[b] Direct conversion receivers contain a local oscillator (LO) which generates both a sine wave at
Neither is the gain perfectly matched between the parallel sections of circuitry dealing with the two signal paths.
Their design must include measures to control IQ imbalance, so as to limit errors in the demodulated signal.
This process requires shifting the LO signal by 90° to produce a quadrature sinusoidal component, and a matched pair of mixers converting the same input signal with the two versions of the LO.
Mismatches between the two LO signals and/or along the two branches of down-conversion mixers, and any following amplifiers, and low-pass filters, cause the quadrature baseband signals to be corrupted, either due to amplitude or phase differences.
Then we can model such imbalance using mismatched local oscillator output signals:
To analyze IQ imbalance in the frequency domain, the above equation can be rewritten as:
In an OFDM system, the base-band signal consists of several sub-carriers.
Complex-conjugating the base-band signal of the kth sub-carrier carrying data
Equivalently, the received base-band OFDM signal under the IQ imbalance effect is given by:
In conclusion, besides a complex gain imposed on the current sub-carrier data
The ICI term makes OFDM receivers very sensitive to IQ imbalances.
To solve this problem, the designer can request a stringent specification of the matching of the two branches in the frond-end or compensate for the imbalance in the base-band receiver.
On the other hand, a digital Odd-Order I/Q-demodulator with only one input can be used,[1][2] but such design has a bandwidth limitation.
The time domain base-band signals with IQ imbalance can be represented by
can be assumed to be time-invariant and frequency-invariant, meaning that they are constant over several sub carriers and symbols.
With this property, multiple OFDM sub-carriers and symbols can be used to jointly estimate
Note that the second term represents interference coming from the mirrored sub-carrier
In MIMO-OFDM systems, each RF channel has its own down-converting circuit.
MIMO system as an example, the received frequency domain signal is given by:
are the IQ imbalance coefficients of the qth receive RF channel.
The received signals at the pilot sub-carriers of the first RF channel are stacked into a vector
Clearly, the above formula is similar to that of the SISO case and can be solved using the LS method.
However, if the noise is added after IQ imbalance, the effective SNR degrades.
The frequency domain compensated signal at the ith symbol and the kth sub-carrier:
Frequency domain OFDM signals under the influence of IQ imbalance is given by:
Such a training scheme easily decouples the IQ imbalance and the channel frequency response.
Furthermore, the accuracy of this ratio estimation can be improved by averaging over several training symbols and several sub-carriers.
Although the IQ imbalance estimation using this training symbol is simple, this method suffers from low spectrum efficiency, as quite a few OFDM symbols must be reserved for training.
Note that, when the thermal noise is added before the IQ imbalance, the ratio