# Fast Compressed Power Spectrum Estimation: Towards A Practical Solution for Wideband Spectrum Sensing

## TL;DR

This paper introduces a fast, low-complexity compressed power spectrum estimation method suitable for real-time wideband spectrum sensing, leveraging multicoset sampling and FFT for efficient FPGA implementation.

## Contribution

It proposes a novel, computationally efficient power spectrum reconstruction technique based on multicoset sampling, enabling practical real-time wideband sensing with FPGA hardware.

## Key findings

- The method achieves low computational complexity using FFT.
- Simulation results confirm the efficiency and effectiveness of the approach.
- The approach offers a new perspective on power spectrum recovery conditions.

## Abstract

There has been a growing interest in wideband spectrum sensing due to its applications in cognitive radios and electronic surveillance. To overcome the sampling rate bottleneck for wideband spectrum sensing, in this paper, we study the problem of compressed power spectrum estimation whose objective is to reconstruct the power spectrum of a wide-sense stationary signal based on sub-Nyquist samples. By exploring the sampling structure inherent in the multicoset sampling scheme, we develop a computationally efficient method for power spectrum reconstruction. An important advantage of our proposed method over existing compressed power spectrum estimation methods is that our proposed method, whose primary computational task consists of fast Fourier transform (FFT), has a very low computational complexity. Such a merit makes it possible to efficiently implement the proposed algorithm in a practical field-programmable gate array (FPGA)-based system for real-time wideband spectrum sensing. Our proposed method also provides a new perspective on the power spectrum recovery condition, which leads to a result similar to what was reported in prior works. Simulation results are presented to show the computational efficiency and the effectiveness of the proposed method.