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IQ imbalance : ウィキペディア英語版
IQ imbalance
IQ imbalance is a performance-limiting issue in the design of direct conversion receivers, also known as zero intermediate frequency (IF) or homodyne receivers. Such a design translates the received radio frequency (RF, or passband) signal directly from the carrier frequency (fc) to baseband using only one mixing stage. The traditional heterodyne receiver structure needs an intermediate-frequency (IF) stage between the RF and baseband signals. The direct conversion receiver structure does not have an IF stage, and does not need an image rejection filter. Due to the lower component count, it is easier to integrate. However, a direct-conversion RF front-end suffers from two major drawbacks: one is IQ imbalance and the other is DC offset. When designing a homodyne receiver, control of IQ imbalance is necessary to limit signal demodulation error.
IQ imbalances occur due to mismatches between the parallel sections of the receiver chain dealing with the in-phase (I) and quadrature (Q) signal paths. The local oscillator (LO) generates a sinewave, and a copy of that sinewave that is delayed by 90 degrees. When the direct LO output is mixed with the original signal, this produces the I signal, whereas when the delayed LO output is mixed with the original signal, that produces the Q signal. In the analog domain, the delay is never exactly 90 degrees. Similarly, analog gain is never perfectly matched for each of the signal paths.
== Definition ==
A direct conversion receiver uses two quadrature sinusoidal signals to perform the so-called quadrature down conversion. This process requires shifting the local oscillator (LO) signal by 90 degrees to produce a quadrature sinusoidal component. When mismatches exist between the gain and phase of the two sinusoidal signals and/or along the two branches of down-conversion mixers, amplifiers, and low-pass filters, the quadrature baseband signals will be corrupted.
Suppose the received passband signal is identical to the transmitted signal and is given by
y(t)=Re\=x_I(t)\cos(2\pi f_c t)-x_Q(t)\sin(2\pi f_c t) \ \ \ \ \ where \ x(t)=x_I(t)+jx_Q(t) \ is \ the \ transmitted \ baseband \ signal
Assume that the gain error is 20\log() dB and the phase error is \varepsilon_\theta degrees. Then we can model such imbalance using mismatched local oscillator output signals.
2(1+\epsilon_A)\cos(2\pi f_c t-\varepsilon_\theta/2),
-2(1-\epsilon_A)\sin(2\pi f_c t+\varepsilon_\theta/2).
Multiplying the passband signal by the two LO signals and passing through a pair of low-pass filters, one obtains the demodulated baseband signals as
\tilde_I(t)=(1+\varepsilon_A)(),
\tilde_Q(t)=(1-\varepsilon_A)().
The above equations clearly indicate that IQ imbalance causes interference between the I and Q baseband signals.
To analyze IQ imbalance in the frequency domain, above equation can be rewritten as
x(t)=\tilde_I(t)+j\tilde_Q(t)=()x(t)+()x^
*(t)=\eta_\alpha x(t)+\eta_\beta x^
*(t)
where (.)^
* denotes the complex conjugate. In an OFDM system, the baseband signal consists of several subcarriers. Complex-conjugating the baseband signal of the kth subcarrier carrying data X_k is identical to carrying X^
*_k on the (-k)th subcarrier:
((X_+jX_)e^)^
*=(X_-jX_)e^=X^
*_ke^
where f_S is the subcarrier spacing.
Equivalently, the received baseband OFDM signal under the IQ imbalance effect is given by
X_k=\eta_\alpha X_k+\eta_\beta X^
*_
In conclusion, besides a complex gain imposed on the current sub carrier data Xk, IQ imbalance also introduces ICI from the mirror subcarrier. The ICI term makes OFDM receivers very sensitive to the IQ imbalance effect. 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 baseband receiver.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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