data rate doubles. We now provide the background for QPSK to serve as background to the applications in UTRA presented in Chapter 4. For all practical purposes we start with M-PSK, where M = 2b, and b = 1, 2 or 3 (i.e. 2- PSK or BPSK, 4-PSK or QPSK and 8-PSK). In the case of QPSK modulation the phase of the carrier can take on one of four values 45°, 135°, 225°, or 315° as we shall see later. The QPSK power spectral density (V -/Hz) could be then defined as (2.7) where fc is the unmodulated carrier frequency, A is the carrier amplitude, and Ts is the symbol interval. When Tb is the input binary bit interval, Ts may be expressed as (2.8) The power spectral density of an unfiltered M-PSK signal occupies a bandwidth which is a function of the symbol rate r's = (1/Ts). Thus, for a given transmitter symbol, the power spectrum for any M-PSK signal remains the same regardless of the number M of symbol levels used. This implies that BPSK, QPSK and 8-PSK signals each have the same spectral shape if Ts remains the same in each case. Spectral Efficiency For a M-ary PSK scheme each transmitted symbol represents log2M bits. Hence, at a fixed input bit rate, as the value of M increases, the transmitter symbol rate decreases; which means that there is in increase in spectral efficiency for larger M. Thus, if for any digital modulation the spectral efficiency Ns, (i.e. the ratio of the input data rate rb and the allocated channel bandwidth B) is given by: (bit/s Hz), (2.9) The UMTS Network and Radio Access Technology the 8-PSK spectral efficiency will be three times as great as that for BPSK. However, this will be achieved at the expense of the error probability. Now allocating the RF bandwidth of a M-PSK signal we should remember that its spec- trum rolls off relatively slowly. Therefore, it is necessary to filter the M-PSK signal SO that its spectrum is limited to a finite bandpass channel region avoiding adjacent chan- nel interference. Using Nyquist filtering or raised cosine filtering prevents the adjacent channel interfere