Analysis of Concatenated Waveforms and Required
STC
Jian Wang*, Eli Brookner**, and Mark Gerecke*
* Raytheon Canada Limited
400 Phillip Street, N2L 6R7, Waterloo, Canada
phone: + (1) 519-885-0110 ext. 768, fax: + (1) 519-885-8672, email: Jian_Wang@raytheon.com
** Raytheon Company
528 Boston Post Rd., MA 01776, Sudbury, USA
phone: + (1) 978-440-4007, email: Eli_Brookner@raytheon.com
Abstract—In modern surveillance radar, pulse compression is
applied to achieve long range coverage while maintaining both low
transmit peak power and desired range resolution. When there is
a requirement to increase the radar’s range without a corresponding increase in the transmitted peak power it is required that a
longer uncompressed pulse be used. As a consequence the blind
range, associated with blanking the receiver whilst transmitting
the pulse, will increase and short range coverage will be lost.
In this paper we initially present a system of concatenated
waveforms that provide simultaneous radar coverage for both
near and far ranges. The solution incorporates a combination of
longer sub-pulses for far range and shorter sub-pulses for near
range. Although the concatenated waveforms have a number of
attractive attributes, they present a challenging problem in that
different sub-pulses will reflect back from different ranges and be
received at the same time. Therefore since each sub-pulse is not
separable at the RF front end a more complex sensitivity time
control (STC) is required. In the second part of this paper we analyze this phenomenon and propose a STC scheme to address the
issue.
Index Terms— STC, Concatenated Waveform, Receiver Saturation.
I. INTRODUCTION
In modern surveillance radar systems, both high range resolution and long range coverage are important features [1]. High
range resolution may be obtained by a short duration pulse.
Since the sensitivity of a radar relies on the energy contained in
the transmitted pulse, far range may be reached by employing a
long duration pulse and/or high transmitter power. Simply increasing the radar pulse length has the side effect of degrading
the range resolution. Alternatively short pulses require higher
transmitter power, which translates to higher cost and lower
reliability [2].
Pulse compression techniques [1-3] allow reduced transmitter power whilst still maintaining long range and high resolution. The reason is that the range resolution does not necessarily
depend on the duration of the pulse but on the bandwidth of the
pulse. The transmitted long pulses can be modulated to increase
their bandwidth, and on receive these pulses are compressed in
the time domain, resulting in a range resolution higher than that
associated with a non-modulated pulse.
However longer pulses increase the blind range simply because the receiver has to be gated off during transmission. One
way to recover the near range is to transmit a separate short
1-4244-1539-X/08/$25.00 ©2008 IEEE
pulse after the long pulse has been fully received. The echoes
from the long pulse are from far range targets and echoes from
the short pulse are from targets at near ranges. This method is
simple but inefficient in that the transmission and reception of
the short pulse unnecessarily increases the duration between two
long pulses. Consequently the radar receives fewer pulses from
far range targets within the 3 dB beamwidth. An alternative
more efficient method is to form a complex pulse with both long
and short pulses concatenated together. After transmission of all
sub-pulses, the receiver collects reflected signals from all subpulses and separates them based on either their frequency or
modulation.
Although the concatenated waveforms have a number of attractive attributes, they inherit a challenging problem in that
different sub-pulses will reflect back from different ranges but
be received at the same time. Since each sub-pulse experiences
different attenuation, it therefore requires its own sensitivity
time control (STC) [2]. However at the RF front end these subpulses are not separable and a traditional STC scheme can not
be directly applied. There is a requirement to configure a more
appropriate STC. In this paper we present a system for concatenated waveform and discuss its limitations. We also propose a
feasible STC scheme to address the STC requirements for concatenated waveforms. This paper is outlined as follows. The
system and method for concatenating pulses are presented in
Section II. A detailed analysis of the STC requirements for the
complex waveforms is presented in Section III and a feasible
STC approach is proposed in Section IV. A sample analysis is
presented in section V and summary is presented in Section VI.
