Maximum Data Rate of the Channel

data rate refers to the data transmission speed through the channel. It is usually calculated per second bits (bps). A higher data rate is represented as Kbps (per second ‘kilobit’, i.e.1000 bps), Mbps (per second ‘megabit’, i.e.1000 Kbps), Gbps (per second ‘gigabit’ bits, i.e.1000 Mbps) and Tbps (‘Tera’ per second bits, i.e.1000 Gbps).

One of the main goals of data communication is to increase data rate. Three factors determine the data rate of the channel:

• channel bandwidth

• the number of signal levels used

• there is noise in the channel

Two theoretical formulas can be used to calculate data rate:

• Nyquist bit rate – noiseless channel

• Shannon's capacity-noisy channel

Nyquist bit rate

Nyquist bit rate was developed by Henry Nyquist, who proved that even in a noiseless perfect channel, there is a maximum limit to the transmission capacity.

The theoretical formula for maximum bit rate is:

maximum bit rate= 2×bandwidth×log ₂ V

Here,maximum bit ratecalculated in bps

Bandwidth is the bandwidth of the channel

V is the number of discrete levels in the signal

For example, if there is a bandwidth of4 KHz noiseless channel is transmitting4a signal with a certain number of discrete levels, then the maximum bit rate will be calculated as:maximum bit rate= 2×4000×log ₂ 4 = 16,000 bps = 16 kbps

Shannon's capability

Claude Shannon expanded Nyquist's work to the actual channel affected by noise. Noise can have various types, such as thermal noise, pulse noise, crosstalk, etc. Among all types of noise, thermal noise is inevitable. The random motion of electrons in the channel produces an extraneous signal not present in the original signal, known as thermal noise. The amount of thermal noise is calculated as the ratio of signal power to noise powerSNR.

signal-to-noise ratio, SNR = average signal power/average noise power

Due toSNRIs the ratio of two powers that vary over a wide range, and is usually expressed in decibels, called SNR _db,, and is calculated as: SNR _db = 10log ₁₀ SNR.

Shannon's capacity gives the theoretically maximum data rate or the capacity of a noisy channel. It is represented as:

Capacity=Bandwidth×log ₂(1 + SNR)

Here,CapacityIs the maximum data rate of the channel, in bps

Bandwidth is the bandwidth of the channel

SNR is the signal-to-noise ratio

For example, if the bandwidth of a noisy channel is4 KHz, and the signal-to-noise ratio is100, then the maximum bit rate can be calculated as:

Capacity= 4000×log ₂(1 + 100）= 26,633 bps = 26.63 kbps