M-ary continuous phase frequency shift keying with modulation index 1/M

In the paper, two techniques for the detection of multilevel continuous phase frequency shift keyed signals with modulation index equal to the inverse of the number of levels (M-ary CPFSK) are described. The first technique is a noncoherent technique which is similar to the conventional differentially coherent detection method of DPSK and the error rate of this detector is equal to the error-rate in DPSK. The second technique is a coherent technique which utilises a coherent carrier, and the detection method is similar to the coherent detection and differential decoding of differentially encoded PSK. The error rate in this case is equal to the error rate in coherent-detection/differential-decoding of PSK. Finally, expressions are derived for the autocorrelation functions and the power spectral density functions of M-ary CPFSK. By numerical computation, it is shown that M-ary CPFSK have approximately the same autocorrelation function and approximately the same power spectral density function regardless of the number levels when M ¿¿ 4. The power spectral characteristics of M-ary CPFSK are compared with those of M-ary PSK.