8-11

Echo detection

• Sonar uses acoustic waves for target detection.

• A transmitted wave hits a target, and the reflected wave (echo) is received.

• The travel time between transmission and reception correlates to the target range.

1. Echo signals are pressure waves converted to voltage via the piezoelectric effect.

2. Signals are amplified and digitized for storage and processing (e.g., integer levels for a 12-bit converter).

3. Key Components:

   • Amplification to handle small signals.

   • Analog-to-digital conversion for processing.

   • Reflectivity indicates the energy reflected back by a target.

1. Echo signals combine:

   • Scaled and delayed versions of transmitted signals (one per target).

   • Additive noise.

2. Equation: e(t)=s(t)∗i(t)+n(t), where

   • e(t)): Echo signal,

   • s(t): Transmitted signal,

   • i(t): Reflectivity function,

   • n(t): Noise.

3. Travel time is proportional to range under constant sound speed but varies with environmental conditions.

A matched filter is a tool used in sonar to detect echoes in noisy environments. Its job is to pick out the desired signal (the echo from a target) and ignore as much noise as possible, maximizing the clarity of the information we want.

How It Works

1. Splitting the Signal

   • The total signal received by the sonar, d(t), has two parts:

     • Desired Signal (ds(t): This is the part of the echo that comes from the target.

     • Noise Component (dn(t)): This is the random noise from the environment.

   The matched filter processes the incoming signal to make the desired signal stand out while reducing the effect of noise.

2. Using the Matched Filter

   • The filter compares (correlates) the received echo with the transmitted signal.

   • It uses the shape of the transmitted signal to identify parts of the received signal that look similar.

   • This correlation helps detect where the echo came from and how strong it is.

In an ideal world, we’d want to perfectly "see" the reflectivity of all targets (how much energy they reflect back). To do this, the signal we send out would need to be incredibly precise, like a perfect spike. But creating such a perfect signal isn’t possible because it would require infinite energy and bandwidth. Instead, we aim to use signals that have sharp, well-defined peaks. This helps us detect echoes more clearly.

Resolution:

• Shorter signals give better resolution, meaning you can tell targets apart more easily.

• However, shorter signals send out less energy, which makes detecting the echo harder (lower signal strength).

Challenges:

• Increasing the strength (amplitude) of the signal can help, but there are limits:

  • Cavitation: If the signal is too strong, it creates bubbles in the water that can damage the equipment.

Complex signals combine two parts:

• The real part represents the "in-phase" part of the wave (similar to the sine wave).

• The imaginary part represents the "quadrature" part (like another sine wave shifted by 90 degrees).

• This complex form makes it easier to analyze details like the phase (timing) and frequency of the signal.

The simplest type of sonar signal is a sinusoidal pulse. Think of it as a wave that’s sent out for a short time.

Amplitude: How strong the wave is.

Frequency: How fast it oscillates.

Duration: How long the wave is transmitted.

1. If targets are far apart, the echoes don’t overlap, and it’s easy to tell them apart.

2. If targets are close together, their echoes can blur into one, making it hard to distinguish them.

Resolution:

• Shorter signals give better resolution, meaning you can tell targets apart more easily.

• However, shorter signals send out less energy, which makes detecting the echo harder (lower signal strength).

Challenges:

• Increasing the strength (amplitude) of the signal can help, but there are limits:

  • Cavitation: If the signal is too strong, it creates bubbles in the water that can damage the equipment.

1. Problem: Short pulses give better resolution (help distinguish closely spaced targets), but they carry less energy, making it harder to detect echoes.

2. Solution: Use pulse compression.

   • This involves modulating the transmitted signal (changing its frequency or phase) so it has a broader bandwidth.

   • The result is a narrower peak in the processed signal, improving resolution without needing to shorten the pulse.

   • Key Benefit: We can now use longer pulses, which carry more energy, to improve detection while maintaining high resolution.

The resolution depends on the bandwidth B, not the pulse length:

• Wider bandwidth = better resolution.

• This means we can make the pulse as long as necessary to boost the signal-to-noise ratio

Pulse Length Limitations

• The pulse duration must still be short enough to avoid overlapping the echo from the nearest target:

  • The pulse must end before the echo from the closest object returns.

A Chirp is a signal where the frequency changes over time.

An LFM chirp is a signal where the frequency changes linearly over time:

• Up-chirp: Frequency increases during the pulse.

• Down-chirp: Frequency decreases during the pulse.

• LFM chirps are popular because:

  • They have a sharp autocorrelation peak, which improves resolution.

  • Their frequency spread helps differentiate targets.

8.6.2 Hyperbolic Frequency Modulated (HFM) Chirp

What is an HFM Chirp?

