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Traditional digital signal processing methods struggle with ultra-wideband long-duration linear frequency-modulated (LFM) signals due to prohibitive sampling rates, massive data loads and exponential computational complexity. Acousto-optoelectronic (AOE) technology, merging acousto-optics’ inherent parallelism with electronics’ programmability, offers a promising real-time alternative for LFM signal compression. However, acousto-optic modulators (AOMs) have a finite temporal aperture, preventing direct processing of signals with (Tc≫Ta) and requiring specialized spatiotemporal integration. This paper presents a theoretical and numerical study of a CCD time delay and integration (TDI)-based AOE processor for long-duration LFM signals. We establish a complete mathematical model covering segmented LFM signals, 6th-order Butterworth band-limited Gaussian noise, Raman-Nath acousto-optic diffraction and Fresnel propagation. Implemented in MATLAB with FFT-accelerated convolution, simulations cover 10 non-overlapping and 19 overlapping segments across 100–200 MHz and 400–800 MHz bands. Results confirm the Gerig-Mostague LFM self-focusing effect in AOMs. At an input signal-to-noise ratio (SNR) of 1, the 10-segment model achieves a peak enhancement factor of 9.7 (near theoretical maximum), while the 19-overlap model reaches 17.9. Output SNR correlates linearly with input SNR, with the 400–800 MHz band delivering higher processing gain. The TDI shift-and-add algorithm efficiently accumulates signal energy across segments and suppresses uncorrelated noise, enabling processing of LFM signals far longer than the AOM aperture. The developed framework and algorithms directly support the design and optimization of AOE processors for radar, radio astronomy and broadband communications. Future work will focus on experimental validation and TDI shift algorithm optimization.

• ABSTRACT
• CONTENTS
• INTRODUCTION
• The purpose of this work
• CHAPTER 1. THEORETICAL FOUNDATIONS
• 1.1.Linear Frequency-Modulated Radio Signals
• 1.2.Acousto-Optic Processes in Modulators
  • 1.2.1Photoelastic Effect
  • 1.2.2Diffraction Regimes
  • 1.2.3Self-Focusing Effect for LFM Signals
• 1.3.Operating Principle of the Acousto-Optic-Electroni
  • Operating Principle
• 1.4.Supplementary derivations and optical signal-flow
• 1.5. Literature-based theoretical relations used in th
  • 1.5.1Matched-filter interpretation and compression gain
  • 1.5.2Refractive-index perturbation produced by sound
  • 1.5.3Bragg condition, Raman-Nath approximation, and fir
  • 1.5.4Gerig-Mostague focusing law for a chirp in an ultr
  • 1.5.5CCD shift-and-add integration as the electronic pa
  • 1.5.6Summary of source-to-model correspondence
• CHAPTER 2. MATHEMATICAL MODELING
• 2.1.Mathematical Model of the LFM Radio Signal
• 2.2.Model of Bandpass Gaussian Noise
• 2.3.Model of Acousto-Optic Diffraction
• 2.4.Consistent parameter definitions derived from the
• CHAPTER 3. NUMERICAL SIMULATION IN MATLAB
• 3.1.Input Signal Generation and Validation
• 3.2.Diffraction Field Calculation Algorithm
  • (1)Convert the time-domain LFM signal to a spatial ph
• 3.3.Time Delay and Integration (TDI) Mode Implementati
• 3.4.Simulation Parameters
• 3.5.MATLAB Implementation and Numerical Consistency
• CHAPTER 4. ANALYSIS OF SIMULATION RESULTS
• 4.1.Input Signal Time-Domain Characteristics
• 4.2.Diffraction Field of Individual Segments
• 4.3.TDI Mode Summation Performance
• 4.4.Signal-to-Noise Ratio Enhancement Analysis
• 4.5.Additional MATLAB Results: Overlapping Segmentatio
• 4.6.Final Noisy Fresnel-FFT Verification from Noise_LF
• 4.7.Discussion in comparison with the cited literature
• 4.8.Model limitations and assumptions
• CONCLUSION
• REFERENCES
• APPENDIX A. MATLAB CODE FRAGMENTS