OFDM Basics

Orthogonal frequency division multiplexing (OFDM) belongs to a family of transmission schemes called multicarrier modulation, which is based on the idea of dividing a given high-bit-rate data stream into several parallel lower bit-rate streams and modulating each stream on separate carriers—often called subcarriers, or tones. Multicarrier modulation schemes eliminate or minimize inter-symbol interference (ISI) by making the symbol time large enough so that the channel-induced delays—delay spread being a good measure of this in wireless channels—are an insignificant (typically, <10 percent) fraction of the symbol duration. Therefore, in high-data-rate systems in which the symbol duration is small, being inversely proportional to the data rate, splitting the data stream into many parallel streams increases the symbol duration of each stream such that the delay spread is only a small fraction of the symbol duration.

OFDM is a spectrally efficient version of multicarrier modulation, where the subcarriers are selected such that they are all orthogonal to one another over the symbol duration, thereby avoiding the need to have non-overlapping subcarrier channels to eliminate inter-carrier interference. Choosing the first subcarrier to have a frequency such that it has an integer number of cycles in a symbol period, and setting the spacing between adjacent subcarriers (subcarrier bandwidth) to be BSC = B/L, where B is the nominal bandwidth (equal to data rate), and L is the number of subcarriers, ensures that all tones are orthogonal to one another over the symbol period. It can be shown that the OFDM signal is equivalent to the inverse discrete Fourier transform (IDFT) of the data sequence block taken L at a time. This makes it extremely easy to implement OFDM transmitters and receivers in discrete time using IFFT (inverse fast Fourier) and FFT, respectively.

In order to completely eliminate ISI, guard intervals are used between OFDM symbols. By making the guard interval larger than the expected multipath delay spread, ISI can be completely eliminated. Adding a guard interval, however, implies power wastage and a decrease in bandwidth efficiency. The amount of power wasted depends on how large a fraction of the OFDM symbol duration the guard time is. Therefore, the larger the symbol period—for a given data rate, this means more subcarriers—the smaller the loss of power and bandwidth efficiency.

The size of the FFT in an OFDM design should be chosen carefully as a balance between protection against multipath, Doppler shift, and design cost/complexity. For a given bandwidth, selecting a large FFT size would reduce the subcarrier spacing and increase the symbol time. This makes it easier to protect against multipath delay spread. A reduced subcarrier spacing, however, also makes the system more vulnerable to inter-carrier interference owing to Doppler spread in mobile applications. The competing influences of delay and Doppler spread in an OFDM design require careful balancing.