OFDM Modulator

OFDM belongs to the class of multi-channel modulation schemes. Due to the fact that several carriers can be transmitted simultaneously during operation, noise does not affect OFDM to the same extent as with single-band modulation.

OFDM divides the high-speed data stream into low-speed subcarriages by decomposing the transmission frequency band into a number of adjacent individually modulated subcarriers. This set of parallel and orthogonal subcarriers carries the data stream, occupying almost the same bandwidth as the broadband channel. By using narrow orthogonal subcarriers, the OFDM signal becomes resistant to fading in the frequency-selective channel and eliminates interference from neighboring subcarriers. Inter-character interference (ISI) is reduced because subcreams with a lower data rate have a character duration longer than the delay spread in the channel.

This image shows the representation of orthogonal subcarriers in the frequency domain in the OFDM waveform.

The transmitter applies the inverse Fast Fourier Transform (OBFT) to characters at a time. Usually, the output of the OBF is the sum of orthogonal sinusoids:

where

Data Symbols They are usually complex and can be from any digital modulation alphabet (for example, QPSK, 16-QAM, 64-QAM, etc.).

The distance between subcarriers is , which ensures the orthogonality of subcarriers during each character period:

The OFDM modulator consists of a series-parallel conversion followed by a bank of integrated modulators, individually corresponding to each subcarrier OFDM.

Individual OFDM subcarriers are allocated as subcarriers of data, pilot or null.

As shown here, subcarriers are designated as subcarriers of data, DC, pilot, or protective band.

Zero-frequency subcarriers allow you to simulate protective bands and the location of zero subcarriers for specific standards, such as various 802.11, LTE, WiMAX formats, or for custom distributions. The location of the zero subcarriers can be determined by assigning a vector of zero subcarrier indexes.

Similar to guard bands, guard intervals protect the integrity of transmitted signals in OFDM by reducing inter-character interference.

The purpose of protective intervals is similar to the purpose of protective strips. You can simulate guard intervals to ensure time separation between OFDM symbols. Guard intervals help to maintain inter-character orthogonality after the signal passes through channels with time variance. Guard intervals are created using cyclic prefixes. Inserting a cyclic prefix copies the last OFDM as the first part of the OFDM symbol.

OFDM benefits from using cyclic prefix insertion as long as the time variance does not exceed the duration of the cyclic prefix.

Inserting a cyclic prefix results in a fractional decrease in user data throughput, since the cyclic prefix takes up bandwidth that could have been used for data transmission.

The window function for OFDM with a raised cosine applies the methods described in [3] to limit spectral expansion by creating a smooth transition between the last sample of one character and the first sample of the next character.

Although the cyclic prefix creates a protective period in the time domain to maintain orthogonality, the OFDM symbol rarely begins with the same amplitude and phase as at the end of the previous OFDM symbol, which causes spectral expansion and, consequently, signal bandwidth expansion due to intermodulation distortion. To limit this spectral expansion, you can create a smooth transition between the last character sample and the first sample of the next character using a cyclic suffix and a window function with an elevated cosine.

To create a cyclic suffix, the operation adds the first samples this character is added to the end of this character. However, to comply with the IEEE® 802.11g standard, for example, an operation cannot arbitrarily lengthen a character. Instead, the cyclic suffix should overlap in time and effectively be combined with the cyclic prefix of the next character. The operation applies two mathematically inverse window functions in this overlapping segment. The first window function with a raised cosine is applied to the cyclic suffix of the symbol and decreases from 1 before 0 for the duration of its action. The second window function with a raised cosine is applied to the cyclic prefix of the symbol and increases from 0 before 1 for the duration of its action. This process ensures a smooth transition from one character to another.

Window function with raised cosine in the time domain , it can be expressed as

where

The length of the cyclic suffix is adjusted by setting the length of the window function, while the length of the suffix is set in the range from 1 up to the minimum length of the cyclic prefix. Although the installation of windows improves spectral recovery, this is due to a decrease in resistance to multipath fading due to a decrease in redundancy in the protective band due to a change in the values of the protective band samples to smooth the intersymbol transition.

These figures show the application of a window function with a raised cosine.