RCG - 12 August 13, 2002

Comments on Reference and Measurement Bandwidths and Application of SE
and OOB Limits & Masks for Radiodetermination Systems.

Input to RCG Meeting 20^th^ to 23^rd^ August, Bolder USA

John Holloway:

AMS Cowes

Monday, 12 August 2002

# 1) Introduction

This paper comments on the requirements of reference and measurement
bandwidths associated with the measurement of radar Out of Band (OOB) &
Spurious Emissions. It also comments of how current limits should be
applied and the appropriate step size to be used.

This paper represents a view from AMS a major UK radar manufacturer.

# 2) Spurious Emissions Definitions

The reference bandwidths for Spurious Emissions are defined in Appendix
3 of the radio regulations as follows:

*- for fixed-frequency, non-pulse-coded radar, one divided by the radar
pulse length, in seconds (e.g. if the radar pulse length is 1 μs, then
the reference bandwidth is 1/1 μs = 1 MHz);*

*-- for fixed-frequency, phase coded pulsed radar, one divided by the
phase chip length, in seconds (e.g. if the phase coded chip is 2 μs
long, then the reference bandwidth is 1/2 μs = 500 kHz);*

-   *for frequency modulated (FM) or chirped radar, the square root of
    the quantity obtained by dividing the radar bandwidth in MHz by the
    pulse length, in seconds (e.g. if the FM is from 1 250 MHz to
    1 280 MHz or 30 MHz during the pulse of 10 μs, then the reference
    band­width is (30 MHz/10 μs)1/2 = 1.73 MHz).*

The levels of spurious emissions are defined as PEP where:

-   *When the term P is used, both the power supplied to the antenna
    transmission line and spurious emissions should be evaluated in
    terms of mean power and mean power in the reference bandwidth
    respectively. When the term PEP is used, both the power supplied to
    the antenna transmission line and spurious emissions should be
    evaluated in terms of peak envelope power and peak envelope power in
    the reference bandwidth respectively. However, when measurement of
    spurious emission in terms of PEP is difficult due to the nature of
    spurious emission (e.g. Gaussian noise), it is allowed to evaluate
    both power supplied to the antenna transmission line and spurious
    emission power in terms of mean power (see Annex 2).*

> **\"1.157** *peak envelope power* (of a radio transmitter)*:  *The
> average power supplied to the antenna transmission line by a
> transmitter during one radio frequency cycle at the crest of the
> modulation envelope taken under normal operating conditions.\"

# 3) Applications of Spurious Emission Limits to Un-modulated Pulses

## 3.1 Reference Bandwidth 

The reference bandwidth specified in must be consistent with the units
PEP is a time related measurement parameter and in principle requires a
infinite bandwidth. In practice however the bandwidth needs to be wide
enough to capture a majority of power in the spectrum. A bandwidth of
2/T captures all the energy in the main-lobe of the spectrum leaving
only the side-lobe power. 1/T however has been shown to be a suitable
approximation. Thus for the un-modulated pulse and the chipped
sub-pulses the reference bandwidth specified in appendix S3 is
consistent with units of PEP.

### 3.1.1 Reccomendation

**It is thus not necessary to propose any changes to the definition of
reference bandwidth for spurious emissions given in appendix 3.**

## 3.2 Measurement Bandwidths

The current proposals are for a measurement bandwidth of 0.5/T this
would result in a loss of:

$$L = \text{20}\text{log}\left( \frac{\text{Bs}}{\text{Br}} \right) = \text{20}\text{log}\left( \frac{\frac{1}{T}}{\frac{0\text{.}5}{T}} \right) = \text{20}\text{log}(2) \approx 6\text{dB}$$

However the Br should be the impulse bandwidth of the receiver typically
this is 1.5 times the quoted receiver bandwidth this would result in a
loss of :

$$L = \text{20}\text{log}\left( \frac{\text{Bs}}{\text{Br}} \right) = \text{20}\text{log}\left( \frac{\frac{1}{T}}{\frac{1\text{.}5 \times 0\text{.}5}{T}} \right) = \text{20}\text{log}\left( 1\text{.}\text{33} \right) \approx 2\text{.}5\text{dB}$$

Whichever is the case if this measurement bandwidth were used then some
correction would need to be applied.

This is a slight deviation from some previous thinking. It was felt that
perhaps for convenience that the losses could be ignored down to
measurement bandwidths of \< 0.5/T and only below that would correction
need to be applied. Upon reflection it is now believed that correction
should always be applied when the measurement bandwidth is \< 1/T.

## 3.3 Recommendations

**It is proposed that the measurement bandwidth used should be 1/T where
possible, not 0.5/T as is currently being proposed. Measurements made
with bandwidths \< 1/T must have the appropriate correction factor
applied.**

# 4) Applications of Spurious Emission Limits to Chirped Pulses

## 4.1 Reference bandwidth

Annex S3 recommends a reference bandwidth of \" *for frequency modulated
(FM) or chirped radar, the square root of the quantity obtained by
dividing the radar bandwidth in MHz by the pulse length, in seconds\"*
i.e.

$$\text{Br} = \sqrt{\frac{\text{Bc}}{T}}$$

This comes from the formula for desensitisation for chirped signals

$$\text{Loss} = \text{10}\text{log}\left( \frac{\text{Bc}}{\text{Br}^{2} \times T} \right)$$

If:

> $$\begin{array}{r}
> \text{Loss} = 0 \\
> \therefore \\
> \left( \frac{\text{Bc}}{\text{Br}^{2} \times T} \right) = 1 \\
> \therefore \\
> \text{Bc} = \text{Br}^{2} \times T \\
> \therefore \\
> \text{Br} = \sqrt{\frac{\text{Bc}}{T}}
> \end{array}$$

This however leads to a very narrow reference bandwidth

Take for example a 100μS pulse chirped at 1 MHz. This would have a
reference bandwidth of:

$$\sqrt{\frac{1}{\text{100}}} = \sqrt{0\text{.}\text{01}} = 0\text{.}1\text{MHz}$$

This results in a very narrow reference bandwidth, considering that in
these types of signals the energy is almost all contained within the
chirp bandwidth.

## 4.2 Measurement Bandwidth

The latest recommended measurement bandwidth is given for this type of
signal is:

$\text{Br} = 0\text{.}5 \times \sqrt{\frac{\text{Bc}}{T}}$ , for the
above signal this would result is a measurement bandwidth of 0.05 MHz.
Stepping this across the full band would result in very long measurement
times. Work has shown that a bandwidth equal to the chirp (1Mz) would
give adequate results for the measurement of PEP. This would be at a
reduction in the number of steps by a factor of 20 times.

Using the Br = Bc does however impose a restriction on the pulse lengths

Assume Bc=Br then if:

$$\begin{array}{r}
\frac{\text{Bc}}{\text{Br}^{2} \times T} = \frac{\text{Bc}}{\text{Bc}^{2} \times T} = \frac{1}{\text{Bc} \times T} \leq 1 \\
\text{Bc} = \frac{1}{\text{Tc}} \\
\therefore \\
\frac{\text{Tc}}{T} \leq 1 \\
\therefore \\
T \geq \text{Tc}
\end{array}$$

Thus T the uncompressed pulse length must always to greater than Tc the
compressed pulse length, this is **[always]{.underline}** the case for a
pulse compression radar.

