Title: Further Considerations of Radar Spurious Emission Masks

Written by: John Holloway

Dated: Friday, 13 May 2005

# Summary

This paper is an input to JRG meeting to be held in Southampton May 2005

This paper reprises four previous papers presented to the Radar JRG and
the previous RCG.

It also presents further thoughts into the applicability of the proposed
design objective for the spectrum roll-off in the OOB domain.

# Introduction

This paper revisits four previous papers presented to the JRG and the
previous RCG. It reappraises the conclusions drawn in the light of the
latest information and thinking.

-   RCG-17: Preliminary Parametric Study of the Bandwidth Requirements
    for FM modulated Pulse Radar Waveforms.

-   JRG 13 Spectrum of chirped radar pulses using non-linear FM

-   JRG 12 Comparison of Methods Used to Predict the Bandwidth of Radar
    Emissions

-   JRG 21 Consideration of the results presented on the relationship
    between current ITU limits on bandwidth and spectrum shape, to the
    theoretical and practical radar emission spectra of Trapezoidal or
    Rectangular type pulses

All the papers are available from the JRG website or by application
direct to the author.

# Preliminary Parametric Study of the Bandwidth Requirements for FM modulated Pulse Radar Waveforms. (RCG 17)

This paper addresses the bandwidth requirements associated with FM
modulated trapezoidal waveforms. It initially dressed the issue of the
Necessary Bandwidth (*Bw~-20dB~*) in particular the ITU equation for the
*Bw~-20dB~*

$$B_{N} \approx \text{Bw}(\text{20})\  = \ \frac{1\text{.}\text{79}}{\sqrt{t\  \cdot \ t_{r}}}\  + \ 2\ B_{c}$$

Which over estimates the bandwidth.

In particular when the time x bandwidth product is large when in
practice *B~w~ (20) → B~c~.*

At the time of writing consideration was being given to using the B~N~
as the fundamental bandwidth for UE specification as opposed to the
*B~w~(40)*

It discussed an empirical formula for the *B~w~(20)* which gave a better
result.

This work has been superseded by the work reported in JRG 12
"Preliminary Parametric Study of the Bandwidth Requirements for FM
modulated Pulse Radar Waveforms". In this the work of "Newhouse" was
discussed this gives a much better approximation to the B~w~(20)
envelope.

The paper concludes:

-   The properties of the pulses are such that even when an accurate
    assessment of the *B~w~(40)* is sued then the current 20 dB/dec
    roll-off is relatively easily achieved.

-   The proposed 40 dB/dec is difficult to achieve just from the natural
    spectrum of the waveform, particularly for some combinations and
    especially when the effects of practical distortions are considered.
    It is known that these can have a great effect at the -60dB
    level[^1].

-   "If the current ITU formula for Bw(-40) is maintained then the
    40dB/dec is achievable in all cases considered." Later work has shed
    some doubt on this conclusion.

-   It must be remembered however that these conclusions are based on
    theoretical waveforms some allowance for practical implementation
    will be required.

# Spectrum of chirped radar pulses using non-linear FM (JRG 13)

The results of this theoretical initial investigation show that:

-   In the majority of cases the theoretical --40 dB bandwidths
    calculated are less than those allowed in the ITU specification for
    a equivalent B factor,

-   Theoretical spectrums also meet the requirements of the --40 dB/dec
    roll-off design objective given in ITU-R 1541 Reference 3.

-   Non-linear FM using typical weighting gives narrower bandwidths than
    the linear case in all the cases tested[^2].

In this initial paper only one chirp has been considered further work is
necessary to confirm the findings above on other practical radar
waveforms.

The ITU formula is based on the pulse length, rise-time and chirp and
assumes linear FM. As non-linear FM gives a reduced bandwidth then there
is a possible argument that this needs to be taken into account in the
formula. The problem with adding a factor for the FM modulation is how
one can specify the shape of the chirp curve in a relatively simple
manner. A possible way may be just to use a multiplying parameter\< 1
based on a "typical" non-linear waveform. This parameter my have to be
dependent on pulse length and rise time. Further study would be needed
to develop such a parameter.

# Comparison of Methods Used to Predict the Bandwidth of Radar Emissions (JRG 14)

Paper "Preliminary Parametric Study of the Bandwidth Requirements for FM
modulated Pulse Radar Waveforms" compared the ITU calculation method
with results achieved from Fourier analysis. This paper compares the
method proposed by Newhouse and concludes it provides a good estimate of
the spectrum envelope.

# Consideration of the results presented on the relationship between current ITU limits on bandwidth and spectrum shape, to the theoretical and practical radar emission spectra of Trapezoidal or Rectangular type pulses (JRG 21)

The paper concludes:

-   On the face of it would seem that the ITU bandwidths are too
    generous and that there is scope to increase the roll-off towards
    the theoretical limit of --40 dB/dec of pulses in particular those
    using FM modulation.

-   What must be remembered in this debate is that the waveforms
    considered are theoretical and that the calculated spectrums based
    on the ITU defined parameters of t, tr & B are based on a
    theoretical Trapezoidal or Rectangular shaped pulses with linear
    frequency shift (non-linear FM is not considered).

-   The theoretical analysis takes no account of practical
    implementation issues associated with these types of pulses. Radar
    pulses are never truly Trapezoidal or Rectangular. The parameters t,
    tr & B used to define the pulse shape are only a very limited set
    and these do not fully represent the pulse shape. For example, the
    rising and falling edges of a pulse are very rarely truly linear as
    this requires an infinite rate of change between the edge and the
    top of the pulse, natural band-limiting will result in a smoothing
    of the pulse which may in turn result in some further limiting of
    the spectrum.

