epdf.pub_special-design-topics-in-digital-wideband-receivers-vgood.pdf
Figure 5.1 Image amplitude as a function of amplitude and phase imbalances. Table 5.1 Required Dynamic Range Versus Required
Amplitude and Phase Balances
image rejection
epdf.pub_digital-synthesizers-and-transmitters-for-software-radio.pdf
sym & asym models
Compensation model: Gain & imbal model (with simplifications)
F3.5|6: . Signal flow graph of symmetrical/asym IQ correction network.
P56) 3.1.3 Asymmetric Compensation Method
The method in [Cav93] is an improved version of the method presented in [Fau91]. The improvement
suggests that a more economical asymmetric form of compensator that results in lower computational
load and faster convergence should be used. The symmetrical correction network in Figure 3-5
requires 4 multipliers and 4 adders, and asymmetric in Figure 3-6 needs 3 multipliers and 3 adders
[Cav93]. Moreover, a simplification is made and division with is neglected in (3.11), since it has no
substantial effect on the results, it produces only scale change of a few percentage points. This therefore
reduces the number of the multipliers to two. The adaptation algorithm itself has only to acquire four
remaining imbalance compensation terms in (3.10). In [Cav93], the LMS algorithm is used, providing an
effective way of achieving convergence.
The DC offset is eliminated by setting I = 0, Q = 0 and adjusting a to minimize the envelope detector
output. A detailed description of this can be found in [Cav93], but the principle is that the DC correction
term a is obtained
in two steps. First, 4 measurements are made in the output with different values of a, and a correction
term is obtained from these measurements. The article suggests that the sum of squared errors between
the measurements and the fitted surface of the input signal is minimized. Second, the measurements are
made with the current optimal correction terms. The correction term is updated and the measurements are
repeated until convergence is achieved. In practice, about eight measurements should be enough to obtain
the terms.
The gain and phase imbalance compensation is achieved next. In asymmetric compensator gain and phase
compensation, terms must be acquired simultaneously; [Cav93] provides an algorithm to do so. Four test
signals are used with the same amplitude, but with four different phases. The adaptation is complete when
all four phases give the same output from the envelope detector. The details are presented in [Cav93].
Fewer than eight iterations are needed to reach a steady state, and each iteration needs four power
measurements at the envelope detector output.
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