Pulse Shaping in Wireless Communication

Pulse shaping is used to modify signals before transmission. It sculpts each pulse of a digital signal carefully to ensure clear and interference-free transmission.

Time Domain x(t): Shows how a signal is modified over time.

·       The dashed line represents the ideal pulse shape.

·       The solid line represents the shaped pulse that reduces inter-symbol interference (ISI).

Frequency Domain X(ω): Shows the signal in the frequency domain after pulse shaping.

·       The pulse shaping helps in limiting the bandwidth of the signal, which reduces interference with neighbouring channels.

Example 1:

Rectangular Pulse Shaping

Consider a digital signal with a rectangular pulse shape. This shape is straightforward but not optimal for transmission because it causes high-frequency components that can interfere with neighbouring channels.

Time Domain

• Original Signal (Time Domain): A rectangular pulse with sharp transitions.

• Issue: Sharp transitions cause high-frequency components.

• Shaped Signal (Time Domain): A smoothed version of the pulse, such as a raised cosine pulse.

• Benefit: Smoother transitions reduce high-frequency components, minimizing ISI.

Frequency Domain:

• Original Signal: Wide bandwidth due to sharp transitions.

• Shaped Signal: Narrower bandwidth, reducing potential interference.

Example 2:

Gaussian Pulse Shaping

Consider a digital signal that uses Gaussian pulse shaping. Gaussian pulses have smooth transitions and minimal high-frequency components.

Time Domain

• Original Signal (Time Domain): An unshaped signal with abrupt changes.

o   Issue: Abrupt changes lead to a broad frequency spectrum.

• Shaped Signal (Time Domain): A Gaussian pulse with smooth transitions.

o   Benefit: Smooth transitions limit the frequency spectrum, reducing interference and improving signal clarity.

 Frequency Domain:

• Original Signal: Wide bandwidth due to abrupt changes.

o   Shaped Signal: Narrower bandwidth, concentrating energy in a specific frequency range.

Pulse shaping is crucial for efficient and clear signal transmission. By shaping pulses to have smoother transitions, the signal's bandwidth is limited, reducing interference with neighbouring channels and improving overall communication quality. Rectangular and Gaussian pulse shaping are examples of how this technique can be applied to achieve better signal performance.