Simple coherent receivers for partial response continuous phase modulation

By using a pulse amplitude modulation representation of the binary continuous phase modulation signals, we develop a new optimum Viterbi sequence detector and a near optimum Viterbi receiver with low complexity. Also, for the modulation index 0.5 where a linear receiver can be used, a minimum mean-squared error linear receiver filter is derived. Their performance is analyzed. The Gaussian minimum shift keying signal (GMSK) is used for illustration. It is shown that a GMSK receiver consisting of two matched filters and a four-state Viterbi algorithm performs with less than 0.24 dB degradation compared with the optimal receiver. The linear receiver is optimum for all values of E , / & (bit energy to noise one-sided spectral density ratio). A design method for its receiver filter is given. The filter is equivalent to a cascade of a matched filter and a Wiener filter estimator. Both an upper and a lower bounds for the bit-error probability are calculated. Simulation results which confirm the analysis are also given.