nt from the origin represents the signal amplitude. The four points 00, 01, 11, and 10 shown in Table 4-11, are known as the modulation constellation, and represent the four carrier phases each with unit amplitude. QPSK modulation is used by IEEE 802.111 at a data rate of 2 Mbps, and by IEEE 802.11a, in combination with OFDM, to achieve data rates of 12 and 18 Mbps. 4-QPSK is a variant of QPSK, as shown in Figure 4-24, which uses carrier phases offset by 45 degrees (i.e. 45, 135, 225 and 315 degrees). Offset QPSK (O-QPSK) is another variation on QPSK in which transmission of the quadrature phase is delayed by half a symbol period. The consequence is that, unlike QPSK, carrier phase transitions can never be more than 90 degrees and, as a result, the carrier phase and amplitude never passes through zero. The advantage is a narrower spectral width, which is important in applications where interference between adjacent channels must be avoided. O-QPSK is part of the IEEE 802.15.4 radio specification used by ZigBee, where 16 channels, each 5 MHz wide, are used in the 2.4 GHz ISM band to enable 16 co-located networks. Use of O-QPSK helps to reduce interference between these closely spaced channels. Differential Phase Shift Keying Differential phase shift keying is a variation on BPSK and QPSK in which the input symbol results in a differential change of phase instead of defining the absolute phase of the carrier. With BPSK, a 0-symbol corresponds to a period of zero phase carrier, while in DBPSK, a 0-symbol corresponds to no change in carrier phase from the previous bit-period. Radio Communication Basics Table 4-12: Differential Quadrature Phase Shift Keying Symbol Phase change 0 degrees 90 degrees 180 degrees 270 degrees Similarly in DQPSK, each symbol translates to a change of phase rather than an absolute carrier phase, as shown in Table 4-12. Although BPSK or QPSK are conceptually simpler, differential phase shift keying, whether DBPSK or DQPSK, has the practical advantage that the receiver only needs to detect rel