 by using the full phase space that BPSK does not. We use another type of graph called a constellation to depict digital modulation schemes. These radial graphs depict amplitude as the distance from the center of the graph and depict degrees of phase radially, from 0 degrees along the X axis to the right, V (t) Signal Pilot Figure 1.10 Quadraphase phase-shift keying (QPSK). Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. Radio Engineering Concepts Radio Engineering Concepts 8-ARY 16QAM Figure 1.11 BPSK, QPSK, 8-ary, and 16QAM constellations. 90 degrees vertically up on the Y axis, 180 degrees horizontally to the left, and 270 de- grees vertically down. Each point on the graph represents an amplitude and phase lation where digital information can be transmitted. In radio we do not call the two di- mensions x and y or real and imaginary as we do in mathematics class. Rather, we call the same two axes in-phase and quadrature. Occasionally there will be some reference to I and Q for in-phase and quadrature. BPSK has two points in its constellation, +1 and - -1.10 In mathematical terms, frequency-phase space is the two-dimensional complex-number space, and the sophis- tication of QPSK takes advantage of the full two-dimensional modulation opportunity. QPSK uses the four complex numbers 1, i, -1, and -i.11 There are more complex schemes that send more bits per time period. For example, there are m-ary schemes and quadrature amplitude modulation (QAM). Figure 1.11 shows BPSK, QPSK, 8-ary, and 16QAM constellations. 10 We call the digital modulation states points. The astronomy analogy stops short of calling them stars. 11Mathematicians (like one of us, Rosenberg) use the letter i for the square root of -1. Electri- cal engineers use the letter j for the same concept. Downloaded from Digital Engineering Library @ McGraw-Hil (www.digitalengineeringlib