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Chapter 5: Problem 40

A 10 GHz bistatic radar has a minimum detectable received signal power of \(-150 \mathrm{dBm},\) an antenna gain of \(26 \mathrm{~dB},\) and a required range of \(100 \mathrm{~km}\). What is the transmitted pulse power in dBm needed to detect a (a) conventional fighter aircraft having an RCS of \(5 \mathrm{~m}^{2}\) ? (b) a stealth aircraft with an RCS of \(0.05 \mathrm{~m}^{2}\) ?

Short Answer

Expert verified
(a) -54 dBm, (b) -74 dBm

Step by step solution

01

Identify Key Parameters

The given parameters are: Frequency = 10 GHz, minimum detectable received signal power = -150 dBm, antenna gain = 26 dB, range = 100 km, RCS for fighter aircraft = 5 m虏, and RCS for stealth aircraft = 0.05 m虏.
02

Convert Range to Meters

Convert the required range from kilometers to meters:\[ 100 \text{ km} = 100 \times 10^3 \text{ m} = 10^5 \text{ m} \]
03

Use the Radar Range Equation

For bistatic radar, the equation is: \[ P_t = \frac{ (4 \times \text{Range}^2 )^2 \times P_r \times G_t \times G_r \times \text{RCS}}{\text{Range}^4} \] Here, Range is replaced back with its equivalent in meters, and we can use the typical values of antenna gains: G_t and G_r 鈮� 26 dB each.
04

Convert Gains to Linear Scale

Convert antenna gains from dB to a linear scale using \( G_linear = 10^{G_\text{dB} / 10} \): \[ G_t\text{(linear)} = G_r\text{(linear)} = 10^{26 / 10} = 10^2.6 = 398.11 \]
05

Calculate Required Transmit Power for Conventional Fighter Aircraft (RCS = 5 m虏)

Plug in the values for the conventional fighter aircraft: \[ P_t = ((4 \times 10^5)^2 \times 10^{-15} \times 398.11^2 \times 5) / (10^5)^4 = 3.98 \times 10^{-9} \text{ W} \] Convert this to dBm: \[ P_t \text{(dBm)} = 10 \times \text{log}_{10}(3.98 \times 10^{-9}) + 30 \text{ dBm} = -54 \text{ dBm} \]
06

Calculate Required Transmit Power for Stealth Aircraft (RCS = 0.05 m虏)

Plug in the values for the stealth aircraft: \[ P_t = ((4 \times 10^5)^2 \times 10^{-15} \times 398.11^2 \times 0.05) / (10^5)^4 = 3.98 \times 10^{-11} \text{ W} \] Convert this to dBm: \[ P_t \text{(dBm)} = 10 \times \text{log}_{10}(3.98 \times 10^{-11}) + 30 \text{ dBm} = -74 \text{ dBm} \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Radar Range Equation
The radar range equation is pivotal in understanding how radar systems detect objects at specific distances. For bistatic radar, which involves a separate transmitter and receiver placed at different locations, the equation is slightly adjusted. The general form is:\[P_t = \frac{ (4 \times \text{Range}^2 )^2 \times P_r \times G_t \times G_r \times \text{RCS}}{\text{Range}^4}\]Where:
  • \(P_t\) is the transmitted power
  • \(P_r\) is the minimum detectable received signal power
  • \(G_t\) and \(G_r\) are the transmitter and receiver antenna gains, respectively
  • RCS is the Radar Cross Section of the target
  • Range is the distance to the target
In our exercise, we determine the required transmitted pulse power to detect different aircraft types by rearranging this equation based on the given parameters.
dBm to Linear Scale Conversion
Decibels-milliwatts (dBm) is a log-scaled unit used to express power relative to one milliwatt. Converting dBm to a linear scale is crucial for calculations involving power equations.The formula for the conversion is:\[G_\text{linear} = 10^{G_\text{dB} / 10}\]For the given antenna gain:\[G_t(\text{linear}) = G_r(\text{linear}) = 10^{26 / 10} = 10^{2.6} \ approx = 398.11\]Converting between these scales makes it manageable to work with gains in complex equations.
Radar Cross-Section (RCS)
Radar Cross-Section (RCS) is a measure of how a target reflects radar signals back to the radar receiver. A larger RCS means the object is more detectable. In simple terms, RCS represents the area of a perfectly reflecting sphere that would return the received power.In our exercise, the conventional fighter aircraft has an RCS of \(5 \text{ m}^2\) while the stealth aircraft has an RCS of \(0.05 \text{ m}^2\). These values directly impact the required transmitted power.The smaller the RCS, the more difficult it is to detect an object, which explains why stealth technologies focus on minimizing RCS.
GHz Frequency
Gigahertz (GHz) frequencies are common in radar systems. They're beneficial because higher frequencies allow for finer resolution and more detail. However, higher frequencies, like 10 GHz used in our problem, also experience greater signal attenuation.In the context of our exercise, knowing the radar operates at 10 GHz helps determine the capabilities and limitations of the radar system, such as the required power levels and how well it can discern between different targets.
Signal Power Detection
Detecting a signal's power is integral in radar systems. The minimum detectable received signal power determines the weakest signal a radar system can recognize despite background noise.Given a minimum detectable received signal power of -150 dBm in our exercise, we calculate the transmitted pulse power necessary for different aircraft. This identifies what power levels are needed to ensure the radar system can function correctly at specified distances, especially under various conditions like RCS and distance.

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Most popular questions from this chapter

An antenna with a gain of \(10 \mathrm{~dB}\) presents an \(\mathrm{RF}\) signal with a power of \(5 \mathrm{dBm}\) to a low-noise amplifier along with noise of \(1 \mathrm{~mW}\) and an interfering signal of \(2 \mathrm{~mW}\). (a) What is the RF SIR? Include both noise and the interfering signal in your calculation. Express your answer in decibels. (b) The modulation format and coding scheme used have a processing gain, \(G_{P}\), of \(7 \mathrm{~dB}\). The modulation scheme has four states. What is the ratio of the energy per bit to the noise per bit, that is, what is the effective \(E_{b} / N_{o}\) after despreading?

A cellular radio system uses a frequency reuse plan with 12 cells per cluster. If ideal 8 -PSK modulation is used, what is the system spectral efficiency in terms of bit/s/Hz/cell?

An OFDM system with 12 data subcarriers, uses a coding rate of \(3 / 4,\) and each subcarrier uses \(16-\) QAM modulation (with a modulation efficiency of \(2.7 \mathrm{bit} / \mathrm{s} / \mathrm{Hz})\) with a bandwidth of \(250 \mathrm{kHz}\). What is the maximum data rate supported?

A free-space \(2 \mathrm{GHz}\) pulsed monostatic radar system transmits a \(2 \mathrm{~kW}\) pulse and has a minimum detectable received signal power of \(-90 \mathrm{dBm}\). What is the antenna gain required to be able to detect a target with a radar cross section of \(10 \mathrm{~m}^{2}\) at \(10 \mathrm{~km} ?\)

A monostatic free-space \(10 \mathrm{GHz}\) pulsed radar system is used to detect a fighter plane having a radar cross section, \(\sigma,\) of \(5 \mathrm{~m}^{2}\). The antenna gain is \(30 \mathrm{~dB}\) and the transmitted power is \(1 \mathrm{~kW}\). If the minimum detectable received signal is \(-120 \mathrm{dBm},\) what is the detection range?
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