Turbo equalizer detection for GFSK digital FM signals

We propose a turbo equalization scheme for GFSK signals with frequency detection. Although the channel is AWGN, there exists severe ISI in the received signal due to the premodulation Gaussian baseband filter in the transmitter as well as the narrowband IF filter in the receiver. We regard them as a real number inner convolutional encoder. At the same time, a recursive systematic convolutional (RSC) encoder can be used as an outer encoder. At the receiver side, the inner ISI equalizer and the outer RSC decoder are serially concatenated with an interleaver, to be iteratively decoded using a MAP (maximum a posteriori) algorithm or SOVA (soft-output Viterbi algorithm) with SISO (soft input/soft output). Through computer simulations, the proposed system shows BER=10^-5 at E_b/N₀=7.3 dB, when we take BT=0.6 (IF filter bandwidth multiplied by symbol duration time) with the RSC code having the coding rate of R=1/2 and the constraint length of K=7, and the iteration number of 3. This means 2.9 dB improvement compared with the conventional concatenation scheme of an ISI equalizer with a hard decision Viterbi decoder.