• In an HFM chirp, the frequency changes logarithmically (more slowly at first and faster later).

Key Differences from LFM Chirp

• HFM chirps are better at handling Doppler effects (frequency shifts due to motion).

• However, they have slightly worse resolution because their autocorrelation peak is broader and sidelobes are higher (less clean separation between echoes).

Frequency Behavior

• LFM chirp: Its frequency content is spread evenly across the bandwidth.

• HFM chirp: Its frequency content is stronger at lower frequencies.

Spectrum Features

• Both chirps have ringing (small oscillations) in their desired frequency range and some leakage into unwanted frequencies.

• Problem: Without any adjustments, chirp signals can have spectral leakage, meaning energy spreads into unwanted frequency ranges. This causes "ringing" in the signal, making it less clean and precise.

• Solution: Apply a window (or taper) to the signal's amplitude to smooth out these effects.

How Does It Work?

• A cosine window is applied to the signal. This reduces abrupt changes at the start and end of the pulse, smoothing the signal.

• The result is:

  • Less spectral leakage: The energy stays focused in the desired frequency range.

  • Reduced ringing: Both in the frequency domain and in the signal’s autocorrelation.

Trade-Offs

• Peak Reduction: While windowing improves cleanliness, it slightly reduces the signal's peak value, which can slightly impact detection strength.

• Balance: Different window shapes can be used depending on the trade-off between reducing ringing and maintaining the peak value.

• No: While LFM and HFM chirps are the most common, other signals can also be used for sonar imaging.

Example: Pseudo-Random Noise Modulation

• Appears random but is generated using a predictable algorithm, so matched filtering can still process the signal.

• Benefits:

  • Creates a narrow autocorrelation peak, which improves resolution.

  • Useful in scenarios where traditional chirps may not perform well.

8.1 Received Data

• Echo signals are captured as pressure waves, converted to voltage, amplified, and digitized for processing.

• The received data combines scaled and delayed echoes from targets, alongside noise.

• The ultimate goal is to detect and analyze target positions based on these signals.

8.2 Echo Model

• The echo signal is a mix of reflected versions of the transmitted signal (one for each target) and environmental noise.

• Travel time of the signal is proportional to the distance of the target, but environmental conditions can affect this relationship.

• Understanding and modeling the echo is critical for accurate target detection.

8.3 Matched Filter

• A matched filter enhances the detection of echoes by maximizing the signal-to-noise ratio (SNR).

• It processes the received signal to amplify desired components (echoes) and reduce noise.

• Applying a matched filter is equivalent to correlating the echo with the transmitted signal for better clarity.

8.4 Signals

• The transmitted signal should have a sharp peak in its autocorrelation to clearly identify targets.

• Complex signals, such as those using in-phase and quadrature components, simplify the processing of signal properties like phase and frequency.

• Instantaneous frequency helps track how the signal’s frequency changes over time, improving target detection.

8.5 Sinusoidal Signals

• Simple sinusoidal pulses are easy to use but have limited resolution when targets are close together.

• Shorter pulses improve resolution but reduce transmitted energy and SNR.

• Amplitude increases can compensate, but physical and hardware limits (e.g., cavitation) restrict this approach.

8.6 Pulse Compression

• Pulse compression allows for long pulses (high energy and SNR) while maintaining high resolution.

• Modulated signals, such as chirps, achieve this by spreading the frequency of the pulse over a range and compressing it during processing.

• Linear Frequency Modulated (LFM) chirps are common due to their sharp autocorrelation peaks, while Hyperbolic Frequency Modulated (HFM) chirps handle Doppler effects better.

8.6.5 Windowing

• Windowing smooths the signal to reduce spectral leakage and ringing but slightly decreases peak signal strength.

• It improves the signal’s clarity, balancing between ripple reduction and maintaining peak detection.

8.6.6 Other Signals

• While chirps dominate sonar applications, other modulated signals, like pseudo-random noise, offer alternative solutions.

• The goal is always to create a clean and sharp autocorrelation for precise target detection.

Fast Time: Measures time within each pulse for sampling the echo.

Slow Time: Tracks sonar position over successive pulses.

These concepts help distinguish between individual echoes and the sonar’s movement.

The Doppler effect (also Doppler shift) is the change in the frequency of a wave in relation to an observer who is moving relative to the source of the wave

Narrow-Beam Sonar

• Uses focused pings that insonify narrow areas of the seafloor.

• Each ping contributes a line of the final image, with resolution dependent on the pulse bandwidth.

Resolution Considerations

• Across-Track Resolution: Depends on the modulation bandwidth.

• Along-Track Resolution: Affected by transducer size, signal wavelength, and range.

Challenges:

• Beam Spreading: Causes distant targets to blur together.

