Radar and sonar systems must balance range resolution with the energy required for reliable detection. Pulse compression resolves this by sending a long, energy-rich pulse and compressing it in the receiver, improving resolution, detectability, and robustness. FPGA implementation ensures real-time processing and low latency in demanding environments.
This technique boosts signal-to-noise ratio and range resolution, enabling weak-target detection without higher transmit power. FPGAs, with their parallel DSP resources, are well-suited for high-speed matched filtering. In this last blog of the DSP Building Blocks series, we explore the high-impact technique of pulse compression using matched filtering, a cornerstone of modern radar and communication systems.
Concept of Pulse Compression
In pulse compression, a linear frequency-modulated chirp is transmitted, and the received echo is correlated with a replica of this signal. The correlation output forms a compressed pulse whose width is inversely proportional to the chirp bandwidth, thereby improving range resolution.
Key Parameters
- Pulse Width (Tp): Duration of transmitted pulse
- Bandwidth (B): Frequency sweep of the chirp
- Compression Ratio (CR): Tp × B
- Range Resolution (ΔR): c / (2 × B)
Where c is the speed of light. For example, with Tp = 20 µs and B = 10 MHz, Compression Ratio = 200, and ΔR ≈ 15 meters.
Matched Filter Principle
A matched filter is designed to maximize the SNR of a received signal in the presence of noise. Mathematically, the filter’s impulse response h(t) is the time-reversed complex conjugate of the transmitted signal s(t):
The convolution between the received signal r(t) and h(t) yields the correlation output:
In FPGA, this operation is realized either through direct convolution or via FFT-based correlation, depending on system bandwidth and available hardware resources.
FPGA Implementation Overview
Hardware Setup
- Platform: ZCU102 FPGA
- Transceiver: ADRV9002 (dual 16-bit ADC/DAC)
- Interface: LVDS (ADC → FPGA)
- Clock Rate:44 MHz sample rate
- DSP Framework: AXI-Stream connected pipeline
The overall design receives digitized chirp echoes from ADRV9002, performs matched filtering in FPGA logic, and streams the compressed output to DDR memory for visualization or range profiling.
Pulse Compression Chain Architecture
The pulse compression system includes the following major components:
1. ADC Front-End (ADRV9002)
- Captures received analog chirp echoes.
- Delivers 16-bit samples via LVDS to the FPGA.
2. AXI-Stream Input Interface
- Converts ADC parallel data to AXI-Stream format.
- Synchronizes clock domains between ADC and DSP fabric.
3. Matched Filter Core
- Implements convolution with stored reference waveform.
- Can be realized using:
Time-domain FIR convolution for shorter filters.
FFT-based multiplication for long chirps (frequency domain).
- Produces a compressed pulse with a sharp peak that indicates target range.
4. Magnitude Calculation and Thresholding
- Computes |I + jQ| magnitude using CORDIC or DSP48E slices.
- Optional thresholding for target detection logic.
5. AXI-DMA and DDR Interface
- Streams process data to system memory.
- Enables visualization or logging via ARM processor.
6. Display/Visualization
- Range profile displayed over HDMI or Ethernet (Qt/Python GUI).
Figure 1: Pulse Compression DSP Chain
Figure 1 shows the FPGA pulse-compression chain, starting with the ADRV9002 ADC feeding high-speed samples via the LVDS interface into the AXI-Stream bridge. The matched filter applies FIR or FFT-based compression, followed by magnitude estimation for target detection. Processed data is transferred via AXI-DMA to DDR memory for ARM-based analysis and display.
Implementation Details
1. Reference Waveform Generation
- A stored replica of the transmitted chirp is generated in MATLAB or Python.
- The waveform is quantized to 16-bit fixed-point and stored in BRAM or external memory.
2. Matched Filter Implementation
Two approaches are common:
a. Time-Domain FIR Implementation
- FIR coefficients = conjugate time-reversed transmitted chirp.
- Suitable for short pulse lengths (< 4K samples).
- Implemented using Xilinx FIR Compiler IP with AXI-Stream I/O.
b. Frequency-Domain (FFT-Based) Correlation
- Both input and reference signals transformed via FFT.
- Multiply conjugate spectra and perform IFFT.
- Efficient for long chirps (> 8K samples).
- Uses Xilinx FFT and Complex Multiplier IP cores.
3. Data Streaming and Control
- AXI-Stream interfaces maintain continuous data flow.
- AXI4-Lite provides software control for filter length, gain, and threshold.
- AXI-DMA moves results to DDR with minimal CPU load.
4. Range Profile Visualization
The compressed pulse output is plotted as amplitude vs range using Python or a custom Qt GUI on the ARM core. Each peak represents a detected target.
Applications and Benefits
Pulse compression using matched filtering is widely used across sensing and communication systems where accurate time-delay or range estimation is required.
- Pulse Radar Systems: Enables real-time detection of target range and velocity.
- Sonar and Ultrasonic Imaging: Enhances resolution for underwater or near-field imaging.
- Communication Systems: Supports spread-spectrum signal detection and fast synchronization.
- Automotive Radar (FMCW): Provides rapid range profiling and multi-object detection in dense traffic.
Implementing pulse compression on FPGA combines deterministic high-speed DSP with flexible real-time processing, making it suitable for demanding environments.
- High Resolution: Compressed pulses deliver fine range and time-delay accuracy without increasing transmit power.
- Real-Time Processing: FPGA pipelines support continuous high-throughput matched filtering.
- Scalable Architecture: FIR or FFT-based designs can be tailored for short or long chirps.
- Multi-Target Capability: Essential for radar systems requiring reliable detection in cluttered scenarios.
Read all the blogs in the DSP Building Blocks series.