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Power and bandwidth efficiency

#### For a system transmitting at maximum capacity, C, the average signal power, S, measured at the receiver input, can be written as S = Eb.C, where Eb is the average received energy per bit. #### The average noise power, N, can also be redefined as, N = N0.B, where N0 is the noise power density (Watts/Hz) #### Using these definitions, the Shannon–Hartley theorem can be written in the form: #### C/B = log2[1 + Eb.C/N0.B]

#### The ratio C/B represents the bandwidth efficiency of the system in bits/second/Hz. The larger the ratio, the greater the bandwidth efficiency. The ratio Eb/N0 is a measure of the power efficiency of the system. The smaller the ratio, the less energy used by each bit (and consequently for each symbol), to be detected successfully in the presence of a given amount of noise. Choosing a power-efficient modem type is particularly important in cellular handsets, for example, where the designer is trying to maximize battery lifetime. #### Power efficiency is covered in detail in Chapter 5 onwards. |