# Noise

The performance of wireless communication systems is highly determined by noise. Particularly if signals are in a fade, the signal-to-noise ratio can be low and bursts of error can occur.

This is other argued that wireless systems, in particular cellular systems with dense frequency reuse, are interference-limited rather than noise-limited. However, any (digital) signal processing algorithm that attempts to remove, cancel or attenuate such interference increases the noise. The ability to separate multiple interfering signals is critically determined by the signal-to-noise ratio.

## Additive White Gaussian Noise (AWGN)

A basic and generally accepted model for thermal noise in communication channels, is the set of assumptions that

• the noise is additive, i.e., the received signal equals the transmit signal plus some noise, where the noise is statistically independent of the signal.
• the noise is white, i.e, the power spectral density is flat, so the auto correlation of the noise in time domain is zero for any non-zero time offset.
• the noise samples have a Gaussian distribution.

Mostly it is also assumed that the channel is Linear and Time Invariant (LTI), sometimes also frequency non-selective.

### Exercise

Which of the above assumptions are realistic in a wireless channel?

Thermal noise poses an insurmountable limit to the performance of communication systems. Even with perfectly designed equipment, a thermal noise floor with a spectral power density of k T0 = 4 10-21 watts/Hz is experienced. Here k is the Boltzmann's constant (k is about 1.38 10-23) and T0 is the temperature of the system. In practical systems, the noise power is n k T0 B, where B is the bandwidth and n is a factor by which the noise spectral density exceeds that of thermal noise. Most communication text books, express the performance of generic communication systems in terms of Eb/N0, where Eb is the received energy per bit and N0 is spectral noise density. Typically, n k T0.

Typical causes why the noise factor n is larger than unity are

• Man made or industrial noise

At 900 MHz, the man made noise power level can easily be 20 dB (100 times) above the thermal level.

### Exercise

Show that the ratio Eb/N0 is a dimension-free unit.