# Blind Compensation of \(I/q\) Impairments in Wireless Transceivers
## 4 Discussion  
Methods that deal with compensating the modulator impairments at the transmitter, using training signals require a feedback path to down-covert the RF signal to baseband or low IF. This feedback path contains a digital demodulator, an ADC and a frequency down-converter, which adds a time delay and phase mismatch to the received signal along with the ADC's distortions. The output of the demodulator in the presence of these effects can be written as: \(y_{\text{delay}}=y(n-t_{d})e^{\lvert\phi_{d}\rvert}\), where \(t_{d}\) is the time delay and \(\phi_{d}\) is the phase shift caused by the feedback path. Prior to system identification, the input and output signals are time and phase aligned. An inaccurate adjustment leads to poor modeling and compensation performance by manifesting itself as dispersion in the gain and phase characteristics of the system.  
For very small time delays, better time resolution (\(1/f_{s}\)) is needed, which places a stringent requirement on the sampling frequency (\(f_{s}\)) of the ADCs. In order to avoid changing the ADC or other hardware for increased sampling rate, signal processing techniques have been used in many works. A popular method for the time adjustment of these signals is the cross-correlation based method [30]. First, a coarse estimation is applied, followed by a Lagrange polynomial-based fine time delay estimation.  
If we consider a function: \(y_{l}=f(x_{l})\), with values of the function known only at \(l=1,2,\ldots,P\), the Lagrange interpolation polynomial of degree \(P\)-1 can be used to find the values of \(y\) at other values of \(x\)[31]. Interpolation of the data using this polynomial is, however, a computationally complex procedure requiring O(\(P^{2}\)) floating-point operations. Similarly, a phase shift adjustment needs to be performed before system identification. However, since the proposed methodology does not require the input/training signal for estimation of the imbalance parameters, it is not affected by the time delay and phase mismatch. Thus, cumbersome alignment techniques can be avoided using this method.  
In addition to timing and phase mismatch, the feedback path can also add an \(I/Q\) imbalance to the received signal. Opting for a different receiver topology, instead of direct conversion, can solve this problem. For example, the method employed in [12] uses a super-heterodyne receiver in the feedback path to avoid receiver imbalance. However, this comes at a cost of hardware complexity and other feedback loop impairments, such as the gain/phase response of the feedback path; and, ADC distortions still need to be considered.  
The method employed in [32] down-converts the RF signal to a low IF, followed by sampling and analog-to-digital conversion. Although, this can help avoid the impact of receiver imbalance and the proposed method can eliminate the effects of gain/phase and impulse response of the feedback loop, methods for timing, frequency and carrier synchronization are still required. The method proposed in [11] solves the problem of phase mismatch by using a diode detector in the feedback path of the transmitter, which calculates the instantaneous power. However, for the technique proposed in this work, no extra hardware in the transmitter is needed, as it does not need a feedback path at the transmitter, making it cost effective and very suitable especially for uplink scenarios. This advantage is due to the blind nature of the estimation procedure, eliminating the need for a feedback path and the resulting distortions.