II. METHOD AND SYSTEM FOR CONCATENATED
WAVEFORMS
A modulated pulse with a long pulse length can be found in
many radar systems. For monostatic radar, the receiver has to
be gated off during transmission, resulting in a minimum blind
range of:
Rb =
cτ L
2
(1)
where c is the speed of light, and τL is the uncompressed pulse
length. A separate short pulse, often referred as a “fill pulse”,
can be transmitted to cover this blind zone as shown in Fig. 1
(a). However the dwelling time on the far range targets is reduced and the corresponding loss is approximately:
Lb = 1 −
τ L +τ S
TR + 2τ L + τ S
(2)
TR is the maximum receiving time determined by the maximum
unambiguous range, and τS is the short pulse length which is in
general the same as the compressed long pulse. In air surveillance radar, the ratio between the total pulse length (long +
short) and the maximum receiving time is around 0.1 and the
corresponding loss is about 0.5 dB according to Eq.(2). In other
words, 10% of the transmitter’s power is wasted.
Long
Short
Long
Short
Transmit
100
1
TR
Receive
Long
Short
(a)
Transmit
101
Receive
Short
Long
(b)
Fig. 1 – Example pulse schemes for simultaneous far and near range
coverage: a) separate long and short pulses b) concatenated long and
short pulses.
The lost transmitter power can be saved by using concatenated waveforms such as a simple example shown in Fig. 1(b).
In this example a short pulse is transmitted immediately following the long pulse. Both short pulse and long pulse echoes are
received simultaneously but from different ranges. The short
pulse returns are separated from long pulse returns based on
their different characteristics. The data can be processed independently or realigned to form the full range coverage for further common processing. Different features can be utilized to
distinguish the echo signals from each pulse, which includes
orthogonal coding, polarization or frequency.
The concatenated pulse waveforms described herein generally consist of sub-pulses with a certain order within a given
pulse repetition interval (PRI). Pulses are arranged such that
longer pulses are transmitted first followed by shorter pulses to
provide a fill for a blanking interval. Therefore, if the required
minimum detection range is within the blind zone of long pulse
(LP), the concatenated waveforms include a short pulse (SP) at
the end to achieve the minimum range. Since the SP already has
good range resolution, pulse compression may not be necessary.
Another attractive attribute of concatenated waveforms is
their flexibility to form complex waveforms for enhanced processing gain. For example, frequency diversity can be achieved
within one PRI with only one transmitter required. An example
of this waveform is shown in Fig. 2, which is specifically applied to an L band En Route radar. (Details can be found in [4]).
This waveform has better azimuth resolution and accuracy
compared to waveforms having PRI alternative frequency diversity.
Fig. 2 – Example of concatenated waveforms with frequency diversity.
In Fig. 2, carrier frequency offsets are introduced for each
sub-pulse which simplify the implementation and also increase
the pulse compression freedom. Any modulation can be applied
to one of the pulses regardless of the modulation applied to the
other pulses. Specific numbers have been shown only for example with the understanding that other values can be selected for
the IF and RF frequencies of these pulses as well as different
time durations. These values are dictated by the specific application where a unique requirement may exist for minimum range,
maximum range, and range resolution etc.
In this case, there are two long pulses optimized for target
detection over the far range, and there are two medium pulses
(MP) optimized for near range target detection. The minimum
coverage requirement for En Route radar is relaxed and there is
no need for a short pulse. The frequency offset between the long
pulses is set to provide sufficient de-correlation for frequency
diversity and separation for filtering. The frequency offset between long and medium pulses is only constrained by the filtering requirement. In Fig. 2 one set of LP and MP is centred at
carrier frequency F1 with +/- 3 MHz; and another set is centered
at F2 with +/- 3 MHz. It should be noted that the pulses do not
have to be centered about the carrier frequency, although this
simplifies the generation of these pulses and the processing of
subsequent reflections.
