Radar Correspondence Group

Subject: Radar protection criteria in case of pulsed interference

Contacts: Hugues de BAILLIENCOURT, +33 2 98 34 12 32,

<hde_bailliencourt@compuserve.com>

**1-Introduction**

Resolves 2 of ITU-R resolution 747 resolves "to continue to study, as a
matter of urgency, the technical characteristics, protection criteria,
and other factors of radiolocation, radionavigation, EESS (active) and
space research service (active) systems that ensure compatible
operations in the band 9 300-9 500 MHz". This document provides element
dealing with on part of this resolves 2 of resolution 747: the
radiolocation and radionavigation protection criteria determination that
ensure compatible operations in the band 9300-9500 MHz. There are two
cases to be study:

-the radionavigation protection criteria against radiolocation and vice
versa

-the radionavigation and radiolocation protection criteria against EESS

For the two above cases, the interfering signals are pulse signals. A
formula for the computation of I in case of pulse like interference
signal is provided in recommendation UIT-R M 1461. This computation is
based on the On Tune Rejection (OTR) equation. This document proposes
some elements about the current OTR equation in the recommendation which
seems to be incorrect and therefore need be modified.

**2-Analysis of current recommendations (ITU-R M 1461) and ITU-R WP 8B
contributions (8B/220 and 221) regarding the OTR equation**

Recommendation ITU-R M 1461 provides guidance for determining the
potential for interference between radars operating in the
radiodetermination service and systems in other services. This
recommendation bases the I/N determination on the following equations:

$$\left( \frac{I}{N} \right)_{\text{IF}} = \left( \frac{I}{N} \right)_{\text{RF}} - \text{FDR}_{\text{IF}}$$

If the OFR is equal to 0 dB then the above equation can be written as
follow:

$$\left( \frac{I}{N} \right)_{\text{IF}} = \left( \frac{I}{N} \right)_{\text{RF}} - \text{OTR}$$

For CW and phase-coded pulsed signals, the OTR factor is given in
recommendation ITU-R M 1461 and document 8B/221 by:

*OTR* 0 for *BR* *BT*

*OTR* 20 log (*BT* / *BR*) for *BR* *BT*

where:

*BR* : receiver 3 dB bandwidth (Hz)

*BT* : transmitter 3 dB bandwidth (Hz).

For chirped pulsed signals, the OTR factor is given in recommendation
ITU-R M 1461 and 8B/221 by :

*OTR* 0 for *BC* / (*BR*2 *T*) 1

*OTR* 10 log (*BC* / (*BR*2 *T*)) for *BC* / (*BR*2 *T*) 1

where:

*T* : chirped pulse width (s)

*BC* : transmitter chirped bandwidth during the pulsewidth, *T*, (Hz).

However Recommendation UIT-R M 1461 states that those equations are
based on Recommendation ITU-R SM 337-4 which gives a more generic
equation for the OTR as follows:

$$\text{OTR}\  = \ \text{10}\ \text{log}\ \frac{\int_{0}^{\infty}{P(f)df}}{\int_{0}^{\infty}{P(f)\left| H(f) \right|^{2}\text{  d}f}}$$

where:

*P*( *f* ) : power spectral density of the interfering signal equivalent
intermediate frequency (IF)

*H*( *f* ) : frequency response of the receiver

The OTR is therefore the ratio between the

As mentioned in recommendation SM 337-4 this OTR can be simplified when
the following simplification on P(f) and H(f) are made:

$P(f) = \frac{P}{\text{Bt}}$ when f is in the transmitter 3dB bandwidth
Bt

$P(f) = 0$ Elsewhere

Where P is the Power of the interfering signal

H(f) = 1 when f is in the receiver 3dB bandwidth Br

H(f) = 0 Elsewhere

When Br\<Bt, the OTR equation can be written as follow:

$$\text{OTR}\  = \ \text{10}\ \text{log}\ \left( \ \frac{\int_{\text{Fc} - \frac{\text{Bt}}{2}}^{\text{Fc} + \frac{\text{Bt}}{2}}{\frac{P}{\text{Bt}}\text{df}}}{\int_{\text{Fc} - \frac{\text{Br}}{2}}^{\text{Fc} + \frac{\text{Br}}{2}}{\frac{P}{\text{Bt}}df}} \right) = \text{10}\text{log}\left( \frac{\frac{P}{\text{Bt}}\text{Bt}}{\frac{P}{\text{Bt}}Br} \right) = \text{10}\text{log}\left( \frac{\text{Bt}}{\text{Br}} \right)$$

For Br\>Bt the equation becomes:

$$\text{OTR}\  = \ \text{10}\ \text{log}\ \left( \ \frac{\int_{\text{Fc} - \frac{\text{Bt}}{2}}^{\text{Fc} + \frac{\text{Bt}}{2}}{\frac{P}{\text{Bt}}\text{df}}}{\int_{\text{Fc} - \frac{\text{Bt}}{2}}^{\text{Fc} + \frac{\text{Bt}}{2}}{\frac{P}{\text{Bt}}df}} \right) = \text{10}\text{log}\left( \frac{\frac{P}{\text{Bt}}\text{Bt}}{\frac{P}{\text{Bt}}\text{Bt}} \right) = \text{10}\text{log}(1) = 0\text{dB}$$

This result is still valid for CW Pulsed and phase-coded signals
therefore the OTR in recommendation ITU-R M 1461 and in the contribution
8B/221 should be for CW pulsed and phase coded signals 10 log (Bt/Br)
and not 20 log(Bt/Br) when Br\<Bt.

