Performance analysis of GMSK frequency detection with decision feedback equalisation in digital land mobile radio

The bit-error-rate (BER) performance of premodulation Gaussian filtered MSK (GMSK) using frequency detection (FD) in conjunction with 1 bit decision feedback equalisation (DFE) is theoretically investigated. The introduction of the premodulation filter causes severe intersymbol interference (ISI) in the waveform of the input to the FM modulator. DFE is used for reducing the ISI effect and therefore improving the BER performance. Applying the analysis to additive white Gaussian noise (AWGN) channels (no fading) shows that a 1-bit DFE attains about 8.5 dB E_b/N₀ improvement at BER = 10^-3 for the premodulation filter bandwidth-time product B_bT = 0.25 (typical for mobile radio applications) when the receiver predetection bandpass filter bandwidth-time product BT is optimised. It is shown that the effect of error propagation due to DFE is negligible and the exact BER can be well approximated by the BER that is obtained assuming the decision 1-bit prior is correct. The analysis is then extended to the case of Rayleigh fading channels. Both predetection and post-detection diversity reception are considered. When two-branch predetection maximal-ratio combining (MRC) is used, the 1-bit DFE attains about 6.3 dB E_b/N₀ improvement at BER = 10^-3 for B_bT = 0.25.