Page 364 - Fundamentals of Radar Signal Processing

that of the nominal echo amplitude. Consequently, clutter attenuation may be as

poor as 20 log (1/0.1) = 20 dB even though the clutter is perfectly stationary.
10
For a two-pulse canceller with an average signal gain G of 2 (6 dB), the
maximum achievable improvement factor is 26 dB.
A more realistic analysis of the limitations due to amplitude jitter can be
obtained by modeling the amplitude of the mth transmitted pulse as A[m] = k(1 +
a[m]), where a[m] is a zero mean, white random process with variance that

represents the percentage variation in transmitted amplitude, and k is a constant.
The received signal will have a complex amplitude of the form k′(1 + a[m])
exp(jϕ), where ϕ is the phase of the received slow-time sample and the constant
k′ absorbs all the radar range equation factors. The average power of this signal,
which is the input to the pulse canceller, is

(5.65)

The expected value of the two-pulse canceller output power will be

(5.66)

The achievable clutter cancellation is thus

(5.67)

For example, an amplitude variance of 1 percent ( ) limits two-pulse

clutter cancellation to a factor of 50.5, or 17 dB. Because the average target
gain G of the two-pulse canceller is G = 2 (3 dB), the limit to the improvement
factor I is 50.5 × 2 = 101, or 17 + 3 = 20 dB.
Another example is phase drift in either the transmitter or receiver. This
can occur due to instability in coherent local oscillators used either as part of
the waveform generator on the transmit side or in the demodulation chains on the
receiver side. Consider the weighted coherent integration of M data samples

y[m] with a zero-mean stationary white phase error ϕ[m]

(5.68)