Page 208 - Fundamentals of Radar Signal Processing

unambiguous range, reducing the volume that can be searched without

ambiguities.

3.4 I/Q Imbalance and Digital I/Q

In Chap. 1, it was shown that the output of a quadrature receiver given a real-
valued bandpass signal as input is the same as would be obtained by using the
equivalent analytic (one-sided spectrum) complex signal with complex
demodulation by the signal exp(–jΩ t). In other words, the quadrature receiver
0
acts to select the upper band of the bandpass signal and shift it to baseband. Any

system that accomplishes this same result can be used to derive the in-phase and
quadrature signals needed for further signal processing.
The quadrature receiver could, in principle, be implemented entirely
digitally. The input signal would be converted to a digital signal after the low-
noise amplifier. The mixing operations would be replaced by multiplications,
and the analog lowpass filters by digital filters. This is not done in practice

because a straightforward implementation would require the A/D converter to
operate at about twice the carrier frequency rather than twice the information
bandwidth of the signal (specifically, 2F + β rather than just β samples per
0
second), a technologically unreasonable requirement. On the other hand, the
conventional analog quadrature receiver also has technological limitations, as
mentioned briefly in Chap. 1. Correct operation assumes that the two channels
are perfectly matched in delay and gain across the frequency band of interest,

there are no DC biases in either channel, and the two reference oscillators are
exactly 90° out of phase. In this section, the effect of I/Q imbalances is
investigated, and then two digital I/Q receiver structures that combat imbalance
errors are described.

3.4.1 I/Q Imbalance and Offset
Figure 1.9 describing the conventional quadrature receiver is repeated below as

Fig. 3.18, but with the addition of an amplitude mismatch factor (1 + ε), a phase
mismatch ϕ, and DC offsets γ and κ in the in-phase (I) and quadrature (Q)
channels, respectively. Take the I channel as the gain and phase reference
without loss of generality, so the gain and phase errors are placed entirely in the
Q (upper) channel. As shown in the figure, the introduction of these errors is
reflected as an undesired gain and phase shift in the Q channel output, along
with the DC offset in each channel. For processing, the I and Q channel outputs

are combined as usual into a single complex signal, x(t) = I(t) + jQ(t). In the
absence of mismatch errors, x(t) = Aexp[jθ(t)]. How are the mismatch errors
manifested in x(t)?