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

JAMMING TO SIGNAL (J/S) RATIO (MONOSTATIC) or: 10log J/S = 10log Pj+ 10log Gja - 10log Pt - 10log Gt - 10log + 10.99 dB + 20log R Note (1): Neither f nor terms are part of the final form of these equations.
If simplified radar equations developed in previous sections are used: 10log (J/S) = 10log Pj + 10log Gja - 10log Pt - 10log Gt - G + (in dB) Note (2): The 20log f 1 term in -G cancels the 20log f 1 term in .
JAMMING TO SIGNAL (J/S) RATIO (BISTATIC) RTx is the range from the radar transmitter to the target. See note (1) above. or: 10log J/S = 10log Pj + 10log Gja - 10log Pt - 10log Gt - 10log + 10.99 dB + 20log RTx
If simplified radar equations developed in previous sections are used: See note (2) above. 10log (J/S) = 10log Pj + 10log Gja - 10log Pt - 10log Gt - G + Tx (all factors dB)
Target gain factor; G = 10log + 20log f1 + K2 (in dB)	One-way free space loss; Tx or Rx = 20log (f1 RTx or Rx) + K1 (in dB)
K2 Values (dB) RCS () (units) m 2 ft 2 f1 in MHz K2 = -38.54 -48.86 f1 in GHz K2 = 21.46 11.14	K1 Values (dB) Range (units) NM Km m yd ft f1 in MHz K1 = 37.8 32.45 -27.55 -28.33 -37.87 f1 in GHz K1 = 97.8 92.45 32.45 31.67 22.13

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 Burn-Through / Crossover Range Section).

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.

J/S for DECM vs. MONOSTATIC RADAR

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

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 ('s) are the same.

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 section:

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:

so:

* Keep R and in the same units.

On reducing the above equation to log form we have:

10log J/S = 10log P_j + 10log G_ja - 10log P_t - 10log G_t - 10log + 10log 4 + 20log R [4]

or: 10log J/S = 10log P_j+ 10log G_ja - 10log P_t - 10log G_t - 10log + 10.99 dB + 20log R [5]

Note: Neither f nor 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:

10log (P_r1 or J) = 10log P_j + 10log G_ja + 10log G_r - (in dB) [6]

From the Two-way Range Equation Section:

10log (P_r2 or S) = 10log P_t + 10log G_t + 10log G_r + G - 2 (in dB) [7]

10log (J/S) = 10log P_j + 10log G_ja - 10log P_t - 10log G_t - G + (in dB) [8]

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 cancels the 20log f ₁ term in .

Target gain factor; G = 10log + 20log f1 + K2 (in dB)	One-way free space loss; Tx or Rx = 20log (f1 RTx or Rx) + K1 (in dB)
K2 Values (dB) RCS () (units) m 2 ft 2 f1 in MHz K2 = -38.54 -48.86 f1 in GHz K2 = 21.46 11.14	K1 Values (dB) Range (units) NM Km m yd ft f1 in MHz K1 = 37.8 32.45 -27.55 -28.33 -37.87 f1 in GHz K1 = 97.8 92.45 32.45 31.67 22.13

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_Tx² or 20 log R_Tx term. Since in the monostatic case R_Tx = R_Rx and _Tx = _Rx , only R or 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 _Tx terms are used for R or 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.

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 Section:

From the Two-way Range Equation Section:

so:

* Keep R and in the same units.

On reducing the above equation to log form we have:

10log J/S = 10log P_j + 10log G_ja - 10log P_t - 10log G _t - 10log + 10log 4 + 20log R _Tx [12]

or: 10log J/S = 10log P_j + 10log G_ja - 10log P_t - 10log G_t - 10log + 10.99 dB + 20log R_Tx [13]

Note: To avoid having to include additional terms for these calculations, always combine any transmission line loss with antenna gain. Neither f nor 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 one way range equation:

10log (P_r1 or J) = 10log P_j + 10log G_ja + 10log G_r - _Rx (all factors dB) [14]

From the two way range equation:

10log (P_r2 or S) = 10log P_t + 10log G_t + 10log G_r + G - _Tx - _Rx (all factors dB) [15]

10log (J/S) = 10log P_j + 10log G_ja - 10log P_t - 10log G_t - G + _Tx (all factors dB) [16]

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 cancels the 20log f ₁ term in .

Target gain factor; G = 10log + 20log f1 + K2 (in dB)	One-way free space loss; Tx or Rx = 20log (f1 RTx or Rx) + K1 (in dB)
K2 Values (dB) RCS () (units) m 2 ft 2 f1 in MHz K2 = -38.54 -48.86 f1 in GHz K2 = 21.46 11.14	K1 Values (dB) Range (units) NM Km m yd ft f1 in MHz K1 = 37.8 32.45 -27.55 -28.33 -37.87 f1 in GHz K1 = 97.8 92.45 32.45 31.67 22.13

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 m² , 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 the One-way Radar Equation Section, 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 Jamming to Signal Ratio - Constant Gain Jamming Section for an example of a jammer operating in the linear region.)

10log J/S = 10log P_j + 10log G_ja - 10log P_t - 10log G_t - 10log + 10.99 dB + 20log R

Note: the respective transmission line losses will be combined with antenna gains, i.e. -5 + 45 = 40 dB & -10 +5 = -5 dB.

* 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 (Polarization Section).