TABLE OF CONTENTS A number of digital modulation techniques have found applications in communications satellite systems. Binary and four-state modulation techniques are more power efficient than the higher-state or higher-ary (8-state, 16-state, ) modulated systems, and for this reason have been more frequently employed. The two and four-state power-efficient systems have a satisfactory probability of error, P e, performance, even if the received carrier-to-noise, C/N, ratio is relatively low. For equal-performance smaller earth station antennas, less satellite power and systems having a higher noise figure can be employed if two- or four-state systems are used. Unfortunately, powerefficient modulation-demodulation (modem) systems are not as bandwidth efficient as the higher-ary modulated systems. Bandwidth efficiency is frequently expressed in terms of the number of transmitted bits/second/hertz (b/s/Hz).
Power efficiency may be expressed in terms of the C/N required to have an acceptable P e performance. This efficiency is also defined in terms of the required average received bit energy-to-noise density ratio for a given P e ; that is, P e = f(E b /N o ). ( Note: If the noise is specified in a bandwidth which is equal to the bit rate, then E b /N o= C/N.) For the linear additive white Gaussian noise (AWGN) channel we define a modulation method as power efficient if to obtain a P e=10 ?8 an Eb/N o<14 dB is sufficient. We define a modulation technique as spectrally efficient
