ver improved sensitivity and selectivity in the baseband processing sections of the transceiver has increased the need for a more accurate (and potentially expensive) time reference. As we shall see later, this in a sense is the Achilles heel of present CDMA systems (their inability to scale to much higher data rates without an inconveniently accurate time reference). In Chapter 2 we showed how OFDM shifts some of the hard work involved here back into the frequency domain. In terms of the user experience, stability therefore translates directly into user data rates and the consistency of the user experience. 3.3 The Role of Binary Arithmetic in Achieving Sensitivity, Selectivity and Stability In 1937, Claude Shannon's MIT thesis 'A symbolic analysis of relay and switching circuits' helped to establish the modern science of using binary arithmetic in wireless (and wireline) communications. The science was consolidated by Richard Hamming in his work on error Making Telecoms Work Table 3.1 Coding distance - sensitivity Coding distance - sensitivity detection and correction codes (1950), digital filtering (1977), coding and information theory (1980), numerical analysis (1989) and probability (1991). Hamming formalised the concept of distance between binary numbers and binary number strings that is in practice the foundation of modern radio system design. In digital radio systems, we take real-world analogue signals (voice, audio, video, image) and turn the analogue signals into a digital bit stream that is then mathematically manipulated to achieve the three 'wanted properties' - sensitivity, selectivity, stability. Note that analogue comes from the Greek word meaning proportionate. Analogue implies that the output of a system should be directly proportionate (i.e. linear) to the input of the system and is continuously varying. To represent these waveforms digitally requires a sampling process that has to be sufficiently robust to ensure that analogue waveforms can reconstructed accurately in the receiver. (Harry Nyq