onsequently, in the case of white noise, 19.37. the noise power is reduced by 3dB and the error rates are the same. PSK requires a synchronous demodulator and synchronism is (19.37) often difficult to maintain, particularly at high carrier frequencies. It is especially difficult to maintain if the transmission takes place through a fading medium or if either the transmitter or receiver is in If the phase of the FSK signal is coherent, a lower error rate can a vehicle whose movement causes a Doppler shift of frequency. The be obtained at low input signal/noise ratios by using two coherent difficulty can be overcome by transmitting a pilot carrier or by using demodulators, with local carriers f and f2 respectively. Since this is a phase locked loop to control generation of the local carrier at the equivalent to a pair of coherent ASK systems, the error probability receiver (Viterbi, 1966). is the same and is given by Equations 19.23 and 19.27. The signal output voltage from a coherent demodulator is propor- tional to cos 0, where 0 is the angle between the incoming and local 19.3.3 Phase shift keying carriers (see Chapter 18). Any departure from 0 = 0 reduces the amplitude of the output signal from the demodulator. However, If phase modulation is used to transmit a digital signal, this is known there is no reduction in the noise output, SO there is an increase in as phase shift keying (PSK). If the signal is binary, the phase of the the error rate. Even if phase synchronism is correctly established carrier is shifted between two positions which are 180° apart. This initially, it may occasionally be lost. There can be a shift of 180° and is sometimes known as phase reversal keying (PRK). this results in a sign inversion of all the output data. If a binary baseband signal, Ym,with values of -1 and +1 is applied The need for accurate carrier recovery can be avoided by using to a product modulator to produce double sideband suppressed differential phase shift keying (DPSK). This does not require the carrier (DSBSC) mod