Target Tracking - MATLAB Simulations for Radar Systems Design - page 412

Similarly,

d
2 R

 

R 2 ≈ R 1 – ------- sin ϕ

(9.14)

 

The phase difference between the two elements is then given by

2π
λ

2π
λ

------ ------ d

φ = ( R 1 – R 2 ) = sin ϕ

(9.15)

where is the wavelength. The phase difference is used to determine the
angular target location. Note that if , then the target would be on the
antennaÓs main axis. The problem with this phase comparison monopulse tech-
nique is that it is quite difficult to maintain a stable measurement of the off
boresight angle , which causes serious performance degradation. This prob-
lem can be overcome by implementing a phase comparison monopulse system
as illustrated in Fig. 9.15 .

λ φ

φ = 0

ϕ

The (single coordinate) sum and difference signals are, respectively, given
by

Σ() S 1 = + S 2

(9.16)

∆() S 1 = – S 2

(9.17)

where the S 1 and S 2 are the signals in the two elements. Now, since S 1 and

S 2 have similar amplitude and are different in phase by φ , we can write

– j φ

S 1 = S 2 e

(9.18)

It follows that

– j φ

∆() S 2 = ( 1 – e )

(9.19)

S 1

∆

ϕ

d

Σ

S 2

Figure 9.15. Single coordinate phase monopulse antenna,
with sum and difference channels.