I was curious as to why IEEE 802.16d (fixed service) uses Orthogonal Frequency Division Multiplexing (OFDM). IEEE 802.16e (mobile) uses Orthogonal Frequency Division Multiple Access (OFDMA). So, what’s the difference between the two, and why is there a difference?
Lets first look at FDM:

In FDM system, signals from multiple transmitters are transmitted simultaneously (at the same time slot) over multiple frequencies. Each frequency range (sub-carrier) is modulated separately by different data stream and a spacing (guard band) is placed between sub-carriers to avoid signal overlap.

OFDM is sometimes referred to as
discrete multi-tone modulation because, instead of a single carrier being modulated, a large number of evenly spaced subcarriers are modulated using some m-ary of QAM. This is a spread-spectrum technique that increases the efficiency of data communications by increasing data throughput because there are more carriers to modulate. In addition, problems with multi-path signal cancellation and spectral interference are greatly reduced by selectively modulating the “clear” carriers or ignoring carriers with high bit-rate errors.
Like FDM, OFDM also uses multiple sub-carriers but the sub-carriers are closely spaced to each other without causing interference, removing guard bands between adjacent sub-carriers. This is possible because the frequencies (sub-carriers) are orthogonal, meaning the peak of one sub-carrier coincides with the null of an adjacent sub-carrier.
In an OFDM system, a very high rate data stream is divided into multiple parallel low rate data streams. Each smaller data stream is then mapped to individual data sub-carrier and modulated using some sorts of PSK (Phase Shift Keying) or QAM (Quadrature Amplitude Modulation). i.e. BPSK, QPSK, 16-QAM, 64-QAM.
OFDM needs less bandwidth than FDM to carry the same amount of information which translates to higher spectral efficiency. Besides a high spectral efficiency, an OFDM system such as WiMAX is more resilient in NLOS environment. It can efficiently overcome interference and frequency-selective fading caused by multipath because equalizing is done on a subset of sub-carriers instead of a single broader carrier. The effect of ISI (Inter Symbol Interference) is suppressed by virtue of a longer symbol period of the parallel OFDM sub-carriers than a single carrier system and the use of a cyclic prefix (CP).
The OFDM spread-spectrum scheme is used for many broadly used applications, including digital TV broadcasting in Australia, Japan and Europe; digital audio broadcasting in Europe; Asynchronous Digital Subscriber Line (ADSL) modems and wireless networking worldwide (IEEE 802.11a/g).