Page 56 - Fundamentals of Radar Signal Processing

“coherent signal processing” as “echo integration, filtering, or detection using

amplitude and phase of the signal referred to a coherent oscillator” (emphasis
added) (IEEE, 1982). Coherency is a stronger requirement than frequency
stability. In practice, it means that the transmitted carrier signal must have a
fixed phase reference for several, perhaps many, consecutive pulses. Consider a
pulse transmitted at time t of the form a(t – t ) sin[Ω(t – t ) + ϕ], where a(t) is
1
1
1
the pulse shape. In a coherent system, a pulse transmitted at time t will be of the
2
form a(t – t ) sin[Ω(t – t ) + ϕ]. Note that both pulses have the same argument (t
2
1
– t ) + ϕ for their sine term; only the envelope term changes location on the time
1
axis. Thus, both sinusoids are referenced to the same absolute starting time and
phase. This is as opposed to the second pulse being of the form a(t – t ) sin[Ω(t
2
– t ) + ϕ], which is nonzero over the same time interval as the coherent pulse a(t
2
– t ) sin[Ω(t – t ) + ϕ] and has the same frequency, but has a different phase at
2
1
any instant in time. Figure 1.12 illustrates the difference visually. In the coherent
case, the two pulses appear as if they were excised from the same continuous,
stable sinusoid; in the noncoherent case, the second pulse is not in phase with
the extension of the first pulse. Because of the phase ambiguity discussed
earlier, coherency also implies a system having both I and Q channels.

FIGURE 1.12 Illustration of the concept of a fixed phase reference in coherent
signals. (a) Coherent pulse pair generated from the reference sinusoid. (b)
Reference sinusoid. (c) Noncoherent pulse pair.

Another requirement is that the I and Q channels have perfectly matched
transfer functions over the signal bandwidth. Thus, the gain through each of the
two signal paths must be identical, as must be the phase delay (electrical length)
of the two channels. Of course, real receivers do not have perfectly matched
channels. The effect of gain and phase imbalances will be considered in Chap.
3. Finally, a related requirement is that the oscillators used to demodulate the I