Sign in Subscribe

RC Raised cosine

Last updated on 


RC (Raised Cosine) is a commonly used pulse-shaping technique in digital communication systems. It is used to shape the transmitted signal in order to minimize inter-symbol interference (ISI) and spectral leakage. The RC pulse shape is widely adopted in various communication standards, including digital modulation schemes like QPSK, QAM, and OFDM.

The RC pulse shape is a smooth and symmetrical waveform that is derived from the mathematical function known as the raised cosine function. It has a specific roll-off factor that determines its bandwidth and shape. The roll-off factor determines the amount of spectral containment of the transmitted signal, where a higher roll-off factor leads to a more compact spectrum.

To understand the RC pulse shape, let's break it down into its key components:

  1. Cosine Function: The cosine function is a periodic waveform that oscillates between -1 and 1. It has a frequency and amplitude. In the context of RC pulse shaping, the cosine function is used to shape the waveform smoothly.
  2. Raised Cosine Function: The raised cosine function is a modification of the cosine function that is tapered at the edges to reduce spectral leakage. The raised cosine function has two parameters: the roll-off factor and the symbol duration.
  3. Roll-off Factor: The roll-off factor, denoted by α (alpha), determines the bandwidth of the RC pulse. It is defined as the ratio of excess bandwidth to symbol duration. The excess bandwidth is the portion of the spectrum beyond the minimum required bandwidth. A roll-off factor of 0 corresponds to a rectangular pulse shape, while a roll-off factor of 1 corresponds to the Nyquist pulse shape.
  4. Symbol Duration: The symbol duration, denoted by T, is the time taken to transmit one symbol. It is inversely proportional to the symbol rate. The RC pulse shape is designed to occupy multiple symbol durations to minimize ISI and maximize spectral containment.

The RC pulse shape is obtained by convolving the raised cosine function with a rectangular pulse of duration T. The resulting waveform exhibits a smooth transition at its edges, which reduces the amount of interference between adjacent symbols.

The advantages of using RC pulse shaping include:

  1. Reduced Inter-Symbol Interference (ISI): The smooth transition of the RC pulse shape helps in reducing ISI, which occurs when symbols from adjacent time intervals interfere with each other. By minimizing ISI, the receiver can distinguish symbols more accurately, leading to improved data transmission quality.
  2. Spectral Containment: The RC pulse shape helps in containing the transmitted signal within the desired bandwidth. The roll-off factor determines the amount of spectral containment, allowing efficient utilization of the available frequency spectrum.
  3. Compatibility: RC pulse shaping is widely used in various communication standards, making it compatible with different systems and facilitating interoperability.

In summary, RC (Raised Cosine) pulse shaping is a technique used in digital communication systems to shape the transmitted signal. It employs a smooth and symmetrical waveform derived from the raised cosine function. By reducing ISI and spectral leakage, RC pulse shaping improves the quality and efficiency of data transmission in communication systems.