Page 64 - Fundamentals of Radar Signal Processing

(1.29)

2 2
The power in the integrated signal component is N A . Provided the noise
samples w[n] are independent of one another and zero mean, the power in the
noise component is the sum of the power in the individual noise samples.
Further assuming each has the same power , the total noise power is now
. The integrated SNR becomes

(1.30)

Coherently integrating N measurements has improved the SNR by a factor
of N; this increase is called the integration gain. Later chapters show that, as
one would expect, increasing the SNR improves detection and parameter
estimation performance. The cost is the extra time, energy, and computation

required to collect and combine the N pulses of data.
In coherent integration, the signal components added in phase, i.e.,
coherently. This is often described as adding on a voltage basis, since the
amplitude of the integrated signal component increased by a factor of N, with the
2
result that signal power increased by N . The noise samples, whose phases
varied randomly, added on a power basis. It is the alignment of the signal
component phases that allowed the signal power to grow faster than the noise
power.
Sometimes the data must be preprocessed to ensure that the signal
component phases align so that a coherent integration gain can be achieved. If
the target had been moving in the previous example, the signal component of the
measurements would have exhibited a Doppler shift, and Eq. (1.29) would
instead become

(1.31)

for some value of normalized Doppler frequency f . The signal power in this
D
case will depend on the particular Doppler shift, but except in very fortunate
cases will be less than A N . However, if the Doppler shift is known in
2
2
advance, the phase progression of the signal component can be compensated
before summing: