Vitis HLS: Matched Filter implementation

The Matched Filter (MF) is a cornerstone of radar signal processing, enabling optimal detection of known signals within noisy environments. Let's consider the implementation of a Matched Filter in both the time and frequency domains using Vitis High-Level Synthesis (HLS), showcasing how to leverage FPGAs for high-performance radar systems.

Why Matched Filters?

Matched Filters maximize the signal-to-noise ratio (SNR) by correlating incoming signals with a predefined template, making them ideal for:

• Pulse Compression: Enhancing range resolution in radar systems.
• Target Detection: Identifying echoes in cluttered or noisy data.
• Time and Frequency-Domain Processing: Supporting applications requiring optimal performance across both domains.

Architecture Overview:

Time-Domain Matched Filter:

The time-domain implementation processes the signal through a series of FIFO buffers and a convolution engine:

• The input signal is convolved with a set of complex coefficients.
• The convolution operation is fully pipelined, ensuring high throughput.
• Input and output are managed through AXI streaming interfaces for seamless data handling.

Frequency-Domain Matched Filter:

The frequency-domain implementation leverages the efficiency of the FFT:

• The input signal is transformed using an FFT block.
• The transformed signal is multiplied by complex coefficients in the frequency domain.
• The result is passed through an IFFT block to reconstruct the matched-filtered signal in the time domain.
• This method minimizes computational complexity for large data sizes by utilizing fast Fourier transforms.

The Synthesis and Implementation Reports reveal the following:

Time-Domain Implementation:

• Lower resource utilization for small data sizes, making it suitable for systems with constrained DSP resources.
• Pipelined with latency scaling linearly with the number of points.

Frequency-Domain Implementation:

• Utilizes more DSPs due to the FFT/IFFT blocks but achieves better scalability for larger input sizes.
• The pipeline optimizes performance by distributing computational tasks across the FFT, multiplier, and IFFT stages.

DSP Blocks vs Number of Points :

The graph illustrates the DSP usage as a function of the number of points:

• Time-Domain Implementation scales linearly due to direct convolution with complex coefficients.
• Frequency-Domain Implementation shows logarithmic growth, leveraging FFT for improved efficiency with increasing input size.

This following plot visualizes the input signal and the output of the Matched Filter (MF) for both time-domain and frequency-domain implementations. It compares the performance of the two approaches across different components of the signal:

Key Observations :

• Accuracy: Both time-domain and frequency-domain matched filters produce highly similar results, demonstrating the correctness of the implementations.
• Sharp Peaks: The output magnitude shows distinct peaks at bins corresponding to the matched components of the input signal, effectively maximizing the signal-to-noise ratio.
• Implementation Comparison: The frequency-domain implementation achieves similar accuracy as the time-domain implementation but is more resource-efficient for larger datasets.

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