e reference as a basis to make its binary or higher level decisions. 9.2.3.5 Digital Modulation of LOS Microwave Radios. Digital systems, typically standard PCM as discussed in Chapter 6, are notoriously wasteful of bandwidth compared their analog counterparts. 6 For example, the analog voice channel is nominally of 4- kHz bandwidth, whereas the digital voice channel requires a 64-kHz bandwidth, assuming 1-bit/Hz occupancy. This is a 16-to-1 difference in required bandwidth. Thus national regulatory authorities, such as the U.S. FCC, require that digital systems be bandwidth conservative. One means that is used to achieve bandwidth conservation is bit packing. This means packing more bits into 1 Hz of bandwidth. Another driving factor for bit packing is the need to transmit such higher bit rate formats such as SONET and SDH (Chapter 19). Some radio systems can transmit as much as 622 Mbps using advanced bit-packing techniques. How Does Bit Packing Work? In the binary domain we can estimate bandwidth to approximately equate to 1 bit/Hz. For example, if we were transmitting at 1.544 Mbps, following this premise, we'd need 1.544 MHz of bandwidth. Suppose now that we turn to higher levels of modulation. Quadrature phase shift keying is one example. In this case we achieve a theoretical packing of 2 bits/Hz. Again, if we are transmitting 1.544 Mbps, with QPSK we would need 1.544 MHz/2 or 0.772 MHz. QPSK is one of a family of modulation schemes that are based on phase-shift keying (PSK). With binary PSK, we might assign a binary 1 to the 0° position (i.e., no phase retardation) and a binary 0 to the 180° phase retardation point. For QPSK, the phase circle is broken up into 90° segments, rather than 180° segments as we did with binary PSK. In this case, for every transition we transmit 2 bits at a time. Figure 9.11 is a functional block diagram of a QPSK modulator. It really only consists of two BPSK modulators where one is out of phase with the other by 90°. 6 A cogent example is FDM using frequency modulation; another