Pulse Compression Ratio Calculator

Pulse compression is a radar technique that transmits a long, frequency- or phase-modulated pulse (carrying enough total energy for long-range detection) and then compresses its matched filter output into a much shorter effective pulse, achieving the fine range resolution of a short pulse without needing the very high peak transmit power a short pulse would require.

Pulse compression ratio (PCR) equals the transmitted pulse's time-bandwidth product, PCR = T x B, where T is the uncompressed pulse duration and B is the swept (modulated) bandwidth. A 10 microsecond pulse swept over 10 MHz has a compression ratio of 100, meaning the compressed pulse is effectively 100 times shorter than the original.

Range resolution after compression is Delta-R = c / (2B), determined entirely by the swept bandwidth B, not by the original (much longer) pulse duration T. This is the core benefit of pulse compression, a 10 microsecond pulse that would normally give 1,500 m resolution can instead deliver 15 m resolution if it is chirped across 10 MHz of bandwidth.

The compressed pulse width (the effective duration after matched filtering) is approximately tau_c = 1/B, the reciprocal of the swept bandwidth. This is the same width a simple unmodulated pulse of duration 1/B would have, which is why pulse compression is often described as giving a long pulse's energy with a short pulse's resolution.

Linear frequency modulation (LFM, or chirp) is the most common pulse compression waveform, sweeping frequency linearly across the pulse. Phase-coded waveforms (Barker codes, polyphase codes, or pseudorandom binary sequences) achieve the same time-bandwidth product benefit using discrete phase shifts instead of continuous frequency sweep, often used in lower-power or spread-spectrum radar and sonar systems.

No, the average transmit power depends on total pulse energy and pulse repetition rate, which pulse compression does not change, it only reshapes that same energy from a long, low peak-power pulse into an effectively much shorter, high peak-power pulse after processing. This lets a system with a lower peak-power transmitter still achieve long detection range while retaining fine resolution.

Range sidelobes are secondary peaks in a compressed pulse's matched filter output that appear alongside the main compressed peak, caused by the finite bandwidth and windowing of the transmitted waveform. High sidelobes can mask a weak nearby target next to a strong one, so real systems apply amplitude weighting (windowing) to the chirp or choose phase codes with inherently low sidelobes, at some cost to the ideal 1/B compressed width.

Modern radar systems commonly use compression ratios from the hundreds to several thousand, limited mainly by the transmitter's ability to generate a clean, accurately modulated waveform over the required bandwidth and duration and by the receiver's dynamic range and processing capability, not by any fundamental physical limit on T x B itself.

PCR in dB = 10*log10(T x B), and this dB figure also represents the matched filter processing gain the compressed pulse achieves over an unmodulated pulse of the same duration, directly improving detectable target SNR by that same amount.

Pulse compression preserves the full 2E/N0 output SNR benefit of the long transmitted pulse's total energy (see the Matched Filter Output SNR Calculator), while simultaneously delivering the fine range resolution of a much shorter pulse, decoupling the historical radar tradeoff between detection range (needing pulse energy) and range resolution (needing pulse bandwidth, not duration).