Pulse compression is a sophisticated radar technique that allows for simultaneous achievement of excellent range resolution (requiring a wide bandwidth) and a high signal-to-noise ratio (requiring high transmitted energy, often achieved with long pulse durations). These two requirements are contradictory for simple rectangular pulses.

Good Range Resolution: Requires a short pulse duration (τ). However, a short pulse means less transmitted energy for a given peak power, leading to a lower signal-to-noise ratio (SNR) and reduced detection range.

High SNR/Long Range: Requires a long pulse duration (τ) to transmit more energy. However, a long pulse leads to poor range resolution.

Pulse compression transmits a long pulse (for high energy/SNR) that is modulated in a specific way (e.g., in frequency or phase). The receiver then processes this long, modulated echo to compress its energy into a much shorter effective pulse, thereby achieving high range resolution.

● Tlong: Transmitted long pulse duration.
● B: Bandwidth of the modulation applied to the pulse.
● Tcompressed: Effective compressed pulse duration (related to 1/B).
● Compression Ratio (CR): The ratio of the long pulse duration to the effective compressed pulse duration.
CR=Tlong ×B (also known as Time-Bandwidth Product).

1. Transmission: A long pulse with a duration Tlong is transmitted. However, its frequency or phase is varied continuously over its duration. This modulation spreads the pulse's energy over a wide bandwidth B.
2. Reception: The radar receives the echo, which is still a long, modulated pulse.
3. Matched Filtering (Compression): The received echo is passed through a "matched filter" in the receiver. A matched filter is specifically designed to recognize the transmitted modulation. It effectively correlates the received signal with a replica of the transmitted signal. This correlation process compresses the energy of the long, modulated pulse into a very short, high-amplitude pulse. The effective duration of this compressed pulse, Tcompressed, is approximately 1/B.

As seen in Section 6.1.1, the range resolution is determined by the effective bandwidth after compression: ΔR=2Bc. This allows high range resolution even with a long transmitted pulse.

The process of pulse compression coherently sums the energy spread across the long pulse duration into a much narrower time interval. This concentrates the signal power while spreading the noise, leading to an SNR improvement roughly equal to the compression ratio (CR). SNR improvement ≈CR=Tlong ×B.

● Principle: The most common form of pulse compression. The instantaneous frequency of the pulse is swept linearly upwards or downwards during the pulse duration.
○ Up-Chirp: Frequency increases linearly with time.
○ Down-Chirp: Frequency decreases linearly with time.
● Transmission: A long pulse of duration Tlong is transmitted, where its frequency changes from f0 −B/2 to f0 +B/2 (or vice-versa) over Tlong.
● Reception and Compression: The received chirp echo is fed into a matched filter, which can be implemented using a dispersive delay line (e.g., Surface Acoustic Wave (SAW) device) or digital signal processing (FFT-based correlation). The filter introduces a frequency-dependent delay such that all frequency components of the chirp pulse arrive at the output at the same time, thereby "compressing" the pulse.

Assume an LFM pulse:
● Long pulse duration Tlong =20 microseconds=20×10−6 s
● Bandwidth B=5 MHz=5×106 Hz
1. Compression Ratio (CR): CR=Tlong ×B=(20×10−6 s)×(5×106 Hz)=100.
2. Effective Compressed Pulse Duration: Tcompressed =1/B=1/(5×106 Hz)=0.2 microseconds.
3. Range Resolution: ΔR=2Bc =2×5×106 Hz3×108 m/s =10−300 =30 meters.
Without pulse compression, a 20-microsecond pulse would yield a range resolution of ΔR=(3×108×20×10−6)/2=3000 meters. Pulse compression in this example improved resolution by a factor of 100. The SNR is also ideally improved by 100 (or 20 dB).

● Principle: Instead of frequency modulation, the phase of the transmitted pulse is shifted at discrete intervals (chips) according to a predefined binary code. Each chip has a constant amplitude and duration.
● Transmission: A long pulse is divided into 'N' equal sub-pulses or "chips." Each chip is transmitted with either a 0-degree or 180-degree phase shift (binary phase shift keying, BPSK) according to a Barker code sequence. Barker codes are specific binary sequences that have optimal autocorrelation properties (i.e., they produce a very strong central peak and minimal sidelobes when correlated with themselves).
● Reception and Compression: The received signal is correlated with a replica of the transmitted Barker code. This compresses the energy of the 'N' chips into a single, much shorter, high-amplitude pulse.

Barker code of length 13: [+1, +1, +1, +1, +1, -1, -1, +1, +1, -1, +1, -1, +1]
Assume a chip duration τchip =0.1 microseconds.
● Long Pulse Duration: Tlong =N×τchip =13×0.1×10−6 s=1.3 microseconds.
● Bandwidth: The bandwidth of a phase-coded pulse is approximately 1/τchip.
B=1/(0.1×10−6 s)=10 MHz.
● Compression Ratio (CR): N=13.
● Effective Compressed Pulse Duration: τcompressed =τchip =0.1 microseconds.
● Range Resolution: ΔR=2Bc =2×10×106 Hz3×108 m/s =15 meters.

● Improved Range Resolution: Achieves fine resolution independent of total pulse duration.
● Improved SNR: Increases the detectable range or allows detection of smaller targets.
● Reduced Peak Power: Can transmit the required energy with lower peak power, leading to smaller, lighter, and more reliable transmitters, and reduced probability of detection by adversaries.

● Processing Sidelobes: The compression process generates range sidelobes, which can obscure weak targets located near strong targets.
● Doppler Sensitivity: Some pulse compression waveforms (especially LFM) can be sensitive to Doppler shifts, causing a mismatch in the filter and leading to reduced compression gain and higher sidelobes for high-speed targets.