FFT window location offsets are often corrected by performing a time-domain correlation with a known training sequence embedded in the transmitted signal. The location of the peak of the correlation allows the receiver to synchronize itself with the incoming signal.

Another potentially harmful situation is the presence of a sampling frequency offset. This condition occurs when the A/D converter output is sampled either too fast or too slow. Recall that F subscript S/2 is the highest available frequency in discrete-time where F subscript S is the sampling frequency. Sampling too fast essentially increases the value of F subscript S/2 and the result is a contracted (i.e., squashed) spectrum. Similarly, sampling too slow decreases the value of F subscript S/2 and results in an expanded spectrum. If the spectrum expands too much, aliasing of the spectrum can occur. Either type of sampling frequency offset results in IBI since the expansion or contraction of the spectrum prevents the received subcarriers from lining up with the FFT bin locations. The effect of sampling too fast is illustrated in Figure 10 and simulation results to demonstrate this effect are shown in Figure 11. A sampling frequency offset can be corrected by generating an error term that is used to drive a sampling rate converter.

Additive white Gaussian noise (AWGN) is the most common impairment encountered in a communications system. In a wireless medium, the noise source is typically considered to be thermal noise that is Gaussian and uniform across the frequency range. Additional noise sources include atmospheric sources and solar radiation. In a contained media, such as a coaxial cable system, thermal noise will be present, but the system may also have other sources that can increase the noise in the system. The effect of AWGN on an OFDM system is similar to its effect on a single carrier system. The signal-to- noise ratio (SNR) is a function of the total signal power over the total noise power across the received channel. The uniform noise contributes to the SNR of each subcarrier in the OFDM system and the net result is equivalent to the effect on single channel systems.

Noise in a communications channel can often be shaped, or "colored", by various effects. These effects can include transmit signal imperfections, transmission channel characteristics, or receiver frequency shaping. The implications of these effects for an OFDM system can be different compared to its single-carrier counterpart. The modulation of the OFDM system can be tailored for the noise characteristics. One method previously mentioned involves lowering the modulation (number of bits/symbol) on subcarriers in a low SNR environment as illustrated in Figure 12. Another method involves sending the same data on several subcarriers, or sending data that can be considered lower priority. In extreme cases, the subcarriers can transmit no data, essentially turning them off.

Impulse noise is a common impairment in a communications system arising from motors or lightning. Impulse noise is typically characterized as a short time-domain burst of energy. The burst may be repetitive or may be a single event. In either case, the frequency spectrum from this energy burst is wideband, typically much wider than the channel, but is present for only a short time period.

One of the most important concepts to understand about OFDM and its properties related to the FFT algorithm is how the algorithm changes the nature of the signal. In a single-carrier system, the symbol can be viewed as occupying all of the available frequency spectrum for the time duration of the symbol. A group of symbols then occupies all of the spectrum for the duration of the whole group, but in a time division arrangement.

OFDM, using the FFT, takes symbols and creates these groups directly and then transforms them. They are no longer time-domain multiplexed, they are now frequency-domain multiplexed. The OFDM symbol is now a collection of these source symbols, and this OFDM symbol now has a much longer duration. Each original symbol occupies only a small frequency region, but now occupies that region for the entire OFDM symbol duration. Figure 13 illustrates this concept. For impulses that are short in duration, the impulse energy masks a smaller percentage of time of each OFDM symbol compared to the single carrier case. Impulse noise can therefore have less of an effect on short duration noise.

Single-carrier interference arises from other sources that may co-exist in the frequency range of interest. These can be generated by nearby circuits or other transmission sources. The single carrier system must handle this interference as a noise source for all information sent. The OFDM system can avoid the frequency region of interference by disabling or turning off the affected subcarriers. Narrowband modulated sources of interference can be considered similar to carrier interference in their impairment.

Noise can also be added to the signal through a frequency-conversion stage. The local oscillator used in the converter will inherently have some phase noise (uncertainty of actual frequency or phase of the signal) that will be transferred to the desired signal. Figure 14 shows the effect of phase noise on a local oscillator. Phase noise is shaped and is primarily concentrated near the carrier (or center frequency) of the signal.

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