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# 2.2 Thermal Noise

## 2.2.1 Additive White Gaussian Noise

In communication systems theory and simulations we often introduce an additive noise n(t) for studying the transceiver performances, as shown in Figure 2.2; either we use its PSD (watts/hertz) when analyzing Eb/N0 or its power (watts) when studying SNR or EVM. Most of the time this noise is assumed additive, white, and Gaussian noise (AWGN).

Why this assumption? In practice the AFE of any real communication system is affected by random fluctuations of the charges (electrons) present in any physical device. These fluctuations are known as thermal noise and are dependent on the temperature, as shown next (Davenport and William, 1958; Ott, 1976). For example, in Figure 2.3 a simple passive resistor R generates an RMS noise voltage equal to

where the angle brackets denote the average operator, k = 1.38 × 10−23 J/K is Boltzmann's constant, T is the temperature in kelvin, R is the value of the resistor in ohms, and B is the integration/measurement bandwidth in hertz.

For example, a 50 Ω resistor and 20 MHz bandwidth will ...

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