beamdwellfactor

Range-dependent loss for rapidly scanning beam

Since R2021a

Syntax

fbd = beamdwellfactor(r,hpbw,scanrate)

Description

fbd = beamdwellfactor(r,hpbw,scanrate) calculates the range-dependent beam-dwell factor fbd for an antenna at the specified range r, half-power beamwidth hpbw, and scan rate scanrate. The beamdwellfactor function assumes that the transmitter and receiver antennas have equal beamwidth and an ideal Gaussian antenna pattern with no side lobes.

Examples

Calculate Beam-Dwell Factor

Calculate the beam-dwell factor for a surveillance radar at 100 linearly-spaced ranges in the interval [0,100000] meters. Specify the beamwidth as 1 degree and the scan rate as 120 degrees per second.

r = linspace(0,100000);
hpbw = 1;
scanrate = 120;
fbd = beamdwellfactor(r,hpbw,scanrate);

Plot the beam-dwell factor as a function of range. Before plotting, convert the range from meters to kilometers.

plot(r*0.001,fbd)
grid on
xlabel('Range (km)')
ylabel('Beam-dwell Factor (dB)')

Input Arguments

r — Range

scalar | vector

Range in meters, specified as a scalar or vector.

Data Types: double

hpbw — Half-power beamwidth

scalar | vector

Half-power beamwidth of the antenna in degrees, specified as a scalar or vector. If hpbw is a vector, then scanrate must be a scalar or a vector of the same size.

Data Types: double

scanrate — Scan rate

scalar | vector

Scan rate of the antenna in degrees per second. If scanrate is a vector, then hpbw must be a scalar or a vector of the same size.

Data Types: double

Output Arguments

fbd — Range-dependent beam-dwell factor

matrix

Range-dependent beam-dwell factor in dB, returned as a j-by-k matrix such that j is the size of r and k is the size of hpbw or scanrate, whichever is larger.

The rows of fbd correspond to the ranges in r. The columns depend on the sizes of hpbw and scanrate.

• If hpbw is a vector and scanrate is a scalar, then the columns of fbd correspond to the half-power beamwidths in hpbw.

• If hpbw is a scalar and scanrate is a vector, then the columns of fbd correspond to the scan rates in scanrate.

• If hpbw and scanrate are both vectors, then the columns of fbd correspond to both the half-power beamwidths in hpbw and the scan rates in scanrate.

Data Types: double

More About

Beam-Dwell Factor

The beam-dwell factor accounts for the misalignment between transmitter and receiver beam axes when a scanning system has a high scan rate and long-range targets.

The equation for the beam-dwell factor, F_bd, is

$$F_{bd}=L{\displaystyle \underset{-\pi }{\overset{\pi }{\int }}{f}^2(\theta )f^2(\theta -\delta )d\theta }$$

where the terms in the equation are:

• L — Normalizing factor that brings F_bd to unity for ẟ = 0

• ẟ = t_d / t₀ — Fractional beamwidth scanned during the delay, where:

  • t_d = 2R / c — Time delay for a target, where R is the range and c is the wave propagation speed

  • t₀ = θ₃ / ω_s — The time the system takes to continuously scan through one beamwidth, where θ₃ is the half-power beamwidth and ω_s is the scan rate

• f(θ) — Antenna pattern

The beamdwellfactor function assumes an ideal Gaussian antenna pattern with no side lobes. The equation for the ideal Gaussian antenna pattern with no side lobes, f(θ), is:

$$f(\theta )=\exp \left[-2(\ln 2)\frac{{\theta }^2}{{\theta }_3^2}\right]$$

References

[1] Barton, David Knox. "Beam-Dwell Factor F_bd." In Radar Equations for Modern Radar, 362. Artech House Radar Series. Boston, Mass: Artech House, 2013.

[2] Barton, David Knox. "Antenna Patterns." In Radar Equations for Modern Radar, 147. Artech House Radar Series. Boston, Mass: Artech House, 2013.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Version History

Introduced in R2021a