## Design Raised Cosine Filters in Simulink

This example illustrates a typical setup in which a transmitter uses a square root raised cosine filter to perform pulse shaping and the corresponding receiver uses a square root raised cosine filter as a matched filter. The example plots an eye diagram from the filtered received signal.

To open the model, enter `doc_rcfilters` at the MATLAB® command line. The following is a summary of the block parameters used in the model:

• Random Integer Generator, in the Random Data Sources sublibrary of the Comm Sources library:

• M-ary number is set to `16`.

• Sample time is set to `1/100`.

• Frame-based outputs is selected.

• Samples per frame is set to `100`.

• Rectangular QAM Modulator Baseband, in the AM sublibrary of the Digital Baseband sublibrary of Modulation:

• Normalization method is set to ```Peak Power```.

• Peak power is set to `1`.

• Raised Cosine Transmit Filter, in the Comm Filters library:

• Filter span in symbols is set to `8`.

• Rolloff factor is set to `0.2`

• AWGN Channel, in the Channels library:

• Mode is set to ```Signal to noise ratio (SNR)```.

• SNR is set to `40`.

• Input signal power is set to `0.0694`. The power gain of a square-root raised cosine transmit filter is $\frac{1}{N}$, where N represents the upsampling factor of the filter. The input signal power of filter is `0.5556`. Because the Peak power of the 16-QAM Rectangular modulator is set to 1 watt, it translates to an average power of 0.5556. Therefore, the output signal power of filter is $\frac{0.5556}{8}=0.0694$.

• Raised Cosine Receive Filter, in the Comm Filters library:

• Filter span in symbols is set to `8`.

• Rolloff factor is set to `0.2`.

• Eye Diagram Scope, in the Comm Sinks library:

• Symbols per trace is set to `2`.

• Traces to display is set to `100`.

Running the simulation produces the following eye diagram. The eye diagram has two widely opened “eyes” that indicate appropriate instants at which to sample the filtered signal before demodulating. This illustrates the absence of intersymbol interference at the sampling instants of the received waveform.

The large signal-to-noise ratio in this example produces an eye diagram with large eye openings. If you decrease the SNR parameter in the AWGN Channel block, the eyes in the diagram will close more.