#### Multipath Height Finding Method

Figure 1: Multipath Height Finding Method

Figure 1: Multipath Height Finding Method

#### Multipath Height Finding Method

The height of a target traditionally is found with a 3-D air-surveillance radar; one that utilizes multiple beams in elevation or employs one or more scanning pencil beams to find the elevation angle of the target. The 3-D radar has been widely used in the past even though it might have been from four to ten times the cost of a 2-D (range and azimuth) air-surveillance radar. A 3-D radar generally has poor height accuracy at low angles because of multipath effects when the main beam of the antenna illuminates the land or sea surface.

Finding target height based on the multipath echo structure in a 2-D wide-bandwidth radar has some important advantages
compared with finding height using conventional 3-D radars.
With sufficient
range resolution,
the direct signal can be separated from the surface-reflected signal.
The time separation between these signals depends on the target height (a flat-earth is assumed).
There are four components to the multipath echo.
The first is the direct path AB and return over the same path. The second is the
path AMB and return via AB, or AMB+AB.
There is also the opposite path of the same length (time delay); that is, AB+AMB. The
fourth path is the path AMB out and back. The time t_{h} in Figure can be found as:

t_{h} = |
2h_{a} · h_{t} |
where | h_{a} = radar antenna heighth _{t} = target heightc _{ } = velocity of propagation, and R _{ } = range |
(1) |

c · R |

If we note that h_{t} /R is the elevation angle sin Θ_{e} to the target, then

sin Θ_{e} = |
c · t_{h} |
where | Θ_{e} = elevation anglet _{h} = run time difference |
(2) |

2 h_{a} |

h_{t} = |
c · R · t_{h} |
(3) |

2 h_{a} |

For example, if h_{a} = 100 ft, h_{t} = 10,000 ft, and R = 50 NM ,
the time t_{h} is 6.69 ns, which requires a
bandwidth
of at least 149.5 MHz.
The higher the elevation angle to the target, the greater will be the separation of the multipath echoes
and the easier it is to measure an accurate time separation t_{h}.
In practice the radar system with pulse compression should have a range resolution of 1 m.