Page 209 - Fundamentals of Radar Signal Processing

FIGURE 3.18 Conventional coherent receiver of Fig. 1.9 with amplitude and
phase mismatch errors and DC offsets.

Inspection of Fig. 3.18 gives

(3.34)

where the time dependence of θ(t) has been dropped to simplify the notation
slightly. Note that the constant α is complex but β is not, and that α = β = 1 in the
absence of gain and phase errors, i.e., if ε = ϕ = 0. Using the identities

(3.35)

in Eq. (3.34) and collecting terms of equal amplitude gives

(3.36)

Equation (3.36) shows that in the presence of amplitude or phase errors, the
complex signal x(t) will not only contain the desired signal component (with a
slightly modified amplitude) Aexp[jθ(t)], but also an image component with a
different amplitude and a conjugated phase function, as well as a complex DC
term. The image component is an error resulting from the amplitude and phase