation procedure. We compared the BER (bit-error-probability) performance of a GSM system with the structured and unstructured channel estimate, and simulation results show the improvement of a Viterbi equalizer in different test channels when a structured channel estimate is used.