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

# 1) Introduction

1 There have been several papers presented to the JRG comparing the
Current ITU formula for the allowed bandwidths of various types of radar
pulses and those achieved from theoretical trapezoidal and rectangular
pulse shapes. The aim of these papers being to provide data to
contribute to the discussion on the adoption, or not, of the current ITU
design aim of --40 dB/dec. Some papers have also discussed the issue of
the accuracy of the current ITU formulas for the --40 dB bandwidth.

2 In many cases these results indicate that particularly for pulsed FM
waveforms the ITU formula over estimates the --40 dB bandwidth and by
implication the --60 dB bandwidth when compared to the theoretical
spectrum calculated from either analytical solutions of from modelling
based of Fourier transform techniques.

3 The accuracy of the ITU formula depends on the exact combination of
the pulse parameters varying from \> 100% to ≈ 50% however for
"practical" pulses the theoretical result tends to be 70 to 90% of the
ITU limit.

4 The work also confirmed that the theoretical natural roll-off of a
rectangular pulse is --20dB/dedc and that of a trapezoidal pulse is
initially --20 dB/dec increasing to --40 dB/dec at a point related to
the rise time.

# 

# 2) Discussion on Results

5 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.

6.  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, t~r~ & B*** are based on a
    theoretical Trapezoidal or Rectangular shaped pulses with linear
    frequency shift (non-linear FM is not considered).

7.  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, t~r~ & 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.

8.  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.

# Practical Implementation Issues

9 Other papers presented on practical measurements, particularly
pertaining for systems using un-modulated pulses (Magnetrons) indicate
that the ITU limits are too tight. In these systems it is well known
that for short pulses the pulse shape deviates significantly from
rectangular and the ITU parameters of ***t & t~r~*** are in some cases
meaningless, especially in the case where it is difficult to see a flat
top to the pulse. Such systems also have other sources of distortion
that cause the widening of the --40 dB bandwidth. Other practical
results for pulse compression type systems indicate that on some
measured systems the ITU limits are generous.

10 However other combinations of waveforms and hardware can be provided
to show that the design aim roll-off is difficult to achieve. This would
be particularly the case if the ITU --40 dB bandwidth formulas were
revised to narrow the allowed --40 dB bandwidth. In some results seen it
is the presence of the wider --40 dB bandwidth that allows the system to
meet the mask.

11 Whilst it may be possible with modern digital signal generation
techniques to generate pulses very close to the theoretical trapezoid,
and possibly pulses tailored further to achieve even better spectra.
These waveforms inevitably become distorted when amplified up to the
final power.

12 The problem is that these distortions are very difficult to model and
hence to predict the resultant Radar spectrum.

13 Current indications are that modern driven transmitters using pulsed
FM waveforms can approach or achieve a performance approaching the
current ITU design aim however some filtering of the output is generally
needed. Compliance however with the design aim mask may be compromised
if as well as adopting the design aim for the OOB roll-off of --40
dB/dec the allowed --40 dB bandwidth is reduced simultaneously as is
being proposed in some papers.

14 Systems that require frequency agility cannot make use of such
"channel limiting filters" and these may well have difficulty with the
design aim. The problem is particularly acute in active phased array
systems where the ability to filter the output is limited by the
available unloaded Q of the output circuit.

# 4) Further Work

15 It would seem that the theoretical spectra of waveforms are now much
better understood and the work of the JRG should move into the practical
domain.

16 Further work is required to assess what can be practically achieved
from current state- of-the-art techniques, it is considered impractical
to require the development of any new and unproven technologies, such a
better amplifying devices for driven systems or
super-low-loss-fast-tuning-high-power filters, in the time frame
required for the adoption, or not, of the design objective (2007).

17 However any changes to the OOB roll-off should reflect what can be
achieved from current "best practice" and not be just based on what was
achieved historically where the need for spectrum control may have not
been paramount.

18 Members should be encouraged to provide as much practical data as
possible over the next work period to support the JRG deliberations, and
to allow the relationship between the theoretical work done so far to
the practical results to be assessed more rigorously. Further
theoretical work in modelling the distortions produced by radar
transmitters would also be of benefit.

3.  **Conclusions**

4.  

19 The current work on theoretical waveform spectra needs to be
supported by more practical studies on how close the theoretical
waveforms can be approached. The --40 dB/dec does represent the
[theoretical maximum roll-off]{.underline} for the types of modulation
studied and achieving it without the use of external filtering,
particularly if the --40d B bandwidth is reduced, may present a serious
problem for frequency agile systems.

20 It may be worth considering using a revised formula that more
accurately represents the true shape of the pulse (in both amplitude and
phase), however the time scale for such an exercise is probably outside
the current time limit of 2007.

***Produced as an input to the ITU Radar JRC meeting 13^th^-15^th^ July
2004***

***John Holloway t, t~r~ & B***

***Systems Engineering dept***

***AMS Radar Systems***

***Newport Road***

***Cowes***

***IoW***

## Friday, 09 July 2004