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ADSP: Frequency Estimation and CRB

Author: Pouya Aminaie

Overview

In this project, we generated a random noise using a given statistical property. Then, we added this noise to our sinusoid waveform. Finally, we estimated the frequency of the generated waveform based on the PSD method. One possible future work can be estimating spatial frequency in radar systems, especially in array antennas. The PSD of the received signal at each element of the array should be taken when needed, and the spatial frequency corresponding to the peak point should be detected. Since the spatial frequency is proportional to the angular distance, the direction of arrival can be calculated. The flowchart below summarize step-by-step procedure of performing the project.

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Contents

  • Section 1: Theory

    • Discusses the theoretical background required for noise generation and frequency estimation.
    • Details the computation of the sample covariance matrix, generation of random vectors, and the use of Power Spectral Density (PSD) for frequency estimation.

  • Section 2: Solutions

    • 2.1 Noise Generation
      • Explanation of noise generation using MATLAB’s mvrnd function.
      • Procedure for calculating the covariance matrix and MSE.
      • Discussion of the Monte Carlo method used in the simulations.
    • 2.2 Frequency Estimation
      • Steps for estimating the frequency of a single sinusoidal signal.
      • Calculation of the covariance matrix in different scenarios.
      • Explanation of MATLAB functions and their roles in the implementation.
      • Results are presented showing MSE vs. SNR and CRB vs. SNR for various parameters.
    • 2.3 Frequency Modulation
      • Analysis of the frequency modulation process and its effect on PSD.
    • 2.4 Arbitrary Modulation
      • Strategy for detecting harmonics using PSD, with examples provided.

  • Section 3: Conclusion

    • Summary of the work, key results, and possible future work, such as estimating spatial frequency in radar systems.

  • Appendix

    • Contains figures and additional explanations that summarize the processes of noise generation and frequency estimation.

Requirements

  • MATLAB (tested with version R2023a)
  • Signal Processing Toolbox

How to Use

Download the following codes and reports from this repository:

  1. ADSP_report.pdf
  2. MyCode_HW1.m
  3. MyCode_HW1_1p3.m
  4. MyCode_HW1_1p4.m