JAMMING TO SIGNAL (J/S) RATIO - CONSTANT POWER [SATURATED] JAMMING

The following table contains a summary of the equations developed in this section.

This section derives the J/S ratio from the one-way range equation for J and the two-way range equation for S, and deals exclusively with
active (transmitting) ECM devices or systems. Furthermore, the only purpose of the ECM considered is to prevent, delay, or confuse the radar
processing of target information.

By official definition, ECM can be either Jamming or Deception. This may be somewhat confusing because
almost any type of active ECM is commonly called "jamming", and the calculations of ECM signal in the radar compared to the target signal in
the radar commonly refer to the "jamming-to-signal" ratio ("J-to-S" ratio). Therefore this section uses the common jargon and the term "jammer"
refers to any ECM transmitter, and the term "jamming" refers to any ECM transmission, whether Deception or Concealment.

Jamming:
"Official" jamming should more aptly be called Concealment or Masking. Essentially, Concealment uses ECM to swamp the radar receiver and
hide the targets. Concealment (Jamming) usually uses some form of noise as the transmitted ECM signal. In this section, Concealment will be
called "noise" or "noise jamming".

Deception: Deception might be better called Forgery. Deception uses ECM to forge false target signals
that the radar receiver accepts and processes as real targets.

"J" designates the ECM signal strength whether it originates from a noise
jammer or from a deception ECM system.

Basically, there are two different methods of employing active ECM against hostile
radars:

Self Protection ECM Support ECM

For most practical purposes, Self
Protection ECM is usually Deception and Support ECM is usually noise jamming. As the name implies, Self Protection ECM is ECM that is used to
protect the platform that it is on. Self Protection ECM is often called "self screening jamming", and also "DECM", which is an acronym for either
"Defensive ECM" or "Deception ECM". The top half of Figure 1 shows self screening jamming (DECM).

The bottom half of Figure 1 illustrates
escort jamming which is a special case of support jamming. If the escort platform is sufficiently close to the target, the J-to-S calculations
are the same as for DECM.

Support ECM is ECM radiated from one platform and is used to protect other platforms. Figure 2 illustrates
two cases of support jamming - stand-off jamming (SOJ) and stand-in jamming (SIJ). For SOJ the support jamming platform is maintaining an orbit
at a long range from the radar - usually beyond weapons range. For SIJ, a remotely piloted vehicle is orbiting very close to the victim radar.
Obviously, the jamming power required for the SOJ to screen a target is much greater than the jamming power required for the SIJ to screen the
same target.

When factoring ECM into the radar equation, the quantities of greatest interest are "J-to-S" and Burn- Through Range.

"J-to-S" is the ratio of the signal strength of the ECM signal (J) to the signal strength of the target return signal (S). It is expressed
as "J/S" and, in this section, is always in dB. J usually (but not always) must exceed S by some amount to be effective, therefore the desired
result of a J/S calculation in dB is a positive number. Burn-through Range is the radar to target range where the target return signal can first
be detected through the ECM and is usually slightly farther than crossover range where J=S. It is usually the range where the J/S just equals
the minimum effective J/S (See Section 4-8).

The significance of "J-to-S" is sometimes misunderstood. The effectiveness of ECM is not
a direct mathematical function of "J-to-S". The magnitude of the "J-to-S" required for effectiveness is a function of the particular ECM technique
and of the radar it is being used against. Different ECM techniques may very well require different "J-to-S" ratios against the same radar.
When there is sufficient "J-to-S" for effectiveness, increasing it will rarely increase the effectiveness at a given range. Because modern radars
can have sophisticated signal processing and/or ECCM capabilities, in certain radars too much "J-to-S" could cause the signal processor to ignore
the jamming, or activate special anti-jamming modes. Increasing "J-to-S" (or the jammer power) does, however, allow the target aircraft to get
much closer to the threat radar before burn-through occurs, which essentially means more power is better if it can be controlled when desired.

