# What are Transmission Bandwidth and System Temperature?

Digital ElectronicsElectronics & ElectricalElectron

In this article, two more important performance parameters of a wireless link are discussed – transmission bandwidth and system temperature.

## Definition of Transmission Bandwidth

High data rates can be achieved with high bandwidths. It is also known that the transmission bandwidth of the signal is limited by the allocated channel bandwidth. An increase in data rate is achieved not necessarily by only having a large channel bandwidth.

Higher the bandwidth, higher is the data rate.

We may also use effective modulation techniques such as M-ary modulation to achieve high data rates. OFDM, for example, proves to be handy under flat fading channel conditions. Since the real-time available channel bandwidth is always limited, we perform compression at the transmitter prior to signal transmission.

Every wireless communication system will have some amount of channel noise present; however the noise varies for different environments. As the channel bandwidth increases, the noise power level also increases and this alters the signal to noise ratio (SNR). The noise power is expressed as

$$N_{p}(in\:Watt)=kTB=N_{0}B$$

k is the Boltzmann constant, B is the channel bandwidth, N0 is the power spectral density (PSD) of the noise and T is the system temperature in Kelvin (K).

From the above relation, we can observe that as the channel bandwidth B increases (or, the channel bandwidth is maintained high due to higher value of signal transmission bandwidth), the noise power also increases linearly. The expression of signal to noise ratio is given by

$$SNR=\frac{S_{p}}{N_{p}};\:SNR(dB)=10log_{10}\frac{S_{p}}{N_{p}}$$

SNR gets altered as the noise power increases. There is a possibility that if the channel is too noisy already and the channel bandwidth is high, the signal might get buried under the noise and ultimately renders it impossible for the receiver to detect and decode the signal.

As channel bandwidth is maintained higher and higher,
The noise power increases and consequently, both the

## System Temperature – Wireless Design Parameter

The noise power also has a linear relationship with the system temperature. If the system operating temperature doubles, the noise power also doubles and the SNR gets altered. The SNR decreases.

$$Noise\:Power(N_{p})=N_{0}B=kT_{s}B$$

In the equation, TS is the system temperature and k is the Boltzmann constant. The product of k and TS is termed the Power Spectral Density.

As the system temperature increases, the noise power

## Numeric example problem with Solution

The power spectral density of the wireless channel noise is 2 x 10-7W/Hz. The transmission bandwidth is 2 MHz. Compute the noise power of the communication system.

Answer − The noise power is expressed as the product of the noise power spectral density and the system bandwidth. From the given data, we determine the noise power as below −

$$N_{p}=N_{0}B=(2\times\:10^{-7})(\frac{W}{Hz}).(2\times\:10^{6})Hz$$

$$N_{p}=4\times\:10^{-1}W=0.4W$$