s followed by the decoder. However, the decoder non coherent FSK, PSK and DPSK. These curves were obtained can be incorporated in the coherent demodulator of the receiver, as from Equations 19.27, 19.32, 19.36, 19.37 and 19.43. For compari- shown in Figure 19.8(b). This is known as differential phase shift son, the error probabilities for unipolar and bipolar baseband trans- keying (DPSK). Then, the output signal of the demodulator is s,(n) mission (from Equations 19.27 and 19.32) are also shown. = +1 if s (n) and s (n - 1) are represented by carriers of the same None of the modulation schemes, except PSK, gives as good an phase and sg(n) = -1 if the phase has shifted by 180° between S (n error performance as bipolar baseband transmission. Coherent ASK - 1) and S (n). However, the phase of S4 will only have shifted is 2 and FSK both achieve as good a performance as unipolar baseband transmission. Non coherent ASK and FSK are about 1 dB worse than has changed in polarity as a result of (n) = -1. Therefore Equation 19.42 is obtained. the corresponding coherent systems. DPSK is about 1 dB worse than (n) = - S1 (n) = Determination of the error probabilities for multilevel systems is more complex and will not be considered here. The reader is referred to Arthurs and Dym (1962), Bylanski and Ingram (1980) (n) = when (n) (19.42) and Taub and Schilling (1986). For 4-level systems, it is found that coherent FSK nearly equals the performance of PSK and ASK gives Although DPSK has the advantage of no errors due to loss of the worst performance (Bylanski and Ingram, 1980). For more than synchronism, the probability of error due to noise is greater than for four levels, a better performance is obtained by using the hybrid PSK. Each input digit to the demodulator contributes to determining modulation schemes described in the next section. Pulse code modulation 19/11 ASK (Noncoherent) FSK (Noncoherent) Baseband (Unipolar) ASK (Coherent) FSK (Coherent) Baseband (Bipolar) Figure 19.11 Signal-space diagram for eight state phase mo