IMPORTANT NOTE: If the signal S is CW or PD and the Jamming J is amplitude modulated, then the J used in the formula has to be reduced from
the peak value (due to sin x/x frequency distribution). The amount of reduction is dependent upon how much of the bandwidth is covered by the
jamming signal. To get an exact value, integrals would have to be taken over the bandwidth. As a rule of thumb however:

C If the frequency of modulation is less than the BW of the tracking radar reduce J/S by 10 Log(duty cycle).

C If the frequency of modulation is greater than the BW of the tracking radar reduce J/S by 20 Log(duty cycle).

For example; if your jamming signal is square wave chopped (50% duty cycle) at a 100 Hz rate while jamming a 1 kHz bandwidth receiver, then
the J/S is reduced by 3 dB from the maximum. If the duty cycle was 33%, then the reduction would be 4.8 dB. If the 50% and 33% duty cycle jamming
signals were chopped at a 10 kHz (vice the 100 Hz) rate, the rule of thumb for jamming seen by the receiver would be down 6 dB and 9.6 dB, respectively,
from the maximum since the 10 kHz chopping rate is greater than the 1 kHz receiver BW.

Figure 3 is radar jamming visualized. The Physical concept of Figure 3 shows a monostatic radar that is the same as Figure 1, Section
4-4, and a jammer (transmitter) to radar (receiver) that is the same as Figure 3, Section 4-3. In other words, Figure 3 is simply the combination
of the previous two visual concepts where there is only one receiver (the radar's).

Figure 3. Radar Jamming Visualized

J/S for DECM vs. MONOSTATIC RADAR

The equivalent circuit shown in Figure 4 applies to jamming monostatic radars
with either DECM or support ECM. For DECM (or escort) v.s. a monostatic radar, the jammer is on the target and the radar receive and transmit
antennas are collocated so the three ranges and three space loss factors (α's) are the same.

Figure 4. Monostatic Radar ECM Equivalent Circuit

J-S Ratio (Monostatic) The ratio of the power received (P_{r1} or J) from the jamming signal transmitted
from the target to the power received (P_{r2} or S) from the radar skin return from the target equals J/S.

From
the one way range equation in Section 4-3:
[1]

Note: To avoid having to include additional terms for these calculations, always combine any transmission line loss with antenna
gain.

From the two way range equation in Section 4.4: [2]

so
[3]

* Keep R and F in the same units.

On reducing the above equation to log form we have:

or 10log J/S = 10log P_{j} + 10log G_{ja} - 10log P_{t} - 10log G_{t} - 10log σ + 10.99 dB + 20log
R [5]

Note: Neither f nor λ terms are part of the final form of equation [3] and equation [5].

J/S Calculations (Monostatic) Using a One Way Free Space Loss - The simplified radar equations developed in previous
sections can be used to express J/S.

From the one way range equation Section 4-3:

10log (P_{r1} or J) = 10log P_{j}
+ 10log G_{ja} + 10log G_{r} - α_{1} (in dB) [6]

From the two way
range equation in Section 4.4:

10log (P_{r2} or S) = 10log P_{t} + 10log G_{t} + 10log G_{r} + G_{σ}
- 2α_{1} (in dB) [7]

Note:
To avoid having to include additional terms for these calculations, always combine any transmission line loss with antenna gain. The 20log f_{1}
term in -G_{σ} cancels the 20log f_{1} term in α_{1}.

J/S for DECM vs. BISTATIC RADAR

The semi-active missile illustrated in Figure 5 is the typical bistatic radar which would require the target
to have self protection ECM to survive. In this case, the jammer is on the target and the target to missile receiver range is the same as the
jammer to receiver range, but the radar to target range is different. Therefore, only two of the ranges and two of the "'s (Figure 6.) are the
same.

