Page 55 - Fundamentals of Radar Signal Processing

FIGURE 1.10 (a) The I channel of the receiver in Fig. 1.9 measures only the
cosine of the phasor θ(t). (b) The Q channel measures only the sine of the
phasor.

(1.20)

Equation (1.20) implies a more convenient way of representing the effect
of an ideal coherent receiver on a transmitted signal. Instead of representing the
transmitted signal by a sine function, an equivalent complex exponential function

is used instead. The echo signal of (1.17) is thus replaced by
5

(1.21)

The receiver structure of Fig. 1.9 is then replaced with the simplified model of
Fig. 1.11, where the echo is demodulated by multiplication with a complex
reference oscillator exp(– jΩt). This technique of assuming a complex
transmitted signal and corresponding complex demodulator produces exactly the

same result obtained in Eq. (1.20) by explicitly modeling the real-valued signals
and the I and Q channels, but is much simpler and more compact. This complex
exponential analysis approach is used throughout the remainder of the book. It is
important to remember that this is an analysis technique; actual analog hardware
must still operate with real-valued signals only. However, once signals are
digitized, they may be treated explicitly as complex signals in the digital
processor.

FIGURE 1.11 Simplified transmission and receiver model using complex
exponential signals.

Figure 1.9 implies several requirements on a high-quality receiver design.
For example, the local oscillator and the transmitter frequencies must be
identical. This is usually ensured by having a single stable local oscillator
(STALO) in the radar system that provides a frequency reference for both the
transmitter and the receiver. Furthermore, many types of radar processing
require coherent operation. The IEEE Standard Radar Definitions defines