Page 235 - Fundamentals of Radar Signal Processing

then cT /2 meters. In general, targets do not arrange themselves precisely at
s
ranges corresponding to the range samples. The receiver then will not sample
the matched filter output precisely at its peak. The result is a reduction in the
measured signal amplitude and therefore an SNR loss.
This is exactly the issue of straddle loss that was discussed in Chap. 3 with
regard to the DFT of frequency domain data. In either case, the finite sampling
rate allows the processor to “miss” the peak response, whether it is the matched

filter output in fast time or the spectrum of a slow-time signal. Straddle loss also
arises in angular sampling with scanning antennas. In any of these cases it can be
reduced with higher sampling rates or various interpolation methods.
Consideration of these methods is deferred to the discussion of pulse Doppler
analysis in Chap. 5 and the analyses of time delay, frequency, and angle
estimation in Chap. 7. All of the methods there can be applied to the fast-time
straddle loss for the various waveforms in this chapter.

4.2.5 Range Resolution of the Matched Filter
By determining the range separation that would result in nonoverlapping echoes,
it was shown in Chap. 1 that the range resolution achieved by a simple pulse of
duration τ seconds is cτ/2 meters. When a matched filter is used, the output due
to each scatterer is now 2τ seconds long, but is also triangular rather than
rectangular in shape. Does the longer matched filter output result in a larger

value of range resolution?
Before considering this question, it is useful to recall that the demodulated
echo from a scatterer at range R meters has not only a delay of t = 2R /c
0
0
0
seconds, but also an overall phase shift of exp[j(–4π/λ)R ] radians. A change of
1
0
only λ/4 in range will cause a change of 180° in the received echo phase. Two
overlapping target responses may therefore add either constructively or
destructively in phase, and small deviations in their spacing can result in large
changes in the composite response. Consider two targets at ranges ct /2 and
0
ct /2 + cτ/2 and assume τ is such that the two matched filter responses add in
0
phase. Then the composite response at the matched filter output is a flat-topped
trapezoid as shown in Fig. 4.5a. Clearly, if the separation between the two
scatterers increases, a dip will begin to develop in the composite response,

even when the separation is such that they remain in phase. If the separation
decreases, the in-phase response will still be a trapezoid, but with a higher peak
and a shorter flat region as the responses overlap more. Because any increase in
separation will result in a dip between the two responses, the separation of cτ/2
meters is still considered to be the range resolution of the matched filter output.
Thus, using a matched filter does not degrade the range resolution. To reinforce
this further, recall that the definition of the Rayleigh resolution is the peak-to-

first null distance. Inspection of Fig. 4.3 shows that cτ/2 is also the Rayleigh
resolution of the simple pulse matched filter output.