EngeeComms.OFDMModulatorBaseband

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

OFDM divides a high-speed data stream into low-speed data sub-streams by decomposing the transmission bandwidth into a number of contiguous individually modulated sub-carriers. This set of parallel and orthogonal subcarriers carries the data stream, occupying almost the same bandwidth as a wideband channel. Through the usage of narrow orthogonal subcarriers, the OFDM signal becomes immune to hiccups in the frequency selective channel and eliminates interference from neighbouring subcarriers. Inter-symbol interference (ISI) is reduced because subflows with lower data rates have symbol durations longer than the channel delay spread.

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

The transmitter applies the inverse fast Fourier transform (IFFT) to N symbols at a time. Typically, the output of the IFFT is the sum of N orthogonal sine waves:

,

where

The data symbols Xk are usually complex and can be from any digital modulation alphabet (e.g. QPSK, 16-QAM, 64-QAM, etc.).

The subcarrier spacing is [Δf = 1/T], which ensures that the subcarriers are orthogonal during each symbol period:

The OFDM modulator consists of a series-parallel transform followed by a bank of N complex modulators individually corresponding to each OFDM subcarrier.

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

As shown here, subcarriers are labelled as data, DC, pilot or guard band subcarriers.

Zero frequency subcarriers allow modelling of guard bands and zero subcarrier locations for specific standards such as different 802.11 formats, LTE, WiMAX, or custom allocations. The location of the null subcarriers can be defined by assigning a vector of null subcarrier indices.

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

The purpose of guard intervals is similar to that of guard bands. You can model guard intervals to provide temporal separation between OFDM symbols. Guard intervals help maintain inter-symbol orthogonality after a signal passes through time-dispersive channels. 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 the usage of cyclic prefix insertion as long as the time variance does not exceed the duration of the cyclic prefix.

Insertion of the cyclic prefix results in a fractional reduction in user data throughput because the cyclic prefix takes up bandwidth that could have been used for data transmission.

The window function for OFDM with increased cosine applies the techniques described in [3] to limit spectral sprawl by creating a smooth transition between the last sample of one symbol and the first sample of the next symbol.

Although the cyclic prefix creates a guard period in the time domain to preserve orthogonality, an OFDM symbol rarely starts with the same amplitude and phase as at the end of the previous OFDM symbol, causing spectral sprawl and hence signal bandwidth expansion due to intermodulation distortion. To limit this spectral sprawl, a smooth transition can be created between the last sample of a symbol and the first sample of the next symbol using a cyclic suffix and a window function with an increased cosine.

To create a cyclic suffix, the operation adds the first samples ) of a given symbol to the end of that symbol. However, to comply with IEEE® 802.11g, for example, the operation cannot arbitrarily lengthen a symbol. Instead, the cyclic suffix must overlap in time and effectively sum to the cyclic prefix of the next symbol. The operation applies two, mathematically inverse, window functions to this overlapping segment. The first windowing function with increased cosine is applied to the cyclic suffix of symbol k and decreases from 1 to 0 over its lifetime. The second window function with increased cosine is applied to the cyclic prefix of symbol k+1 and increases from 0 to 1 over its lifetime. This process provides a smooth transition from one symbol to the next.

The window function with increased cosine, , in the time domain can be expressed as:

,

where:

The cyclic suffix length is adjusted by setting the window function length, with the suffix length set between 1 and the minimum cyclic prefix length. Although windowing improves spectral recovery, this comes at the expense of reduced immunity to multipath hiccups due to reduced redundancy in the guard band due to changing guard band sampling values to realise inter-symbol transition smoothing.

These figures show the application of the window function with increased cosine.