As well as not truly representing the pulse the there are other affects
that are not represented at all in ITU formula effects related to AM to
PM conversion and other sources of noise from amplifying devices are not
covered in the theoretical analysis submitted to date.

# Conclusions to Date

These conclusions are based on frequency agile radars or active phased
array radars in both of these cases it is not possible to use a channel
filter to improve the roll-off of the transmitted spectrum. It may be
possible to improve the roll-off at the edge of the agile band by using
a band-limiting filter (strictly speaking the OOB limits only apply to
radars operating in shared bands or at the band edge). It is most likely
however that all radar bands will be shared as time progresses so the
OOB limits are likely to be applied more and more radars.

Thus for the waveforms under consideration pulse shaping is the only
option to control the spectrum.

## Linear FM

To date the following conclusions can be drawn theoretical trapezoidal
pulses do have the fundamental ability to meet the the requirements of a
40 dB/dec roll-off however when the B~w~(40) is based on the ITU
equations, problems occur when the ITU bandwidth \< 1/πt~r~. The
equation tends to over estimate the B~w~(40) in particular when the high
power version is used and this compensates for the fact that the maximum
theoretical roll-off is 40 dB/dec which is difficult to achieve in
practice.

If an accurate determination of the B~w~(40) is made then the 40 dB/dec
from this bandwidth would be difficult to meet for this class of radar,

There are two issues however that have to be considered.

-   Transmitters do not tens to produce purely trapezoidal pulses, as
    they do not have sharp corners. This tends to reduce the extent of
    the spectrum.

-   Transmitters have other sources of error particularly AM to PM
    effects that tend to spread the spectrum particularly at the lower
    levels.

## Non Linear FM

The following comments can be made on Non-linear

-   Non-linear FM has a narrower B~N~ if the ITU equation is used gives
    a better margin when the 40 dB/dec is used.

-   If an accurate determination of the B~W~(40) is made then Non-linear
    FM would find it difficult to meet the 40 dB/dec design aim.

-   It may be difficult to generate a simple equation to estimate the
    B~w~(40) given the number of variables involved.

More practical results are needed to under write these conclusions BAE
Systems will hope to have some measured results later this year.

**Annex 1 Further Thoughts on the proposed OOB design aim**

## Linear FM

In the revision of ITU document 1541 annex 8 a design aim was set which
increases the roll-off in the OOB region from 20dB/dec to 40 dB/dec.
Several doubts have been raised at the applicability of such a roll-off
to practical systems this work indicates that for certain classes of
waveform the roll-off cannot be achieved in theory.

Consider the Figure below.

**Envelope of Trapezoidal Pulse.**

![](media/image1.wmf)

The 40 dB/dec roll-off region starts of at ***1/(t~r~π)*** in an FM
modulated waveform the ***1/(t~r~π)*** point still controls the start of
the 40 dB/dec roll off point all that happens is that the 20dB point →
Bc → 40 dB point

***50 μs Pulse 50ns rise-time varying chirp***

![](media/image2.png){width="2.5034722222222223in"
height="2.2270833333333333in"}![](media/image3.png){width="2.626388888888889in"
height="2.3361111111111112in"}

1 MHz 2MHz

![](media/image4.png){width="2.626388888888889in"
height="2.3361111111111112in"}![](media/image5.png){width="2.3715277777777777in"
height="2.109722222222222in"}

3 MHz 4MHz

![](media/image6.png){width="2.5034722222222223in"
height="2.2270833333333333in"}![](media/image7.png){width="2.626388888888889in"
height="2.3361111111111112in"}

5 MHz 10 MHz

The 40 dB roll off point is fixed as the chirp increases until the point
where the 20dB/dec roll-off region has disappeared and the 40 dB point
falls within main lobe of spectrum.

This effect then gives a potential issue with the design aim. This
occurs when the 40 dB beam width point calculated by the ITU formula is
\< ***1/(t~r~π)*** this occurs in the case below. In these curves the
Newhouse envelopes are used as they give a god approximations.

![](media/image8.png){width="2.625in" height="2.34375in"}

This shows that there is a potential issue with the 40 dB/dec roll off.

## Non-linear

Consider the spectrum below, this is a FM modulated pulse radar with 25
mS pulse and a rise time between 15 to 18 ns and a 2.5 MHz chirp.
Although this result is noise limited the following bandwidths have been
estimated from this measurement. These are compared with those
calculated using the ITU equations.

The measured B~w~ (20) is \< 50% that calculated, the B~w~ (40) \< 50%
calculated and the B~w~ (60) » 8 % of that calculated if the new design
aim was used then the result would be \< 50% of that calculated.

**Figure 1 Annex 1**

![](media/image10.wmf){width="5.802777777777778in"
height="3.857638888888889in"}

The measured B~w~ (20) is \< 50% that calculated, the B~w~ (40) \< 50%
calculated and the B~w~ (60) » 8 % of that calculated if the new design
aim was used then the result would be \< 50% of that calculated.

***Table 1 Annex 1***

![](media/image11.wmf){width="5.764583333333333in"
height="1.3055555555555556in"}

This spectrum well exceeds both the current requirements and the design
aim. This is a result of an over estimation of the 20 and 40 dB
bandwidths giving rise to a very generous 60 dB requirement. If a more
accurate calculation of the B~w~(40) could be achieved say for example
10 MHz then the B~w~(60) at » 35 MHz would exceed the 3.2 ratio required
by the design aim.

[^1]: · Section 3 of this paper discusses some further concerns about
    the 40 dB/dec roll-off

[^2]: These two pulses may not be equivalent in operational radar terms,