In the following equations:

"Tx = The one-way space loss from the radar
transmitter to the target for range R_{Tx}

"Rx = The one-way space loss from the target to the missile receiver for range R_{Rx}

Like the monostatic radar, the bistatic jamming and reflected target signals travel the same path from the target and enter the receiver
(missile in this case) via the same antenna. In both monostatic and bistatic J/S equations this common range cancels, so both J/S equations
are left with an R_{Tx} or 20 log R_{Tx} term. Since in the monostatic case R_{Tx} = R_{Rx} and
α_{Tx} = α_{Rx} , only R or α_{1}
is used in the equations. Therefore, the bistatic J/S equations [11], [13], or [14] will work for monostatic J/S calculations, but the opposite
is only true if bistatic R_{Tx} and α_{Tx} terms are used for R or α_{1}
terms in monostatic equations [3], [5], and [8].

The equivalent circuit shown in Figure 6 applies to jamming bistatic radar. For DECM
(or escort) vs. a bistatic radar, the jammer is on the target and the radar receive and transmit antennas are at separate locations so only
two of the three ranges and two of the three space loss factors ("'s) are the same.

Figure 6. Bistatic Radar ECM Equivalent Circuit

J-to-S Ratio (Bistatic) When the radar's transmit antenna is located remotely from the receiving antenna
(Figure 6), the ratio of the power received (P_{r1} or J) from the jamming signal transmitted from the target to the power received
(P_{r2} or S) from the radar skin return from the target equals J/S. For jammer effectiveness J normally has to be greater than S.

From the one way range equation in Section 4-3: (R_{Jx}
= R_{Rx}) [9]

From the two way range equation in Section 4.4: [10]

so [11]

* Keep R and F in the same units.

On reducing the above equation to log form we have:

Note: To avoid having to include additional terms for these calculations, always combine any transmission
line loss with antenna gain. Neither f nor λ terms are part of the final form of equation [11] and equation [13].

Bistatic J/S Calculations (Bistatic) Using a One Way Free Space Loss - The simplified radar equations developed
in previous sections can be used to express J/S.

From the two way range equation in Section 4-4: 10log (P_{r2} or S) = 10log P_{t} + 10log G_{t} + 10log
G_{r} + G_{σ} - α_{Tx} - α_{Rx} (all factors dB)
[15]

Note: To avoid having to include additional terms for these calculations,
always combine any transmission line loss with antenna gain. The 20log f_{1} term in -G_{σ} cancels the 20log f_{1}
term in α_{1}.

Saturated J/S (Monostatic) Example (Constant Power Jamming)

Assume that a 5 GHz radar has a 70 dBm
signal fed through a 5 dB loss transmission line to an antenna that has 45 dB gain. An aircraft is flying 31 km from the radar. The aft EW antenna
has -1 dB gain and a 5 dB line loss to the EW receiver (there is an additional loss due to any antenna polarization mismatch but that loss will
not be addressed in this problem). The aircraft has a jammer that provides 30 dBm saturated output if the received signal is above -35 dBm.
The jammer feeds a 10 dB loss transmission line which is connected to an antenna with a 5 dB gain. If the RCS of the aircraft is 9 m^{2},
what is the J/S level received by the tracking radar?

Answer: The received signal at the jammer is the same as the example in Section
4-3, i.e. answer (1) = -32.3 dBm @ 5 GHz. Since the received signal is above -35 dBm, the jammer will operate in the saturated mode, and equation
[5] can be used. (See Section 4-10 for an example of a jammer operating in the linear region.)

* The answer is still 6.25 dB if the tracking radar operates at 7 GHz provided the antenna gains and the aircraft
RCS are the same at both frequencies.

In this example, there is inadequate jamming power at each frequency if the J/S needs to be 10
dB or greater to be effective. One solution would be to replace the jammer with one that has a greater power output. If the antenna of the aircraft
and the radar are not the proper polarization, additional power will also be required (see Section 3-2).

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