OFDM, orthogonal frequency-division multiplexing, is a widely used digital modulation method in wireless communications, such as WLAN, LTE, DVB-T, and 5G.

OFDM belongs to the class of multicarrier modulation schemes. OFDM decomposes the transmission frequency band into a group of narrower contiguous subbands (carriers), and each carrier is individually modulated. You can implement this type of modulation with an inverse fast Fourier transform (IFFT). By using narrow orthogonal subcarriers, the OFDM signal gains robustness over a frequency-selective fading channel and eliminates adjacent subcarrier crosstalk.

At the receiving end, you can demodulate the OFDM signal with a fast Fourier transform (FFT) and equalize it with a complex gain at each subcarrier. Combining OFDM with MIMO can improve communication speed without increasing the frequency band.

In the figure above, the waveforms of single-carrier modulation and multicarrier modulation are represented in the frequency domain (top) and the time domain (bottom). Since the multiple data streams can be transmitted simultaneously with multiple carriers, OFDM is not influenced by noise to the same degree as single-carrier modulation. That’s because the time per symbol can be lengthened by the number of carriers.

## The Principles of OFDM

An OFDM signal aggregates the information in orthogonal single-carrier frequency-domain waveforms into a time-domain waveform that can be transmitted over the air. The subcarriers use QPSK or QAM as the primary modulation method.

The inverse discrete Fourier transform equation for this is:

$$f(x) = { 1 \over N} \sum_{t=0}^{N-1} F(t) e^{i \frac{2 \pi xt}{N}} $$

In OFDM, when the amplitude of each subcarrier reaches the maximum, the carriers are arranged at intervals of 1 / symbol time so that the amplitude of other subcarriers is 0, thereby preventing interference between symbols.

Moreover, OFDM of a multicarrier transmission is effective in multipath environments because the influence of multipath is concentrated on specific subcarriers compared with a single-carrier transmission. In the case of a single-carrier transmission, the multipath affects the whole.

The arrival time difference between the direct wave and the reflected wave increases when the signal is transmitted over a long range. In that situation, the number of subcarriers is larger than in a smaller service range.

## OFDM Technology in 5G Systems

During the specification of the 5G standard, various technologies based on OFDM had been considered. CP-OFDM (cyclic prefix OFDM) is used in LTE and was also selected for the 3GPP Release 15 standard. This technique adds an upper-level signal called a cyclic prefix to the beginning of the OFDM symbol. CP-OFDM suppresses intersymbol interference (ISI) and intercarrier interference (ICI) by inserting the data for a certain period of time from the trailing end of the OFDM symbol as the cyclic prefix at the beginning of the OFDM symbol.

## Pros and Cons of OFDM

### Advantages of OFDM

Multiple users can be assigned to OFDM subcarriers. Frequency can be efficiently used by orthogonal (1 / symbol time interval). It is resistant to transmission distortion due to multipath, making demodulation possible by error correction without using a complicated equalizer.

### Disadvantages of OFDM

Because the amplitude of the signal changes significantly, it is necessary to design an amplifier that has a higher peak-to-average power ratio, smaller-than-average transmit power allowed by the amplifier, or an amplifier with a wide dynamic range. Particularly when the carrier interval is narrow, the effect of OFDM becomes weaker against the Doppler shift, so it is preferable to use an amplifier with a wide dynamic range.

## OFDM Using MATLAB

MATLAB^{®} and related toolboxes, including Communications Toolbox™, WLAN Toolbox™, LTE Toolbox™, and 5G Toolbox™, provide functions to implement, analyze, and test OFDM waveforms and perform link simulation. The toolboxes also provide end-to-end transmitter/receiver system models with configurable parameters and wireless channel models to help evaluate the wireless systems that use OFDM waveforms. Specifically, as a part of wireless communication system design, you can use these OFDM capabilities to analyze link performance, robustness, system architecture options, channel effects, channel estimation, channel equalization, signal synchronization, and subcarrier modulation selections.

MATLAB functions and Simulink^{®} blocks for OFDM modulation provide adjustable parameters such as training signal, pilot signal, 0 padding, cyclic prefix, and points of FFT.

It is also possible to generate and analyze standard-compliant and custom OFDM waveforms over the air by using the Wireless Waveform Generator app in Communications Toolbox with Instrument Control Toolbox™ to connect MATLAB to RF test and measurement instruments.