# Matched filter in digital communications

Matched filter simulation

In this scenario, a pulse is sent and shall be detected at the receiver. It might represent a symbol for digital transmission or a radar pulse. The received pulse might be almost hidden in noise.

It is a matter of detecting the pulse in an optimal way. Which receive filter achieves the best signal-to-noise ratio? Compare different combinations of sender side pulse shapers and receiver side filters.

## Start

This simulation provides different filters for pulse shaping and receive filter. These are for instance:

 Rectangular pulse Half-sine pulse shaper

To make results comparable, all filters are power-normalized. This means, the pulse energy is equal for all of them.

Determine the energy E of both pulses!

Pulse energy:

## Noise

Now let's look at the noise. White Gaussian noise is added (AWGN channel). Determine the noise power of the detected signal!

• Switch off the digital signal source. Then the signal d(t) consists only of the noise part.
• Measure the signal power using the power meter - right click on d(t).
• Speed up the simulation by pressing F3 several times and see how the power converges to a value.

Noise power:

Does the noise power differ for the different filters?

## Signal

Now let's look at the signal. The sent pulse passes the receive filter. Determine the maximum amplitude of the detected signal!

• Switch off the noise source. Then the signal d(t) consists only of the signal part.
• Regard the oscilloscope showing the detected signal.
• The best signal power is achieved when the signal d(t) is sampled at its maximum amplitude.

 Detected signal for a pulse - receive filter combination Detected signal for another pulse - receive filter combination

Which combinations of pulse shaper and receive filter show the maximum amplitude?

What is the corresponding signal power of the optimal sampled detected signal d'(t)?

Signal power:

## Signal-to-noise ratio

The signal quality is measured as the ratio of signal power to noise power.

Determine the SNR for the best filter combinations - using the measured values!

Signal-to-noise ratio:

The receive filter achieving the best SNR for a given sender side pulse shape is called 'Matched filter'. How can the SNR be calculated using the given energy of the sent pulse and the noise power-spectral-density N0? Find out the formula.

Signal-to-noise ratio:

Noise power-spectral-density N0
 Detected signal for a pulse - receive filter combination Detected signal for another pulse - receive filter combination