Receiver structures for an optimal noncoherent receiver when a transmitted signal experiences a random frequency shift are derived. Error rate performance, obtained by simulation, is then developed and compared with the standard noncoherent correlator. Results indicate that 1) ignoring the frequency shift by using a standard noncoherent correlator leads to severely degraded performance relative to the optimal noncoherent receiver and 2) even the optimal noncoherent receiver accommodating a random frequency shift exhibits degraded performance as the unknown frequency range grows.

Continuous-phase frequency shift keying (CPFSK) is discussed and theoretical predictions for symbol error probabilities are derived, where the memory inherent in the phase continuity is used to improve performance. Previously known results concluded that binary CPFSK can outperform coherently detected PSK at high SNR. New results presented here show thatM-ary CPFSK outperforms more tranditionally usedM-ary modulation systems. Specifically, coherently detected quaternary CPFSK with a five-symbol interval decision can outperform coherent QPSK by 3.5 dB, and octal coherent CPFSK with a three- symbol decision can outperform octal orthogonal signaling by 2.6 dB at high SNR. Results for coherently detected and noncoherently detected CPFSK are derived. These performance improvements are estimates derived from symbol error probability upper bounds. Monte Carlo simulation was performed which then verified the results.