Carrier frequency offset (CFO) is one of many non-ideal conditions that may affect in baseband receiver design.
In designing a baseband receiver, we should notice not only the degradation invoked by non-ideal channel and noise, we should also regard RF and analog parts as the main consideration.
Otherwise, mismatch in carrier frequency can result in inter-carrier interference (ICI).
A standard-compliant communication system usually requires oscillators to have a small enough tolerance and thus bounds CFO.
In addition, if the transmitter or the receiver is moving, the Doppler effect adds some hundreds of hertz in frequency spreading.
Compared to the CFO resulting from the oscillator mismatch, the Doppler effect in this case is relatively minor.
, results in attenuation in magnitude, phase shift, and ICI, while the integer carrier frequency offset,
Note that the phase shift is identical in every subcarrier and is also proportional to the symbol index
An estimate of the CFO, if within a certain limit, can be obtained simultaneously when the coarse symbol timing is acquired by the algorithms mentioned earlier.
, then another best linear unbiased estimator (BLUE) exploiting the correlation of the repeated segments is possible.
The BLUE estimation algorithm starts with computing several linear auto-correlation functions with
With some modification, this estimator can also be applied to preambles consisting of several repeated segments with specific sign changes.
segments of the preamble are multiplied by their respective signs, and then the same method as the BLUE estimator can be applied.
In the IEEE 802.16e OFDM mode standard, the oscillator deviation is within ±8 ppm.
With the highest possible carrier frequency of 10.68 GHz, the maximum CFO is about ± 171 kHz when the transmitter LO and the receiver LO both have the largest yet opposite-sign frequency deviations, which is also equivalent to ± 1 1 sub carrier spacing
From the previous discussion, it is clear that the estimated CFO obtained simultaneously in the coarse symbol boundary detection has ambiguity in frequency.
The coefficients of the matched filter are the complex conjugate of the long preamble and they are modulated by a sinusoidal wave whose frequency is a possible integer CFO mentioned above.
The output of the matched filter will have a maximum peak value if its coefficients are modulated by the carrier with the correct integer CFO.
However, we can use only one set of matched filter hardware that handles different integer CFOs sequentially.
In addition, as suggested previously in the symbol timing detection subsection, the coefficients of the matched filter can be quantized to -1, 0, 1 to reduce hardware complexity.
As a result, a single CFO set is to be estimated for the multiple receive antennas.
Another fractional CFO estimation algorithm for MIMO-OFDM systems applies different weights to the receive signals according to the respective degrees of channel fading The preamble is designed so that each transmit antenna uses non-overlapping sub carriers to facilitate separation of signals from different transmit antennas.
The magnitude of the cross-correlation output reflects the channel fading between the corresponding transmit and receive antenna pair.
Then, the CFO is estimated based on the phase of delay correlation of weighted signals.
Besides, the CFO contained in the received signal may very well be time-varying and, thus, it needs to be continuously tracked.
The received signal also suffers from sampling clock offset (SCO), which may cause a gradual drift of the safe DFT window in addition to extra phase shift in the received frequency-domain signals.
The phase shifts in the received frequency-domain signals caused by the CFO are identical at all subcarriers provided that the ICI is ignored.
On the other hand, the SCO causes phase shifts that are proportional to the respective sub carrier indices.
The received signals contain ICI and noise, and therefore the phases deviate from the two ideal straight lines.
In order to suppress the ICI and thereby reduce SNR degradation, the residual CFO must be sufficiently small.