## 4.3 Recommendations

**It is thus proposed in order to minimise the number of steps that the
initially the measurement bandwidth be made equal to the chirp. For
measurements made with narrower bandwidths then the down to**
$\text{Br} = \sqrt{\frac{\text{Bc}}{T}}$ **there will be no loss.**

**Below this the result will be desensitised by the above factor and a
correction will have to be made. In the limit the Br used will probably
be dependent on the dynamic range that can be achieved and the size of
the chirp being used.**

# 5) Out of Band Emission Limits Definition

The OOB mask is defined in terms of dB~pp~ the shape is based on
theoretical spectrum in terms of spectral power density

The spectral power density is expressed in dBm/kHz and hence implies a
reference bandwidth of 1 KHz. In ITU-R SM 1541 the shape of the spectrum
is expressed in relative terms in dBpp.

*\"Decibels relative to the maximum value of the peak power, measured
with the reference bandwidth within the occupied bandwidth. The in-band
peak power is expressed in the same reference bandwidth as the OOB peak
power. Both the in-band and the unwanted emissions should be evaluated
in terms of peak values. For radar systems, the reference bandwidth
should be selected according to Recommendation ITU-R M.1177.\"*

![](media/image1.wmf){width="3.160416666666667in"
height="3.0104166666666665in"}

The application of the OOB limits does not apply to radars operating
within wholly radio determination bands however it does apply at the
edges of the band.

ITU-R SM 1541 allows for the masks to be offset:

*\"Figure 25 shows the OoB mask for primary radars, specified in terms
of psd and expressed in units of dBpp. The mask rolls off at 20 dB per
decade from the 40 dB bandwidth to the spurious level specified in RR
Appendix 3*[^1]*. The B--40 dB bandwidth can be offset from the
frequency of maximum emission level, but the necessary bandwidth (RR
No. 1.152) and preferably, the overall occupied bandwidth (RR
No. 1.153), should be contained completely within the allocated band.\"*

This has resulted in much less attention being paid to the measurement
of OOB limit than to the SE levels. However there are some classes of
radar where the shape of the OOB mask is important and where its
accurate measurement is very important.

These radars, in particular, the solid-state pulse compression radars
produce output spectra, which approach the theoretical limit.

In modern frequency agile radars it is not possible to provide filtering
in some radar types long pulse solid state, for example the shape of the
spectrum is controlled in general from the signal generation. It is thus
proving possible to generate spectra close to the theoretical spectrum
shape used to develop the masks.

These spectra are symmetrical and little scope for off-setting masks is
to be had. Because of the agile nature the shape essentially is fixed
over the whole band and little band edge filtering is possible.
Filtering of the output can only be of the most rudimentary kind aimed
at reducing spurious emissions.

Whilst it could be argued that concentrating on the measurement of OOB
limits is premature. It is felt necessary that he measurement method is
agreed early to prevent future problems when the possibility of the
application of OOB limits throughout the band, triggered by band
sharing, has to be addressed. Also when the introduction of the new much
tighter \"design aim\" is to be applied.

In these type of radars it is essentially that any errors in measuring
the shape of the OOB spectra are minimised.

## 5.1 Reference bandwidth

The reference bandwidth is described in given in 1541 as follows:

*\"The bandwidth required for uniquely defining the out-of-band limits.
If not explicitly given with the OOB limit, the reference bandwidth
should be 1% of the necessary bandwidth. For radar systems the reference
bandwidth should be selected in line with Recommendation ITU-R
M.1177\".*

### 5.1.1 Non-Chirped signals

Recommendation ITU-R SM.853 provides guidance for determining the
necessary bandwidth (20 dB below the peak envelope value) for
rectangular and trapezoidal pulses. For these systems, the necessary
bandwidth *BN* is the smaller of:

$B_{N}\  = \ \frac{1\text{.}\text{79}}{\sqrt{T \times T_{r}}}\ \text{or}\ \frac{6\text{.}\text{36}}{T}$

where T is the pulse duration (at half amplitude) and T*~r~* is the rise
time, both in seconds[^2].

1% of this would be

$$B_{\text{ref}}\  = \ \frac{0\text{.}\text{0179}}{\sqrt{T \times T_{r}}}\ \text{or}\ \frac{0\text{.}\text{0636}}{T}$$

### 5.1.2 Chirped Signals

In such systems the necessary bandwidth is approximately the chirp
bandwidth this is particularly true for long time bandwidth product
pulses.

