Cyclic Prefix in OFDM: Definition and Role in Wireless Communication

Introduction

A cyclic prefix (CP) is a crucial element in Orthogonal Frequency Division Multiplexing (OFDM), a widely adopted technique in wireless communication systems such as LTE, Wi-Fi, and 5G. The cyclic prefix is essentially a copy of the end portion of an OFDM symbol, appended to the beginning of that same symbol. This clever addition addresses the challenges of intersymbol interference (ISI) and preserves the orthogonality of subcarriers. This guide dives into the function, importance, and implementation of the cyclic prefix in ensuring reliable data transmission in modern wireless networks.

In OFDM symbol transmission, ISI arises at the receiver due to the delay spread of the channel. To mitigate ISI, a guard interval is inserted between consecutive OFDM symbols. This guard interval is what we refer to as the cyclic prefix (CP). The duration of the CP is designed to be greater than the delay spread of the channel, effectively preventing ISI.

Functions of Cyclic Prefix (CP) in OFDM

The cyclic prefix (CP) is an integral component of OFDM systems, providing several critical functions to enhance performance and reliability in wireless communication. Its main functions include the following:

1. Mitigating Intersymbol Interference (ISI):

   • The cyclic prefix acts as a buffer, absorbing delayed signals caused by multipath propagation.
   • By ensuring that delayed copies of a symbol do not interfere with the subsequent symbol, it effectively eliminates ISI.

2. Preserving Subcarrier Orthogonality:

   • Multipath effects can disrupt the orthogonality of OFDM subcarriers, leading to intercarrier interference (ICI).
   • The CP helps maintain orthogonality by converting the linear convolution of the channel into circular convolution, enabling simple frequency domain equalization.

3. Simplifying Equalization:

   • The CP enables efficient equalization using the Fast Fourier Transform (FFT) by ensuring that channel effects appear as a diagonal matrix in the frequency domain.
   • This reduces computational complexity and simplifies receiver design.

4. Handling Multipath Delays:

   • By extending the OFDM symbol with a CP longer than the expected delay spread of the channel, it ensures that multipath reflections do not distort the original signal.

5. Providing Robustness in Frequency Selective Channels:

   • The CP enhances the system’s ability to handle frequency selective fading by maintaining the integrity of subcarriers across the channel’s bandwidth.

While the cyclic prefix adds redundancy to the transmitted signal, its benefits in combating ISI and ICI, as well as enabling efficient signal processing, far outweigh its cost in terms of spectral efficiency. This makes it indispensable in modern OFDM-based systems such as 4G LTE, 5G, and Wi-Fi.

Implementation of CP in OFDM packet

The implementation of a cyclic prefix (CP) in OFDM involves inserting a copy of the tail end of the OFDM symbol at the beginning of the same symbol. This prepares it for transmission over a wireless channel. This process is essential to mitigate intersymbol interference (ISI) and maintain subcarrier orthogonality.

The following figure depicts S1 and S2 as OFDM symbols. Tg is the guard time interval and Ts is the data symbol period. Therefore:

$OFDM\ symbol\ time = T_g + T_s$

There are four common options for the length of the cyclic prefix, typically expressed as a fraction of the symbol time (number of FFT samples): 1/4, 1/8, 1/16, and 1/32. For example, if we use an FFT size of 1024 samples and a CP length of 1/8, then the guard interval will be 128 samples long.

Here is a step-by-step explanation of how a cyclic prefix is implemented:

1. Generate OFDM Symbols:

   • Divide the input data stream into multiple parallel streams.
   • Map the data onto subcarriers using modulation techniques like QAM or PSK.
   • Perform an Inverse Fast Fourier Transform (IFFT) to convert the frequency-domain subcarriers into a time-domain OFDM symbol.

2. Extract Cyclic Prefix Segment:

   • Select the last portion of the OFDM symbol, typically equal to the channel delay spread or a fixed fraction of the symbol duration (e.g., 1/4 or 1/8 of the symbol duration).

3. Prepend the Cyclic Prefix:

   • Copy the extracted portion from the end of the OFDM symbol and paste it at the beginning of the same symbol.
   • The extended symbol now contains the cyclic prefix followed by the original OFDM symbol.

4. Transmit the Extended Symbol:

   • The transmitter sends the extended symbol (cyclic prefix + original symbol) over the wireless channel.
   • The total transmission duration increases slightly due to the added cyclic prefix, introducing redundancy.

5. Processing at the Receiver:

   • The receiver removes the cyclic prefix before performing the Fast Fourier Transform (FFT) on the received signal.
   • This ensures that only the original OFDM symbol is processed while maintaining the orthogonality of subcarriers.

Key Considerations in Implementation

• Length of the Cyclic Prefix: The length must be longer than the channel’s maximum delay spread to avoid ISI. A longer CP ensures better protection but reduces spectral efficiency.

• Spectral Efficiency Trade-off: Since the CP does not carry new information, it introduces redundancy. The trade-off between redundancy and channel protection must be optimized.

• Channel Conditions: The CP length may be dynamically adjusted based on channel conditions in adaptive systems.

Conclusion

The cyclic prefix plays an essential role in enhancing the performance of OFDM systems by mitigating intersymbol interference and preserving signal integrity. While it introduces some redundancy, its benefits in maintaining efficient communication and handling multipath propagation make it indispensable in wireless communication technologies.

The cyclic prefix is a standard feature in OFDM based technologies like LTE, 5G, Wi-Fi, and DVB-T. It ensures reliable data transmission over multipath channels, enabling these systems to achieve high speed, efficient wireless communication.

Understanding the cyclic prefix helps optimize network design and improve overall data transmission quality.