Have you ever wondered just "how" OFDM subcarriers are able to be spaced so tightly together without any guard band in-between? Most Wi-Fi textbooks will simply state that the spacing of the subcarriers allows the harmonics to overlap, thus canceling out any interference.

OFDM divides a given channel into many narrower subcarriers. The spacing is such that the subcarriers are orthogonal, so they won’t interfere with one another despite the lack of guard bands between them. This comes about by having the subcarrier spacing equal to the reciprocal of symbol time. All subcarriers have a complete number of sine wave cycles that upon demodulation will sum to zero.

This tells us that the spacing of the subcarriers is directly related to the useful symbol time (more specifically, the amount of time the transmitter spends performing IFFT). Because of this relationship, the resulting sinc frequency response curves from each subcarrier create signal nulls in the adjacent subcarrier frequencies thus preventing * inter-carrier interference (ICI)*. OFDM is a form of frequency division multiplexing (FDD), which typically requires guard bands between carriers and specialized hardware with bandpass filters to remove interference. OFDM eliminates the need for these which increases spectral efficiency and reduces cost and complexity of the system since all functions can be completed with digital signal processing (DSP).

To illustrate, let's take a look at the Wi-Fi OFDM channelization. Each 20 MHz channel, whether it's 802.11a/g/n/ac, is composed of 64 subcarriers spaced ** 312.5 KHz** apart. This spacing is chosen because we use 64-point FFT sampling. 802.11a/g use 48 subcarriers for data, 4 for pilot, and 12 as null subcarriers. 802.11n/ac use 52 subcarriers for data, 4 for pilot, and 8 as null.

And we also know that a standard Wi-Fi symbol is 4us, composed of ** 3.2us IFFT** (useful symbol duration) and 0.8us long guard interval. (If using a short guard interval of 0.4us then the total symbol time is 3.6us).

So, as stated earlier, "subcarrier spacing is equal to the reciprocal of symbol time." Let's examine:

- Subcarrier spacing = 312.5 KHz
- Useful symbol duration = 3.2us IFFT
- Reciprocal = 1 cycle / 0.0000032 sec = 312,500 cycles/sec = 312.5 KHz

Since IFFT is used for modulation the spacing of the subcarriers is such that at the frequency where we evaluate the received signal (the center frequency of each subcarrier) all other signals are zero. And this in turn drives the duration of the useful symbol time and is the reason why we use 3.2us IFFT.

Another advantage of OFDM is that by using a reduced symbol rate of 250,000 symbols per second the negative effects of multipath distortion are reduced. Since each symbol occupies more time, there is more resilience to delay spread which is caused by multipath when signal reflections cause multiple copies of the same transmitted symbol to arrive at the receiver at slightly different times. Compare the OFDM symbol rate to 802.11b DSSS and Bluetooth both having over 1M symbols per second (DSSS actually has 11M symbols per second if we consider the 'chipping' rate).

However, multipath also has a negative effect on OFDM, especially when clients are mobile. The orthogonality of the subcarriers can be lost when movement and multipath are present because signal delays (the *delay spread*) impact the reciprocal relationship of the subcarriers and the useful symbol time (IFFT). Without proper orthogonality between subcarriers, inter-carrier interference (ICI) would result from this doppler shifting. The fix for this is to include a cyclic prefix with each symbol, which is part of the guard interval, that allows channel estimation and equalization. Thus, * contrary to popular belief, the guard interval is actually not empty airtime* but actively used for cyclic prefixing to allow proper OFDM operation in a multipath environment.

Despite the slower symbol rate, we still have much higher data rates due to the increase in carriers being modulated by an order of magnitude, from 1 (DSSS) to 48 (OFDM in 11a/g) and 52 (OFDM in 11n/ac) per 20 MHz channel. We take a serial data stream and perform parallel data transmission across the frequency domain.

Now you know just how Orthogonal Frequency Division Multiplexing (OFDM) really works.

Cheers,

Andrew

P.S. - These are deep subjects that involve complex maths. Search on any of this any you're likely to end up finding research papers with difficult math equations. However, you may be interested in reading this laymen's FAQ on OFDM.