tted power is in the sidebands which convey the information. Compared with FSK and ASK which have only half of their power in the sidebands, this gives a 3dB advantage. Hence, the bit error probability is given by Equation 19.32. Consequently, for the same transmitted power, PSK gives a much lower error rate than FSK or PSK signals may have more than two levels. For example, a 4-level PSK signal uses four carrier phases, separated by 90°. It is therefore sometimes known as quadrature phase shift keying (QPSK). In order to transmit a binary baseband signal, a pair of binary digits is combined to form a 4-level signal (00, 01, 10, 11) corresponding to the four phases transmitted. At the receiver, each of the four output values is used to generate two consecutive binary output digits. By this means, the digit rate on the transmission path and the required bandwidth are halved. Alternatively, a higher digit rate can be achieved with a given bandwidth. Multiphase PSK in therefore used in digital radio sys- tems for terrestrial links (de Bellin, 1991) and for satellite communi- cation systems (Evans, 1987; Nouri, 1991). The penalty for the increased data rate obtained with multiphase PSK is a lower immunity to noise. Figure 19.7(a) shows that, for two phase PSK, an interfering voltage must exceed V before an Figure 19.7 Signal-space diagrams for pulse phase modulation: (a) binary PSK; (b) 4-phase PSK error can occur by detecting a '1' as '0' or vice versa. Figure 19.7(b) shows that, in four phase PSK, the tolerable interfering voltage is reduced by a factor of 1/V2, i.e. 3dB. This is a disadvantage in the case of impulsive noise, such as that encountered on some switched equivalent to two non-coherent ASK systems, SO a similar error rate telephone connections (Alexander et al., 1960; Williams, 1966). performance may be expected. It has been shown (Schwartz et al., However, the bandwidth required for four phase PSK is only half 1966) that the error probability is approximately given by Equation that for two phase PSK. C