o next-generation radio systems. 2.13.8 How Fourier Transforms Add Value In the context of OFDM, Fourier transforms add value by improving the performance of higher bit rate radio systems both in local area and wide-area radio networks. The 'cost' is additional clock cycle/processor bandwidth but this in turn helps sell silicon. The ownership of the intellectual value that has been built around the FFT, in particular the compression/discard algorithms that speed up the transform will also become increasingly significant as higher-order FFTs are deployed over the next three to five years. The efficiency of these algorithms and their mapping to optimised DSP and microcontroller architectures will translate directly into mobile phone and radio system performance including power budgets and supportable bit rates. At the beginning of this section we stated that wireless systems are not bandwidth limited but power limited. Data rates can be increased by increasing transmit power but this degrades receive sensitivity internally within the user's transceiver and externally increases the noise floor visible to all other users. And pragmatically we only have a finite amount of transmit power available in a portable/mobile device, which is determined by battery capacity. 2.13.9 Power Drain and Battery Capacity Table 2.14 shows typical battery densities. Lithium ion batteries using a liquid electrolyte deliver better energy density (120 Wh/kg) but also have a relatively high self-discharge rate. Lithium metal batteries, using a manganese compound, deliver about 140 Wh/kg and a low self-discharge rate, about 2% per month compared to 8% per month for lithium ion and 20% per month for lithium polymer. Lithium thin film promises very high energy density by volume (1800 Wh/l). However, delivering good through-life performance remains a nontrivial task. These very high density batteries like to hold on to their power, they have high internal resistance. This is not inherently well suited to devices that have to produce energy in b