For linear chirped pulsed signals the above simplifications should be:

$P(f) = \frac{P}{\text{Bc}}$ when f is in the transmitter 3dB bandwidth
Bt

$P(f) = 0$ Elsewhere

Where P is the Power of the interfering signal

H(f) = 1 when f is in the receiver 3dB bandwidth Br

H(f) = 0 Elsewhere

When Br\<Bc, the OTR equation can be written as follow:

$$\text{OTR}\  = \ \text{10}\ \text{log}\ \left( \ \frac{\int_{\text{Fc} - \frac{\text{Bc}}{2}}^{\text{Fc} + \frac{\text{Bc}}{2}}{\frac{P}{\text{Bt}}\text{df}}}{\int_{\text{Fc} - \frac{\text{Br}}{2}}^{\text{Fc} + \frac{\text{Br}}{2}}{\frac{P}{\text{Bt}}df}} \right) = \text{10}\text{log}\left( \frac{\frac{P}{\text{Bt}}\text{Bc}}{\frac{P}{\text{Bt}}\text{Br}} \right) = \text{10}\text{log}\left( \frac{\text{Bc}}{\text{Br}} \right)$$

For Br\>Bc the equation becomes:

$$\text{OTR}\  = \ \text{10}\ \text{log}\ \left( \ \frac{\int_{\text{Fc} - \frac{\text{Bc}}{2}}^{\text{Fc} + \frac{\text{Bc}}{2}}{\frac{P}{\text{Bt}}\text{df}}}{\int_{\text{Fc} - \frac{\text{Bc}}{2}}^{\text{Fc} + \frac{\text{Bc}}{2}}{\frac{P}{\text{Bt}}df}} \right) = \text{10}\text{log}\left( \frac{\frac{P}{\text{Bt}}\text{Bc}}{\frac{P}{\text{Bt}}\text{Bc}} \right) = \text{10}\text{log}(1) = 0\text{dB}$$

Therefore, the OTR in recommendation ITU-R M 1461 and in the
contribution 8B/221 should be for linear chirped pulsed signals 10 log
(Bc/Br) and not 10 log(Bc/(Br^2^T)) when Bc\<Bt.

This is in accordance with the measurements results presented in
document 8B/220 as shown in the following table which provides the
measurement results compare to the one obtain by the recommendation
formula and the one obtain by the formula propose in this paper.

+--------+-------+----------+-------+-------+-------+-------+-------+
| Wa     | T     | Pulse    | Ch    | Rec   | Pe    | 1/OTR | 1/OTR |
| veform | ransm | width    | irped | eiver | rcent | obt   | from  |
|        | itted | (µs) at  | band  | band  | diffe | ained | M     |
|        | Pulse | de       | width | width | rence | with  | .1461 |
|        | width | tector/p |       |       | (8B   | the   |       |
|        | « T » | rocessor | Bc    | Br    | /220) | pro   | (     |
|        |       |          | (MHz) | (MHz) |       | posed | Br^2^ |
|        | (in   | Output   |       |       | (X    | f     | \* T  |
|        | µs)   | receiver |       |       | perce | ormal | /Bc)  |
|        |       |          |       |       | ntage |       |       |
|        |       |          |       |       | of    | (B    | (l    |
|        |       |          |       |       | the   | r/Bc) | inear |
|        |       |          |       |       | t     |       | in %) |
|        |       |          |       |       | ransm | (l    |       |
|        |       |          |       |       | itted | inear |       |
|        |       |          |       |       | pulse | in %) |       |
|        |       |          |       |       | v     |       |       |
|        |       |          |       |       | iewed |       |       |
|        |       |          |       |       | by    |       |       |
|        |       |          |       |       | the   |       |       |
|        |       |          |       |       | rece  |       |       |
|        |       |          |       |       | iver) |       |       |
+--------+-------+----------+-------+-------+-------+-------+-------+
| Ra     | 10    | 5.1      | 10    | 5     | 51    | 50    | 2500  |
| dioloc |       |          |       |       |       |       |       |
| ation1 |       |          |       |       |       |       |       |
+--------+-------+----------+-------+-------+-------+-------+-------+
| Ra     | 10    | 1.0      | 50    | 5     | 10    | 10    | 500   |
| dioloc |       |          |       |       |       |       |       |
| ation2 |       |          |       |       |       |       |       |
+--------+-------+----------+-------+-------+-------+-------+-------+
| Ra     | 1.65  | 0.20     | 80    | 5     | 12    | 6.25  | 51.56 |
| dioloc |       |          |       |       |       |       |       |
| ation3 |       |          |       |       |       |       |       |
+--------+-------+----------+-------+-------+-------+-------+-------+
| EESS 1 | 2     | 0.20     | 80    | 5     | 10    | 6.25  | 62.5  |
+--------+-------+----------+-------+-------+-------+-------+-------+
| EESS 2 | 16    | 1.0      | 80    | 5     | 6.3   | 6.25  | 500   |
+--------+-------+----------+-------+-------+-------+-------+-------+
| EESS 3 | 17.7  | 1.2      | 80    | 5     | 6.8   | 6.25  | 5     |
|        |       |          |       |       |       |       | 53.12 |
+--------+-------+----------+-------+-------+-------+-------+-------+
| EESS 4 | 1.7   | 0.20     | 80    | 5     | 11.8  | 6.25  | 53.12 |
+--------+-------+----------+-------+-------+-------+-------+-------+

