# What is CP-OFDM?

What is Cyclic Prefix-Orthogonal Frequency Division Multiplexing or CP-OFDM?

Can you answer this question?

#### Editorial Team - everything RF

May 11, 2023

CP-OFDM or Cyclic Prefix-Orthogonal Frequency Division Multiplexing, is an improvement on the OFDM technique designed to reduce the effects of Intersymbol Interference (ISI) and enable simplified signal processing at the receiver. It utilizes the method of cyclic prefix in the OFDM architecture.

Cyclic Prefix refers to the prefixing or placing of the last few samples of the OFDM symbol before the start of the symbol, while retaining these samples at the end of the symbol as well. In CP-OFDM, the last few samples of the OFDM symbol (data) are taken and prefixed at the first of the symbol as shown in the above figure. The CP symbols are placed in such a way that they act as guarding interval between any two different OFDM symbols. As a result, this guard interval helps to eliminate the effects due to ISI from the previous symbol. Since the prefixed symbol is cyclical in nature i.e. the CP symbol repeats the end of the OFDM data, the resulting CP-OFDM data is periodic or cyclic, unlike the case of OFDM.

To extract the output signal at the receiver, the receiver convolves or multiplies the channel impulse response with the input signal, in the time domain. This process is called the linear convolution. Conventional OFDM systems utilize this method to extract the output signal before processing to decode the original OFDM symbols. However in CP-OFDM, since the signal is periodic (or circular) in nature, the resulting response is extracted using another method called circular convolution, which involves convolving the channel impulse response and the input OFDM signal in the frequency domain. Before performing circular convolution, a Discrete Fourier Transform (DFT) is performed to first convert the incoming time-domain signal into a frequency domain signal. As a result, the receiver will receive a discrete set of parallel sub-carriers or OFDM symbols in the frequency domain. This ability to process the signal in the frequency domain in discrete sets allows the receiver to utilize simple signal processing techniques such as the single-tap equalizer, thereby simplifying the receiver processing and design compared to traditional OFDM receiver designs. Thus, compared to traditional OFDM, CP-OFDM offers a better choice in terms of further mitigating the effects of ISI resulting due to multipath reflections and achieving a higher performance while maintaining a simplified receiver hardware design.

A Simple Illustration of Cyclic Prefixing in CP-OFDM

The prefixing procedure in CP-OFDM can be observed in the following diagram and signal representations.

Cyclical appending of tail symbol in CP-OFDM

K = Length of the FFT/IFFT symbol and KCP = length of the cyclic prefix symbol

From the above vector representations, it can be observed that the cyclic prefix symbol is taken as the last few samples of the OFDM symbol and placed at the beginning of this data, while retaining the tail symbols at the end. Because the overall OFDM symbol contains an additional CP symbol along with the data, the total time duration of the entire symbol is given by,

An illustration of this is given by the below figure that represents the time duration of the entire symbol.

Time Domain of CP-OFDM Symbol

The architecture of Cyclic Prefix-OFDM

The architecture of CP-OFDM is similar to an OFDM design except that a cyclic prefix is added to and removed from the OFDM symbol in the transmitter and receiver chains. In the transmitter chain, an input data is initially generated. This data is encoded and then set to Forward Error Correction (FEC) block which performs two dimensional operation i.e. it detects and corrects the errors in binary bits. The FEC usually corrects random errors that occur after encoding, digitizing, quantizing, and other pre-processing steps. However, it is possible for burst errors to be present in the data. Burst errors are present in sequences or groups and primarily occur due to lightning and other similar effects that cause a sudden surge in signal power or an impulse signal. These errors cannot be corrected by FEC block and hence, the data is sent to the interleaver section. The interleaver further improves by eliminating burst errors and correcting the data. The new data is then modulated (mostly digital) and sent to the IFFT, which transforms back the frequency domain signal to time domain for inclusion of cyclic prefix symbol. The CP algorithm adds cyclic prefix or guard interval to the OFDM symbol and sends it over to other front-end chains for transmission.

The receiver, upon receiving the OFDM packets, performs reverse operation of the transmitter. It initially removes the cyclic prefix symbols by circularly convolving the channel impulse response with the received signal, which results in the originally transmitted packets. The symbols are then demodulated or demapped, de-interleaved, FEC decoded, and then extracted.

Limitations of CP-OFDM

While the CP-OFDM offers significant advantages over the traditional OFDM waveform and systems, there are a few limitations that need to be equally considered in order to further optimize the system design without making large compromises.

1. Reduced System Throughput: It should also be noted that by increasing the overall duration of the OFDM symbol after cyclic prefix, there is a reduction in the system throughput. This is due to the redundant data placed at the beginning of the OFDM symbol.
2. Due to the inherent complexities of the channel, it can be difficult to change the rate of change of the CP symbol duration. In severe multipath environments, this is an inevitable consequence, which results in a reduction in the performance of CP-OFDM. Therefore, better channel coding in conjunction with equalization and intelligent algorithms will be necessary to maintain a low BER even in such environments.
3. CP-OFDM will require more transmit power than traditional OFDM scheme. This is because the bandwidth of total symbol is increased, resulting in a correspondingly lower power.

Applications of CP-OFDM

Due to the advantage of better time synchronization and easy mitigation of frequency offset to preserve orthogonality, this technique can be very useful in high mobility environments between different cells and also in Doppler environments. It is also useful for LTE and 5G NR (standalone) wireless infrastructure where synchronization needs to be maintained between different base stations for better channel estimation and fine tuning of time and frequency synchronization. They can also be used in applications where traditional OFDM plays a key role such as indoor scenarios and other severe multipath environments involving a large number of objects and buildings. CP-OFDM, owing to their excellent resilience against phase noise, can also complement multi-antenna technologies like MIMO and massive MIMO to support multi-user applications in dense urban environments.