of trans- mission time interval, or time t. A binary phase shift keying (BPSK) signal constellation is illustrated in Figure 7.13 where the offset phase Q (t) = 0° denotes transmission of a 0 and Q (t) = 180° denotes transmission of a 1. The receiver again compares the received signal's phase against a boundary level, in this case amplitude = =0, and detects whether a 0 or a 1 was transmitted. Digital Modulation Amplitude (Quadrature) Amplitude (in-phase) (180°) Figure 7.13 BPSK signal constellation Modulated signal Figure 7.14 BPSK modulated signal Amplitude Amplitude (Quadrature) (Quadrature) Amplitude Amplitude (in-phase) (in-phase) (180°) (180°) Figure 7.15 BPSK signal with noise, and its distribution The transmitted signal for the same bit series as in the 2-ASK example is shown in Figure 7.14. Note that during each transmission time interval the signal phase indicates whether a 0 or a 1 is transmitted. In a manner similar to ASK, additive noise and interference result in erroneous detection of transmitted data. The addition of noise and the distribution of the received signal are shown in Figure 7.15. Again, some received signal points cross the detection boundary and therefore are detected erroneously. The probability of error is similarly calculated to that of ASK, taking the normal probability distribution and the area under the curve from -00 to 0. Similar to ASK, the PSK signal constellation can be designed to accommodate a number of phase levels to represent multiple bits in each transmission time interval. Figure 7.16 shows BPSK, 4-PSK (generally known as quadrature PSK or QPSK), 8-PSK and 16-PSK signal constellations. The axes are denoted as in-phase and quadrature (I and Q) to show the phase of the modulated signal. The in-phase axis represents the phase of a local oscillator which is Broadband Telecommunications Technologies and Management A(/2) -A () A (0) -((() A (0) -A(3/2) 8-PSK 16-PSK Figure 7.16 BPSK, QPSK, 8-PSK, and 16-PSK signal constellations 1.0E+00 1.0E-01 16-PSK 1.0E-02 8-PSK 1.0E-03 