**3- Applicability of the recommendation ITU-R SM 337-4 OTR definition
to the radars receivers**

In the time domain the input of the filter is s(t) and the output is
s(t)\*h(t) that we will call y(t)

The OTR equation can be written in the time domain as follows using the
Parseval theorem.

$$\text{OTR}\  = \ \text{10}\ \text{log}\ \frac{\int_{0}^{\infty}{P(f)df}}{\int_{0}^{\infty}{P(f)\left| H(f) \right|^{2}\text{  d}f}} = \text{10}\ \text{log}\ \frac{\int_{0}^{\infty}{\left| s(t) \right|^{2}dt}}{\int_{0}^{\infty}{\left| y(t) \right|^{2}dt}}$$

The principle of the radar video integrator is that radar signal returns
from a point target consist of a series of pulses, which corresponds to
the DWELL time, generated as the radar antenna beam scans past the
target, all of which fall in the same range bin in successive periods
(synchronous with the radar's transmitted pulses). It is this series of
synchronous pulses from a target which permits integration of target
returns to enhance the weak signals. The integrator also suppresses
asynchronous pulsed interference (pulses that are asynchronous with the
radar's transmitted pulses) since the interfering pulses will not be
separated in time by the radar period, and thus will not occur in the
same range bin in successive periods. This implies that the radar will
integrate the received signal only during the range gate periods of time
and therefore not all the time as in the time domain OTR equation.

The following figure presents the above mechanism.

For one particular range bin the radar will received the wanted
interfering signal as during particular times. Therefore the interfering
signal for a range bin number M (I~M~(t)) can be determined by the
following equation:

$$I_{M} = \int_{\text{Dwell}\text{.}\text{time}}^{}{I(t)\text{.}\text{RG}_{M}(t)\text{dt}}$$

where

I(t) is the interfering signal after the receiver filter

RG~M~(t) equal to 1 for particular times duration corresponding to range
bin number M and equal to 0 elsewhere.

The following figure provides an example of the relation between RG(t),
I(t) and I(t)xRG(t).

It should be noted that I(t) corresponds here to the interference at
processor/detector and therefore after the filter.

Therefore the OTR equation for a particular range gate should be in the
time domain:

$$\text{OTR}\  = \ \text{10}\ \text{log}\ \frac{\int_{\text{to}}^{t1}{\left| s(t) \right|^{2}dt} + \int_{t1}^{t2}{\left| s(t) \right|^{2}dt} + \text{.}\text{.}\int_{t_{N - 1}}^{t_{N}}{\left| s(t) \right|^{2}dt}}{\int_{\text{to}}^{t1}{\left| y(t) \right|^{2}dt} + \int_{t1}^{t2}{\left| y(t) \right|^{2}dt} + \text{.}\text{.}\int_{t_{N - 1}}^{t_{N}}{\left| y(t) \right|^{2}dt}} = \text{10}\ \text{log}\ \frac{\sum_{}^{}\left( \int_{t_{N - 1}}^{t_{N}}{\left| s(t) \right|^{2}dt} \right)}{\sum_{}^{}\left( \int_{t_{N - 1}}^{t_{N}}{\left| y(t) \right|^{2}dt} \right)}$$

**Conclusions**

In this case it can be seen that the OTR is not constant and depends on
the translation of I(t) compare to RG(t). This brings the difficulty to
provide an equation for the OTR which provides a unique value. The OTR
can vary from - to a value that should be determined by further study.

It is therefore proposed to study the variation of the OTR and therefore
to have its statistical characteristics in function of the interfering
pulses width, duty cycle ....