# Inter-Carrier Interference for OFDM

The price for the optimum subcarrier spacing is the sensitivity of OFDM to frequency errors. If the receiver’s frequency is some fractions of the subcarrier spacing (subcarrier bandwidth) then we encounter not only interference between adjacent carriers, but in principle between all carriers. This is known as Inter-Carrier Interference (ICI) and sometimes also referred to as Leakage Effect in the theory of discrete Fourier transform.

The effect is illustrated on the following figure. It shows the spectral power density of an OFDM system with five subcarriers. If we have an exact match between receiver and transmitter frequency and we would like to get the symbol transmitted in subcarrier 2, then there is no interference from the other subcarriers.

This is due to the fact, that at the center frequency of subcarrier 2 all other subcarriers have a null point of their power spectrum. But if we have a little frequency drift between transmitter and receiver, then we decode the symbol of subcarrier 2 a little bit offset from its true center frequency. But now two effects begin to work. First subcarrier 2 has no longer its power density maximum here – so we loose some signal energy. Second the other subcarriers 0, 1, 3 and 4 have no longer a null point here. So we get some noise from each other subcarrier.

The result is a lower signal to noise ratio by a decreased signal level and an increased noise level. This is the inter-carrier interference effect for OFDM. As one can see this strongly depends on the ratio between absolute frequency offset between transmitter and receiver and the subcarrier spacing. To limit the influence of the ICI on OFDM systems completely by hardware we would have to have receivers and transmitters with under 0.1 ppm frequency stability.

This would drastically increase the cost and complexity of hardware. Thus quite a big part of the OFDM software in the receiver deals with frequency correction using the cyclic prefix, but also reference or pilot signals sent with the signal.