ative changes in carrier phase. The BPSK or QPSK receiver always needs to know the absolute phase reference of the carrier and this reference can be difficult to maintain, for example, if the phase of the received signal is varying due to multipath interference. Other variants on PSK and DPSK include 8-DPSK, which extends the DQPSK keying table to encode 8 data symbols using phase changes separated by 45 degrees rather than by 90 degrees, and t/4-DQPSK which, by analogy with 4-QPSK, uses carrier phase changes similar to Table 4-12 but offset by 45 degrees (i.e. 45, 135, 225 and 315 degrees). n/4-DQPSK and 8-DPSK are used in the enhanced data rate (EDR) Bluetooth 2.0 radio for 2 Mbps and 3 Mbps data rates respectively. Frequency Shift Keying Frequency shift keying (FSK) is a simple frequency modulation method in which data symbols correspond to different carrier frequencies, as shown in Table 4-13 for BFSK. Table 4-13: Binary Frequency Shift Keying Symbol Carrier frequency fo - f1 fo + f1 Chapter Four The sudden carrier waveform changes in simple FSK generate significant out-of-band frequencies and, as a result, FSK is inefficient in terms of spectrum usage. This situation can be improved by passing the input bit stream through a filter to make the frequency transitions more gradual. A Gaussian filter is one type of filter with a specific mathematical form, and use of this as a pre-modulation filter results in Gaussian frequency shift keying (GFSK). GFSK is used in the Bluetooth radio for standard data rate transmission, with a carrier frequency fo of 2.40 to 2.48 GHz and frequency deviation f1 of between 145 and 175 kHz. Spectral efficiency is particularly important as the FHSS frequency hopping channels are only separated by 1 MHz. Quadrature Amplitude Modulation Quadrature amplitude modulation (QAM) is a composite modulation technique that combines both phase modulation and amplitude modulation. In BPSK or QPSK, a constant carrier amplitude with 2 or 4 different phases is used to represent the input data symbol