8 Coherent Radar Systems
163
U pd1 = U 1 cos ϕ,
U pd2 = U 1 sin ϕ, .
(8.16)
Assuming that during the reception of a burst of pulses from one target, the phase
relationships do not change, we obtain the following results of separate accumulation:
l 1 = nU 1 cos
l 2 = nU 1 sin
(8.17)
The voltage at the output of the processing circuit when the phase is not known
U out =
l
2
1 + l
2
2 = nU 1 .
(8.18)
coincides with the voltage (8.15) at the output of the processing circuit with the
known initial phase.
Note that an important condition for effectiveness of the examined processing
method (as well as the method of full coherence) is the maintaining of a constant
initial phase of receiving and reference oscillations during the time of receiving
the entire target pulse burst (the time the radio beam passes through the target). In
particular, a rigid phasing of the reference oscillation with respect to the probing
one is required. The latter is a “phase mediator” between the reference and receiving
oscillations. Thus, in the examined processing method, the observer, not knowing
the initial phase, uses its constancy during the time of receiving target pulses.
If the coherence of reference oscillations in different burst pulses repetition periods
is not maintained, the transition from formula (8.16) to formula (8.17) becomes
impossible, i.e., the best summation of burst signals in amplitude, carried out in the
video pulse accumulator, is violated. Indeed, the violation of the coherence of the
reference oscillations will cause different phase shifts ϕ for different burst pulses;
instead of ideal accumulation in accordance with formula (8.17), the impulses will
be summed up according to the less favorable law:
⎧
⎪ ⎪ ⎨
⎪ ⎪ ⎩
l 1 = nU 1
n
k=1
cos ϕ k ,
l 2 = nU 1
n
k=1
sin ϕ k .
(8.19)
In particular, two impulses, for which ϕ 1 = 0 and ϕ 1 = π /2, will give, in
accordance with formula (8.19) the following:
l 1 = 1U 1 + 0U 1 = U 1
l 2 = 0U 1 + U 1 = U 1 .
(8.20)
In this case, the output voltage of the processing circuit will be:
163
U pd1 = U 1 cos ϕ,
U pd2 = U 1 sin ϕ, .
(8.16)
Assuming that during the reception of a burst of pulses from one target, the phase
relationships do not change, we obtain the following results of separate accumulation:
l 1 = nU 1 cos
l 2 = nU 1 sin
(8.17)
The voltage at the output of the processing circuit when the phase is not known
U out =
l
2
1 + l
2
2 = nU 1 .
(8.18)
coincides with the voltage (8.15) at the output of the processing circuit with the
known initial phase.
Note that an important condition for effectiveness of the examined processing
method (as well as the method of full coherence) is the maintaining of a constant
initial phase of receiving and reference oscillations during the time of receiving
the entire target pulse burst (the time the radio beam passes through the target). In
particular, a rigid phasing of the reference oscillation with respect to the probing
one is required. The latter is a “phase mediator” between the reference and receiving
oscillations. Thus, in the examined processing method, the observer, not knowing
the initial phase, uses its constancy during the time of receiving target pulses.
If the coherence of reference oscillations in different burst pulses repetition periods
is not maintained, the transition from formula (8.16) to formula (8.17) becomes
impossible, i.e., the best summation of burst signals in amplitude, carried out in the
video pulse accumulator, is violated. Indeed, the violation of the coherence of the
reference oscillations will cause different phase shifts ϕ for different burst pulses;
instead of ideal accumulation in accordance with formula (8.17), the impulses will
be summed up according to the less favorable law:
⎧
⎪ ⎪ ⎨
⎪ ⎪ ⎩
l 1 = nU 1
n
k=1
cos ϕ k ,
l 2 = nU 1
n
k=1
sin ϕ k .
(8.19)
In particular, two impulses, for which ϕ 1 = 0 and ϕ 1 = π /2, will give, in
accordance with formula (8.19) the following:
l 1 = 1U 1 + 0U 1 = U 1
l 2 = 0U 1 + U 1 = U 1 .
(8.20)
In this case, the output voltage of the processing circuit will be: