Modulation, Resolution and Signal Processing in Radar, Sonar and Related Systems

Abstract

Acknowledgments


1. Introduction


2. Discriminating and Resolving Power

(a) General

(b) Simple Systems

(i) A Single, Simple Pulse

(ii) "Pure" Continuous Wave

(c) Pulse Trains

(i) A Simple Pulse Train

(ii) Irregularly Spaced Pulses

(d) Long, Modulated Pulses

(i) A Single, Long Pulse

(ii) Trains of Long, Modulated Pulses


3. Generalized Resolving and Discriminating Power in the Range-Doppler and Time-Bandwidth Planes

(a) Review of Examples

(b) Ab Initio Derivation of Resolving and Discriminating Power

(i) Resolving Power

(ii) Relations Between Resolving and Discriminating Power

(iii) General

(c) Limiting Resolving Power


4. Intra-Pulse Modulated Systems

(a) Phase-Modulated Single Pulses

(i) Random Phase-Shift Modulation

(ii) Quantized Phase Shifts

(b) Single, Long, Frequency-Modulated Pulses

(i) Quasi-Random Frequency Steps

(ii) Linear Frequency Modulation

(iii) Hyperbolic Frequency Modulation

(iv) Multiple Linear Frequency Modulation

(c) On-off Modulation of Single Pulses

(d) Relations Between Certain Long-pulse Systems

(i) Single, Long, Modulated Pulses

(ii) Trains of Long, Modulated Pulses


5. Pulse Stretching and Coherent Recompression

(a) General

(b) Pulse Stretching and Recompression by a Common Network

(c) Delay Lines for Pulse Stretching or Compression

(i) Dispersive Lines for Frequency-Modulation Systems

(ii) A Delay-Line Loop to Generate Stepped-Frequency Modulation

(iii) The Number of Elements in a Delay Line

(d) Generalized Signal-Space Transformations


6. Allowing for Target Velocity

(a) The Effects of Target Velocity

(b) Common Features in the Doppler Effect and Pulse Compression

(c) Practical Doppler Requirements


7. Doppler-Determination and Anti-Clutter Techniques

(a) Within-Pulse, Time-shared Doppler Discrimination

(b) A Delay-Line Integrator with Between-pulse, Time-Shared Doppler Discrimination

(c) "Split-Pulse" Velocity Measurement

(i) Time-Spaced Pulses

(ii) Frequency-Spaced Pulses

(d) Moving-Target Indication (M.T.I.)

(e) Non-Linear Interference-Suppression Techniques


8. Interactions Between Modulation, Data Processing and Aerial Design

(a) Aerial Gain

(b) Aerial Response Time

(c) Extension of Resolution Limit to Include Aerial Scan

(d) Combined Resolution in Range, Doppler and Angle

(e) Modulation Scanning of a Linear-Array Aerial

(f ) Modulation Scanning of a Circular Array

(g) Pattern Synthesis from Incomplete Aerial Arrays

(i) Interferometers

(ii) Aperture Synthesis from Limited Samples

(iii) Some Features of Incompletely Filled Apertures

(iv) Sequential Aperture Synthesis

(v) Analogies in the Frequency and Time Dimensions

(h) The Constant-area Coverage Law

(i) General

(ii) The Gain of a "Cosec2" Aerial

(j) "Cosecant" Vertical Taper of Observation Time


9. Ambiguity Functions

(a) The Concept of the Ambiguity Function

(i) Range Side Lobes

(ii) The Range-Doppler Ambiguity Function

(b) Formulation of the Ambiguity Function

(c) The Power in an Ambiguity Function


10. Discrimination and Side-Lobes

(a) Generalized Discrimination

(b) Side-lobes in an Ambiguity Function

(i) The Total Relative Side Lobe Energy

(ii) The Significance of Side Lobes

(iii) Relative Side-Lobe Amplitudes

(c) The Effect of Taper

(i) The Use of Taper

(ii) Variants of Taper

(iii) Tapered, Weighted Phase-Step Modulation

(d) Varying Resolution Requirements


11. The Characteristics of Trains of Modulated Pulses

(a) The Spectrum of a Pulse Train

(b) The Ambiguity Function of a Pulse Train

(c) Limiting Doppler Resolution of a Pulse Train

(i) The Effect of Discrete Sample Pulses

(ii) The Resolution of Multiple Doppler Frequencies

(d) Within-Pulse Coarse Doppler Resolution


12. The Combination and Processing OF "Noisy" Signal Sources

(a) The Optimum Weighted Addition of "Noisy" Signals

(i) The Addition of Signal-to-Noise Ratios

(ii) The Coherent Addition of Signal Power

(iii) The Combination of Noise Powers

(b) The Effects of Power Taper

(i) Pre-Amplifier Taper

(ii) Post-Amplifier Taper

(c) The Effect of Signal Sources with Non-uniform or Unequal Frequency Spectra

(d) Video Signal Processing

(i) Matching Signal Envelopes

(ii) Signal Recognition

(e) Diversity Operation


13. Logical and Non-Linear Processing

(a) The Exploitation of Redundancies

(b) Multiplicative Processing

(c) The Effect of Multiplication on Accuracy

(d) The Practical Effects of Multiplicative Processing

(e) Comparison of Multiplicative and Directly-Generated Ambiguity Functions

(f) Correlation with a "Noise-Free" Reference Signal

(g) Monopulse


14.The Reception of Signals of Large Time-Bandwidth Product via a Varying Propagation Path

(a) General

(b) Doppler Tolerances for Linear f.m. and Pseudo-Random "Noise"

(c) The Effects of Rapid Random Signal Perturbations on Matchedfilter Reception

(d) The "Optimum" Mix of Coherent and Non-Coherent Integration

(e) Tolerances in Direction of Arrival and Further Generalizations


15. Practical Considerations, Future Prospects and Past Results

(a) Network Designs

(b) Transmitter Considerations

(c) Data-Processing Considerations

(d) Practical Examples

(e) Prognosis

Postscript

Appendix I. The Choice of Range Discrimination

(a) The Case for High-Range Discrimination

(b) The Radar Return from a Simple Geometric Body

(c) The Choice of "Optimum" Range Discrimination

(d) Detector Bandwidth

Appendix II. Geometric Derivation of the Response Characteristics of Some Simple Filters, and of the Radiation Patterns of Simple Aerial Arrays

(a) Derivation of the "Sin x/x" Characteristic

(i) The Response of a Correlator or "High-Q" Resonator

(ii) The Far-Field Pattern of a Uniformly Radiating Aperture

(b) Modification of the Lobe Pattern

(i) Emphasis of the Main Lobe

(ii) Reduction of Side Lobes

Appendix III. The Optimum Gain of a Recirculating Intergrator

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