MATLAB Source Code Example for Raised Cosine Roll-Off System Implementation

Raised cosine roll-off systems represent a fundamental pulse shaping technique primarily employed in digital communication systems to mitigate Inter-Symbol Interference (ISI). When implementing this system in MATLAB, the process typically involves the following key steps: Parameter Configuration: Begin by defining essential parameters for the raised cosine roll-off filter, including sampling rate, roll-off factor (α), symbol duration, and filter length. The roll-off factor determines the filter's transition bandwidth and typically ranges between 0 and 1. Time-Domain Response Generation: Generate corresponding filter coefficients based on the time-domain expression of the raised cosine roll-off filter. In MATLAB, this can be achieved through direct formula calculation or by utilizing built-in functions such as `rcosdesign`, which automatically computes normalized filter coefficients with specified parameters. Frequency-Domain Analysis: Employ Fourier Transform (FFT) to convert the time-domain response to frequency domain, enabling observation of the filter's amplitude-frequency characteristics to ensure compliance with Nyquist's ISI-free criterion. MATLAB's `fft` function combined with frequency vector generation facilitates comprehensive spectral analysis. Filter Application: Apply the generated filter coefficients to input signals for pulse shaping or matched filtering operations. This optimizes bandwidth utilization while minimizing intersymbol interference through convolution operations using MATLAB's `filter` or `conv` functions. Simulation and Verification: Conduct performance testing through simulation, such as examining eye diagrams using `eyediagram` function or analyzing bit error rates with custom BER calculation scripts. This verifies whether the system meets design specifications and identifies potential optimization areas. This implementation approach not only serves basic communication system simulations but can also be extended to analyze more complex multicarrier or broadband modulation techniques through appropriate parameter adjustments and system integrations.