Orthogonality In 4G Wireless Communications
4G Communications
before talking about the orthogonality,first i should discuss the 2 problems Inter-symbol interference (ISI) and inter-carrier interference (ICI)
1-Inter-symbol interference (ISI):
Usually refers to interference of an OFDM symbol by previous OFDM symbols. In a multipath environment, a transmitted symbol takes different times to reach the receiver through different propagation paths.
From the receiver‘s point of view, the channel introduces time dispersion in which the duration of the received symbol is stretched. Extending the symbol duration causes the current received symbol to overlap previous received symbols and results in inter-symbol interference (ISI).
2-Inter-carrier interference (ICI):
Interference caused by data symbols on adjacent subcarriers. ICI occurs when the multipath channel varies over one OFDM symbol time. When this happens, the Doppler shifts on each multipath component cause a frequency offset on the subcarriers, resulting in the loss of orthogonality among them.This situation can be viewed from the time domain perspective, in which the integer number of cycles for each subcarrier within the FFT interval of the current symbol is no longer maintained due to the phase transition introduced by the previous symbol.
Finally, any offset between the subcarrier frequencies of the transmitter
and receiver also introduces ICI to an OFDM symbol.
Solutions to avoid interference:
A smart choice of carrier frequencies can eliminate the interference between sub channels and render the multicarrier idea effective.
Assume that we have two carriers exp(i2πf1t) and exp(i2πf2t) and the symbol duration is Ts.
The received signal is X1(t) exp(i2πf1t) + X2(t) exp(i2πf2t) . In order to get X1(t), let‘s multiply the received signal by exp(-i2πf1t) and integrate over Ts.
Note that the time dependence has removed as X1(t) and X2(t) is constant over Ts.
To eliminate the interference on X1, we want the second term to be zero. This occurs when exp (i 2π(f1-f2)Ts)= 1. That is 2π (f1−f2) Ts=2πm ,where m is integer.
The smallest separation between the two carriers that satisfies orthogonality and, thus, eliminates intra-carrier interference (ICI) is f1−f2=1/Ts .
Using uniformly-spaced subcarriers with a spacing 1/Ts ,i.e., orthogonal subcarriers explains the‘ O‘ of OFDM.
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