• Improving Resolution: Achieved by limiting range, using larger transducers, or increasing frequency.

What is Synthetic Aperture Sonar (SAS)?

• SAS uses wide-beam transducers, meaning a target is insonified by multiple pings as the sonar moves.

• This approach requires combining data from successive pings to "synthesize" a large aperture, improving resolution.

Key Benefits of SAS

• Improved Resolution:

  • SAS achieves twice the resolution of a real aperture of the same size because it measures the phase history of a target across multiple pings.

  • This allows detailed imaging even with low-frequency signals and at greater ranges.

• Alias-Free Imaging:

  • Proper sampling (e.g., λ/2\lambda/2λ/2) ensures no aliasing in the visible region, enhancing image clarity.

Why SAS Resolution is Twice as Good

• SAS measures the phase history of a target across the synthetic aperture, which provides more spatial frequency information compared to a single real aperture measurement.

• This doubles the along-track resolution.

Key Points

• SAS improves resolution and allows for effective imaging at longer ranges without relying on high-frequency signals.

• It requires careful sampling and advanced processing but delivers significant benefits over traditional sonar methods.

• SAS transforms wide-beam echo data into detailed, high-resolution images, making it ideal for mapping and imaging large underwater areas.

The principle of synthetic-aperture sonar is to move the sonar while illuminating the same spot on the sea floor with several pings. When moving along a straight line, those pings that have the image position within the beamwidth constitute the synthetic array. By coherent reorganization of the data from all the pings, a synthetic-aperture image is produced with improved along-track resolution. In contrast to conventional side-scan sonar (SSS), SAS processing provides range-independent along-track resolution. At maximum range the resolution can be magnitudes better than that of side-scan sonars.

1. Pulse Compression: Widens the beam for Synthetic Aperture Sonar (SAS), ensuring targets appear in multiple pings.

2. Key Output: Data from pulse compression forms the basis for image reconstruction.

1. Expected Signal Generation:

   • The sonar system calculates what the echo from an ideal point target (a small reflective spot) at a specific location should look like. This is based on the sonar's known signal and the physics of sound propagation.

2. Comparison (Correlation):

   • The calculated "ideal" echo is compared to the actual received signal at every possible point in the seafloor image.

3. Resulting Image:

   • The degree of match (correlation) determines the intensity of the pixel at each location. A strong match indicates a reflective target at that spot.

Time domain correlation excels in scenarios where precision is more important than speed, such as imaging a small area with fine detail. It provides an accurate estimate of reflectivity by directly comparing the expected signal to the received signal. This makes it a useful benchmark for validating the results of faster but less precise methods like backprojection.

1. Core Idea: Projects received signals onto all possible positions on the seafloor and sums these projections to estimate the reflectivity function.

2. Steps:

   1. For each ping, determine the range of each sample.

   2. Project the signal onto potential target positions.

   3. Sum the projections across multiple pings.

3. Advantages: Efficient and commonly used for SAS image reconstruction.

1. Phase Alignment: Reconstruction depends on the phase of recorded signals being accurate.

   • Timing errors in recording can cause loss of coherence and image blurring.

2. Sonar Position Accuracy: Even small inaccuracies in sonar motion (e.g., a 1 cm sway) lead to blurring.

3. Sound Speed Errors: Misestimating the speed of sound (e.g., by 25 m/s) distorts the reconstructed image.

1. Limit Projections: Focus backprojection on areas within the transducer’s main lobe to reduce noise.

2. Increase Sampling Rate: Using finer sampling (e.g., D/4D/4D/4 instead of D/2D/2D/2) minimizes aliasing.

3. Motion Corrections: Incorporate accurate sonar motion tracking to prevent blurring.

4. Speed of Sound Adjustments: Ensure accurate estimates to properly map echo times to ranges.

Which to Use?

• Time Domain Reconstruction:

  • Best for complex scenarios where motion is irregular or sound speed varies significantly.

  • Used in cases where accuracy is critical and computational time is less of a concern.

• Frequency Domain Reconstruction:

  • Preferred for large-scale imaging where speed is important, and the environment is well understood (e.g., uniform motion and sound speed).

  • Commonly used in real-time applications or when processing large amounts of data efficiently is necessary.

11.1 Two-Dimensional Spatial Frequency

• In sonar imaging, the data exists in two dimensions:

  • Along-track direction (u or x-axis): Where the sonar moves.

  • Across-track direction (r or y-axis): Perpendicular to the sonar's motion.

• The spatial frequency is determined by the wavelength λ and the angle θ of the wave relative to these axes:

• Using Fourier transforms, spatial frequency resolutions and ranges are defined by the sampling grid and image size.