nce, as well as the intersymbol interference (ISI) due to filtering. The raised-cosine spectra are characterized by a factor AB, known as the excess bandwidth factor. This factor lies in the range 0-1, and specifies the excess bandwidth of the spec- trum compared to that of an ideal bandpass spectrum (aB = 0) for which the bandwidth would be B = rs. Typical values of AB used in practice are 0.3-0.5 [3]. Thus, for M-PSK transmission using the Nyquist filtering with roll-off AB the required bandwidth will be given by =rs(1+a). (2.10) Then the maximum bit rate in terms of the transmission bandwidth B, and the roll-off factor AB can be defined as (2.11) However, if we assume an M-PSK with an ideal Nyquist filtering (i.e. OB = 0) the signal spectrum is centred on fc, it is constant over the bandwidth B = 1/Ts, and it is zero out- side that band. Then the transmitted bandwidth for the M-PSK signal, and the respective spectral efficiency are given by Islog,M and ns= (2.12) Bit Error Rate (BER) Performance In M-PSK modulation, the input binary information stream is first divided into b bit blocks, and then each block is transmitted as one of M possible symbols; where each symbol is a carrier frequency sinusoid having one of M possible phase values [3]. Among the M-PSK schemes, BPSK and QPSK are the most widely used. Nevertheless, here we review only the QPSK scheme. In QPSK each transmitted symbol (Figure 2.3) represents two input bits as follows: Input bits Transmitted symbols A cos(w(t + 45°) A cos(wct + 135°) A cos(wct + 235°) A cos(wct + 315°) System Analysis Fundamentals The conversion from binary symbol to phase angles is done using Gray coding. This coding permits only one binary number to change in the assignment of binary symbols to adjacent phase angles, thereby minimizing the demodulation errors, which in a digital receiver result from incorrectly selecting a symbol adjacent to a correct one. Figure 2.3 illustrates a block diagram frequently used for any form of M-PSK modula- tion. For QPSK, the multiplexer ba