What is processing gain in radar, and how is it quantified for N integrated pulses?

What is processing gain in radar, and how is it quantified for N integrated pulses?

• A. SNR improvement is approximately 10 log10(N) dB.
• B. SNR improves by 20 log10(N) dB.
• C. SNR is not affected by coherent integration.
• D. SNR improves linearly with N without a logarithmic scale.

Answer: (C)

Processing gain from integrating multiple pulses comes from how the signal and noise behave when you sum across pulses. If you coherently align and add N pulses, the signal components add in phase, so the total signal amplitude grows by a factor of N. The signal power, which is proportional to the square of the amplitude, would naively seem to grow as N^2, but the noise across pulses is uncorrelated and adds in power, so the total noise power grows only linearly with N. The net effect is that the signal-to-noise ratio after coherent integration improves by a factor of N, which in decibels is 10 log10(N) dB. For example, if you coherently integrate 4 pulses, the SNR improves by a factor of 4, corresponding to about 6 dB of processing gain. This is why the best description states that the SNR improvement from N integrated pulses is approximately 10 log10(N) dB. The option suggesting a 20 log10(N) gain would imply doubling the amplitude gain translates into power, which isn’t how SNR is measured in this context. Saying there is no SNR improvement is incorrect because coherent integration directly boosts detectability by increasing the SNR. Saying the gain increases linearly without a logarithmic scale ignores that SNR is expressed as a ratio of powers, and power ratios translate to a logarithmic (dB) scale.

Processing gain from integrating multiple pulses comes from how the signal and noise behave when you sum across pulses. If you coherently align and add N pulses, the signal components add in phase, so the total signal amplitude grows by a factor of N. The signal power, which is proportional to the square of the amplitude, would naively seem to grow as N^2, but the noise across pulses is uncorrelated and adds in power, so the total noise power grows only linearly with N. The net effect is that the signal-to-noise ratio after coherent integration improves by a factor of N, which in decibels is 10 log10(N) dB.

For example, if you coherently integrate 4 pulses, the SNR improves by a factor of 4, corresponding to about 6 dB of processing gain.

This is why the best description states that the SNR improvement from N integrated pulses is approximately 10 log10(N) dB. The option suggesting a 20 log10(N) gain would imply doubling the amplitude gain translates into power, which isn’t how SNR is measured in this context. Saying there is no SNR improvement is incorrect because coherent integration directly boosts detectability by increasing the SNR. Saying the gain increases linearly without a logarithmic scale ignores that SNR is expressed as a ratio of powers, and power ratios translate to a logarithmic (dB) scale.