Non-linear continuous phase modulation has constant envelope and spectral efficiency, which are desirable for public safety communication systems where both bandwidth and power are limited. A practical design of an innovation based receiver for partial response CPM was recently developed for public safety applications. It is in the form of a linear predictive demodulator with a coefficient look up table. The demodulator shows great performance over multipath fading channels without channel equalization and promises a significant contribution to public safety communication. The work in this thesis is focussed on developing and analyzing modern techniques to improve the receiver performance while maintaining a feasible implementation complexity. Suitable soft output algorithms are incorporated into the demodulator allowing a subsequent convolutional decoder to perform soft decoding. By modifying the design criteria of the predictive demodulator and introducing a feedback loop, an iterative detection scheme is formed for the concatenated structure of demodulator, deinterleaver and decoder. Spatial diversity combining techniques are summarized and a very low complexity combining scheme is developed. It selects the best received sample sequence by considering the average energy of each sequence. In addition, the demodulator is extended to have dual coefficient look up tables supporting its detection by having parallel prediction processes and combining their results. This leads to an improvement in overall demodulator performance. A theoretical proof that only half the number of coefficients need to be stored in memory is also given. Matlab simulations on a Rayleigh fast fading multipath channel have shown that the proposed techniques significantly improve the overall detection accuracy. Each of them provides a good gain in signal to noise ratio or delay spread and when combined, a significant performance gain is achieved.