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excellent protection against noise because the information is contained withinits phase. Noise mainly affects the amplitude of the carrier.In the M-PSK schemes, the phase of the carrier takes on one of Mpossible values or symbols. The (stream of ) input binary data is first dividedinto b-bit blocks. Each block is transmitted as one of M possible values orsymbols. Each symbol is a carrier frequency sinusoid having one of Mpossible phase values spaced 2p=M apart. Then, for the nth M-tuple say,the M-PSK phase of (3.1) will exist in all intervals:f n 2 0; 2pM ; 4p 2ðM; ...; 1Þp M MTo ensure that each transmitted binary digit contains an integral number ofcycles, the unmodulated carrier frequency f c ¼ k c =T s ; where k c is a fixedinteger. For example, if the amplitude of (3.1) has a plus or minus unity value,that is, A ¼1, then k c ¼ 2. A pair of signals that differ in phase by 180 isreferred to as antipodal signals.For M-PSK, a symbol durationT s ¼ T b log 2 M¼ bT bð3:2Þproviding there is no reduction in information throughput, where T b is theinput binary interval.From this M-PSK generalization, one can derive the most importantmodulation schemes used in satellite communications: BPSK, QPSK orOQPSK, and 8-PSK. The derivation is as follows.3.2.1 Binary PSKWhen the index b ¼ 1; M ¼ 2, a binary PSK is derived. It is also referred to asBPSK or 2-PSK. In this case, the binary input baseband data vðtÞ modulatesconstant amplitude, constant frequency in such a way that two phase valuesdiffering by 180 (recall 2p=M, where M in this case is 2) represent the binarysymbols 0 and 1, respectively. The corresponding BPSK symbol expressioncan be written assðtÞ ¼AvðtÞ sin o c tð3:3ÞThe BPSK signal constellation (space) diagram is shown in Fig. 3.2, where Iand Q represent the in-phase and in-quadrature axes, respectively.Copyright © 2002 by Marcel Dekker, Inc. All Rights Reserved.