## 5.2 Measurement bandwidth OOB measurements

Because however the measurement is made in dBpp, and provided the shape
of the spectrum is not distorted by the measurement then the definition
of measurement bandwidth is not meaningful as the application of
desensitisation for these measurements is not applicable, in this case.
In ITU-R SM 1541 gives the following guidance:

*\"The bandwidth which is technically appropriate for the measurement of
a specific system. In common spectrum analysers this is generally
referred as the resolution bandwidth.*

*NOTE 1 -- The measurement bandwidth may differ from the reference
bandwidth, provided the results can be converted to the required
reference bandwidth.\"*

### 5.2.1 Non-chirped Signals

The theory suggests that to accurately resolve the full details of the
spectrum of an un-modulated pulse in the OOB region a measurement
bandwidth of \< 5% of the main-lobe with of 2/T, that is \<0.1/T is
required. However the requirement of the 1177 measurement is to
accurately resolve the envelope of the spectrum, not the full detail of
the spectrum.

Work has shown that 0.05/T fully resolves the peaks and nulls of the
spectrum. However 0.2/T still accurately resolves the envelope of the
spectrum if not the nulls.

### Chirped Signals

Work has suggested that in order to resolve the shape of a chirped
spectrum that a measurement bandwidth of 0.1 Bc provides adequate
results.

## Reccomendations

**It is thus recommended that for the measurement of the OOB spectrum
shape then the following bandwidths be used. 0.2/T for un-chirped
signals and 0.1Bc for chirped signals.**

# 6) Measurement Step Size

**It is recommended that the measurement step size is equal to 1/2 of
the measurement bandwidth. This prevents errors of up to 3 dB that can
occur if a step size equal to the measurement bandwidth is used.**

# 7) Application of limit masks

**The limit masks for SE measurements shall be offset by a factor
related to the receiver desensitisation loss calculated as described in
this paper.**

**The mask for the measurement of the OOB mask shall be referenced to
the peak of spectrum whatever the bandwidth is, providing that the
bandwidth is narrow enough not to disturb the shape of the spectrum.**

# 8) Other ITU-R M 1177 issues

**There are several other issues that need to be considered :**

## 8.1 Indirect method

**It is recommended that the indirect method be removed and not
recommended in ITU-R M 1177.**

## Composite pulses

**Guidance should be given in ITU-R M 1177 on how composite pulse
trained should be measured. The limits should be based on the worst case
pulse however due allowance for differing desensitisation needs to
considered.**

## 8.3 Scanning Antennas

**Guidance on the methods to be adopted for multi-function
electronically scanning antennas should be given.**

John Holloway

AMS Radar Systems Division

Engieering

Cowes

I.o.W

England

Tel ++44 (0) 1983 202577

Fax ++44 (0) 1983 202886

<John.r.holloway@amsjv.com>

Mobile 07801 716745

[^1]: ^6^ Appendix** **3 specifies a spurious attenuation of
    43 + 10 log* *(*PEP*), or 60 dB, whichever is less stringent. (PEP:
    peak envelope power).

[^2]: ^1^ The pulse duration is the time, (s) between the 50% amplitude
    (voltage) points. For coded pulses, the pulse duration is the
    interval between 50% amplitude points of one chip (sub‑pulse). The
    rise time is the time taken (s) for the leading edge of the pulse to
    increase from 10% to 90% of the maximum amplitude on the leading
    edge. For coded pulses, it is the rise time of a sub-pulse; if the
    sub-pulse rise time is not discernable assume that it is 40% of the
    time to switch from one phase or sub-pulse to the next. When the
    fall time of the radar is less than the rise time, it should be used
    in place of the rise time in these equations. Using the smaller of
    the two expressions in equation (35) avoids excessively large
    calculated necessary bandwidth when the rise time is very short.