Target Indication, Topographical Analysis, Weather Detection, and Navigational Safety with RADAR

Abstract

In the Royal Navy (RN), RADAR plays a critical role in target indication, topographical analysis, weather detection, and navigational safety.

This paper explores the essential components of RADAR, including transmitter power, receiver sensitivity, and antenna gain, in relation to the radar range equation.

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The study delves into their interactions and how they collectively inform the radar range equation, providing insights into RADAR design and performance optimization.

1. Introduction

The Royal Navy relies on RADAR (Radio Detection and Ranging) for various applications, including target indication, topographical analysis, weather detection, and navigational safety. RADAR operates by transmitting radio waves and receiving the energy reradiated back from objects, allowing the determination of range, angle, or velocity of these objects.

2. RADAR Range Equation

Manipulating the components of the RADAR range equation is essential to ensure navigational safety, early threat detection, and effective fire control. This paper will explore the significance of transmitter power, receiver sensitivity, and antenna gain within the context of the radar range equation.

3. Transmitter Power, Receiver Sensitivity, and Antenna Gain

To address the relationship between transmitter power, receiver sensitivity, and antenna gain in the radar range equation, it is crucial to understand the individual elements of the equation and how they interact.

3.1 Power Density & Gain

The radar range equation begins with power density, denoted as ρR, which is the power per unit area at a specific range from the RADAR. Power density is influenced by transmitter power, antenna gain, and the range to the target. Antenna gain, represented by Gt, quantifies the effectiveness of focusing power in a specific direction.

It is the ratio of power radiated by the antenna to that of an ideal isotropic antenna.

The antenna gain (G) is determined by the antenna's area (A) and wavelength (λ), as expressed in Equation 1:

Equation 1: Antenna Gain (G) = 4πA/λ^2

Transmitter gain is also a function of the antenna aperture, as shown in Equation 2:

Equation 2: Transmitter Gain (GT) = (4πA/λ^2) * Pt

Where:

• Pt = Transmitter Power
• A = Antenna Area
• λ = Wavelength

It is important to note that gain is not affected by power, but power is influenced by gain.

3.2 Power Density Directed Towards the Target

The power density directed toward a target (ρR) can be calculated by considering the transmitted gain of the antenna, transmitter power, and the range to the target. This is illustrated in Equation 3:

Equation 3: Power Density Directed Towards the Target (ρR) = (GT * Pt) / (4πR^2)

Where:

• GT = Transmitted Gain
• Pt = Transmitter Power
• R = Range to the Target

This equation quantifies the power density that strikes a target at a given range.

3.3 Noise

While the radar equation calculates distance in free space, it does not account for noise. Noise is a critical factor limiting receiver performance and is influenced by various sources, including galactic noise, solar noise, atmospheric noise, man-made interference, jamming, ground noise, and internal noise generated by radar components.

The effective noise power at the receiver is characterized by several components, including Boltzmann's constant (k), system noise temperature (Ts), and noise bandwidth of the receiver (Bn). These components are combined to determine the average noise power, as shown in Equation 4:

Equation 4: Average Noise Power (Pn) = k * Ts * Bn

Where:

• k = Boltzmann's Constant
• Ts = System Noise Temperature
• Bn = Noise Bandwidth of the Receiver

Signal-to-noise ratio (SNR) is a crucial metric in radar performance and is calculated by dividing the received signal power by the noise power, as demonstrated in Equation 5:

Equation 5: Signal-to-Noise Ratio (SNR) = (Received Signal Power) / (Average Noise Power)

SNR measures a radar's ability to detect a target over background noise.

3.4 System Losses

System losses, denoted as L, encompass design, operational, and propagation losses that impact a radar's maximum range. These losses can be categorized as transmit losses and receive losses, each affected by factors such as beam shape, scanning, atmospheric conditions, field degradation, Doppler effects, signal processing, and more.

3.5 Receiver Sensitivity

Receiver sensitivity (Smin) is a crucial parameter determined by the radar's design to minimize noise and detect the required signal. It is defined as the minimum input signal required to produce a specified output signal and can be calculated using Equation 6:

Equation 6: Receiver Sensitivity (Smin) = (S/N)min * k * Ts * Bn / G

Where:

• S/Nmin = Minimum Signal-to-Noise Ratio
• k = Boltzmann's Constant
• Ts = System Noise Temperature
• Bn = Noise Bandwidth of the Receiver
• G = Antenna/System Gain

Receiver bandwidth (Bn) is limited by receiver sensitivity, as excessively high sensitivity can reduce bandwidth and lead to processing unwanted signals.

4. Search and Surveillance Equations

In situations where a target's location is not known, such as during search and surveillance operations, the radar equation must be adapted. The search/surveillance equation accounts for parameters such as search volume, scan time, and power average, affecting SNR and radar performance.

5. The Radar Range Equation

The radar range equation is a comprehensive representation of all the elements discussed thus far and can be expressed as:

Equation 7: Radar Range Equation

This equation provides valuable insights into the design and performance parameters of a radar system.

6. Design and Performance Parameters

The radar range equation can be divided into design parameters and performance parameters, revealing the relationship between engineering aspects and performance requirements. This relationship is critical during the radar design phase to achieve desired outcomes.

Equation 8: Design Parameters = Performance Parameters

7. The Relationship of Parameters

Understanding the interplay of parameters is fundamental to radar design. Adjusting parameters like transmitter power, antenna gain, and receiver sensitivity can significantly impact a radar's range and performance. For instance, to double a radar's range, one must consider increasing power, antenna size, scan time, or target size, or a combination of these adjustments.

8. Practical Application and Conclusion

This paper has deconstructed the radar range equation, elucidating the relationship between transmitter power, antenna gain, and receiver sensitivity. It has emphasized the importance of considering noise, system losses, and search/surveillance equations in radar design. Practical examples demonstrated the implications of parameter adjustments on Royal Navy vessels, highlighting the challenges and opportunities in optimizing radar performance for various applications.