2.4 Modulated Signals 3higher or lower than the nominal carrier frequency for that bit period. Note that MSK is very similar to BFSK except that the two frequencies in MSK are spaced at half the separation compared to BFSK. This means that MSK is more spectrally ef-ficient than BFSK. Also, note that MSK is a form of continuous phase modulation. That means that there are no discontinuities in the phase of the transmitted wave-form (FSK has no such restriction). This modulation has many properties similar to BPSK and QPSK and will have a bit-error probability that is the same as QPSK as shown in Figure 2.16. 2.4.4 Quadrature Amplitude Modulation (QAM)Quadrature amplitude modulation (QAM) can be thought of as an extension of QPSK. In QAM, the symbols are distinguished by having both different phases and amplitudes. Thus, instead of four possible phases as in QPSK, a larger number of both phases and amplitudes are used to define which bit has been transmitted. Thus, rather than a constellation of four symbols, in QAM the constellation has 16, 64, 256, or more phase and amplitude locations corresponding to different bits being transmitted. The constellation for 16-QAM is shown in Figure 2.21. In 16-QAM, four bits are transmitted simultaneously for a spectral efficiency of 4 bits/sec/Hz. Similarly, 64-QAM and 256-QAM achieve a spectral efficiency of 6 and 8 bits/sec/Hz respectively. QAM has the advantage over MPSK in that for a given spectral efficiency, it will often achieve an equivalent bit error rate at a lower Eb/No. The probability of bit error for QAM is given by : -æöæö-æö»×ç÷ç÷ç÷èøèø-èø12222(1)3log ( ) 2,log1bbBooELLEPLQNLNL (2.107)where LM=, which is also the number of amplitude levels in one dimension. So for instance, in the case of 64-QAM, L = 16. The bit error rate can also be expressed as: -æöæö-æö»××ç÷ç÷ç÷èøèø-èø1222222(1)3log ( ) 21,log1logssBooELLEPLQNLNLL (2.108)The bit error probability is shown in Figure 2.22. Figure 2.21 Phase plot of a 16-QAM modulated signal.