Like the carrier frequencies, transmitter and receiver sampling frequencies used by the DAC and ADC are generally slightly mismatched. This impairment is known as SFO and will degrade the system performance.

Due to the SFO the received signal *x*(*t*) is sampled at *n*(*T*_{s} + Δ*T*) instead of the ideal *nT*_{s}:

2.99

The SFO is defined as

in which *F*_{s} is the ideal sampling frequency, *F*_{s} = 1/*T*_{s}, and Δ*T*/*T*_{s} is the relative sampling clock offset. Because Δ*T*/*T*_{s} is generally specified in ppm and then much smaller than one, we can approximate Equation 2.100 as

2.101

in which δ is the normalized relative sampling clock accuracy/precision generally specified in ppm. For example, 50 ppm precision for a sampling clock running at 100 MHz means a possible SFO of 5 kHz.

Let us suppose that the receiver is impaired by an SFO but perfectly synchronized on the symbols; in this case the OFDM baseband signal is expressed as

2.102

in which *N* is the total number of subcarriers within the OFDM symbol (including DC and guard bands), *s _{k}* is ...

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