# JRG-58

January 15, 2006

# JRG 1A-1C-8B -- Radar Out-of-Band Emissions

# Drafting Group 1 -- FMCW Modulated Waveforms

# Report to 17-19 January 2006 meeting in Boulder, Colorado, USA

## Introduction

At its' May 2005 meeting the JRG 1A-1C-8B resolved that a drafting group
be formed to review the out-of-band emission limits given in ITU-R
SM.1541 for primary radars using FMCW waveforms. This drafting group is
to operate entirely via email correspondence and report back to the next
JRG 1A‑1C‑8B meeting with recommended changes to ITU-R SM.1541 (if any).
The first task undertaken by the group was to formulate a working
program based around the terms-of-reference provided to the group in
JRG-46 Rev 1 (repeated below). This working program is given in
JRG-DG1-1 Rev 1 and shows the current membership of the group. This
report to the January 2006 meeting of JRG 1A-1C-8B should be read in
conjunction with the drafting group work program.

## Terms-of-Reference

1.  Review the current necessary bandwidth (-20 dB) and --40 dB
    bandwidth formulas for FMCW modulated waveforms; and, if
    appropriate, recommend more representative formulas. Priority 1.

2.  Clarify the definition of frequency deviation (Bd) for FMCW
    waveforms. Priority 1.

3.  Review the feasibility of the application of a 40 dB/decade roll-off
    from the --40 dB bandwidth for practical combinations of waveform
    parameters. Priority 2.

Priority 1 Milestone: December 15, 2005

Priority 2 Milestone: June 15, 2006

Relevant JRG Contributions: JRG-7, page 158, and JRG-39

## Work Program

1.  Resolve definition of necessary bandwidth to be adopted.

> Progress:
>
> There has been no formal discussion of this issue within the group,
> however contribution JRG-XX to the Boulder meeting of JRG 1A-1C-8B by
> Leith Mudge suggests that the 20 dB bandwidth as measured from the
> theoretical FMCW spectrum be adopted as the practical working
> definition of necessary bandwidth. This is opposed to the current
> definition given in ITU-R SM.1541, which is "...twice *Bd*, the
> maximum frequency deviation:$B_{N}\  = \ 2\ B_{d}$".
>
> **Complete subject to acceptance by Boulder JRG meeting**

2.  Clarify the definition of frequency deviation (*B~d~*) for FMCW
    waveforms.

> Progress:
>
> Research has shown that the NTIA RSEC definition of *B~d~* is
> unambiguously the frequency deviation from the centre frequency. As
> the current definitions of *B~N~* and *B~-40~* for FMCW waveforms in
> ITU-R SM.1541 are derived from the NTIA RSEC, this definition applies.
>
> **Complete**

3.  Establish a suitable parameterised model for the bounds of the
    emission spectrum of a linear FMCW waveform.

> Progress:
>
> Contribution JRG-50 to the Boulder meeting of JRG 1A-1C-8B by Andy
> Stove contain details of a potential parametric model for the spectral
> enveloped of FMCW waveforms. Leith Mudge is continuing work on
> assessing the applicability of the "Newhouse method" to calculate the
> spectral envelope.
>
> **Incomplete in progress**

4.  Through simulations and/or measurements establish the ability of the
    parameterised model established in step above to correctly model the
    emission spectrum of linear FMCW waveforms.

> Progress:
>
> A Matlab program has been written by Leith Mudge that numerically
> solves the analytical equations derived by performing a Fourier
> Transform of an equation representing the time domain linear FMCW
> waveform. This plots the spectrum of an FMCW waveform and is also
> capable of precisely calculating the values of *B~-20~* (the necessary
> bandwidth if this definition is accepted by the JRG) and *B~-40~*.
> This is capable of being used to compare either of the parameterised
> models proposed in step 3 above with the theoretical spectral
> envelope. Measurements have not been attempted at this stage
>
> **Incomplete in progress**

5.  Use the parameterised model established in steps 3 and above to
    derive more representative formulas for *B~N~* and *B~-40~*.

> Progress:
>
> The potential parametric model proposed in JRG-50 has not been used
> yet to derive values for *B~N~* (*B~-20~* ) and *B~-40~.* Leith Mudge
> has derived potential formulae for *B~-20\ ~*and *B~-40~* using the
> "Newhouse method" but these results are yet to be presented to the
> group.
>
> **Incomplete in progress**

6.  Review the feasibility of the application of a 40 dB/decade roll-off
    from *B~-40~* (derived from the new formula) for practical
    combinations of waveform parameters.

> Progress:
>
> This step has not been started.
>
> **Incomplete not started**