A sample portion of a radar receiver is shown in Fig. 3 for
processing reflections of the concatenated pulse waveform of
Fig. 2. After a low-noise amplifier (LNA), the return signals are
separated into F1 or F2 based frequency paths through two
bandpass filters. The F1 centered filter has a sufficient bandwidth to pass both F1 LP and F1 MP reflected signals. A similar
characteristic applies to the F2 centered bandpass filter. The
mixers then down-convert the output of the bandpass filters
respectively to the IF band based on oscillation frequencies LO1
and LO2. The reflected MP waveform is then separated from
the reflected LP waveform by a second stage bandpass filter.
The separated signals are digitized and pulse compressed.
III. STC ANALYSIS
Sensitivity time control is in general required in the RF front
end to protect the receiver from saturation due to nearby clutter.
STC reduces the receiver gain at close ranges where clutter
echoes are large and maximum sensitivity is not generally required. The gain will continually increase as echoes return
from further range and reach the maximum when the clutter
barely exceeds the noise level. In air traffic control radars STC
is applied to control land clutter as well as angel clutter (such
as birds and insects). The selection of gain versus time characteristic is dictated by the type of clutter encountered.
The use of concatenated waveforms makes the application
of STC more complex since different pulses reflect back at the
same time but from different ranges. Ideally a distinct STC
value should be selected for each pulse depending on its true
range. However this is not practical since it is not feasible to
separate the pulses at the RF front end. It can be noted that a
similar but more extreme result exists in high PRF pulse Doppler radar [1], where STC is not feasible due to the excessive
number of multi-trip signals.
where γ is the parameter describing the surface property and
ψ(R) is the grazing angle. For range R the grazing angle can be
determined by [6]:
h
h
1 +
 2r
R
e
 
ψ ( R ) = sin −1 
 R
−
 2r
e




 ≈ sin −1  h − R 
 R 2r 

e 


(8)
where h is the effective radar height (site elevation above mean
sea level plus radar antenna height minus terrain elevation above
mean sea level), R is the radar slant range and re is the effective
earth’s radius. Although for low grazing angle this model tends
to overestimate the reflectivity due to propagation factors, it still
provides a basis for the analysis with a loose upper bound of the
clutter’s power as a worst-case scenario. A high grazing angle of
near 90° is not of interest since our primary focus is ground
based radar with grazing angle generally less than 45° .
At range R the land clutter will arrive at the radar receiver
with the following radar cross sections (RCS):
σ ( R) = σ ° (R ) A(R ) = γ tan(ψ ( R ))Rθ B
cτ
2
(9)
where θB is the 3-dB antenna beamwidth, A(R) is the radar resolution cell and τ is the compressed pulse length (assume all
pulses have the same length after pulse compression). In the
following analysis we assume tan(ψ) to be 1, which provides
more conservative clutter power estimation for grazing angles
less than 45° . At time instant t, the clutter power from the first
long pulse is as follows on the receiver front end:
Fig. 3 – Example of receiver processing of the 4 – pulses waveforms.
In this section the STC requirements are analyzed for the
waveform with specific parameters as shown in Fig. 2. However the analysis procedures and conclusions can be readily
extended to other concatenated waveforms.
At time instant t the received signals are reflected from
different ranges for different pulses and determined as follows:
RL1 (t ) = (t + T + τ M 2 + τ M 1 + τ L 2 + τ L1 + 3∆ ) c / 2
(3)
RL 2 (t ) = (t + T + τ M 2 + τ M 1 + τ L 2 + 2∆ ) c / 2
(4)
RM 1 (t ) = (t + T + τ M 2 + τ M 1 + ∆ ) c / 2
(5)
RM 2 (t ) = (t + T + τ M 2 ) c / 2
(6)
where τL1 is F1 (first) long pulse length, τL2 is F2 (second) long
pulse length, τM1 is F2 (first) medium pulse length, τM2 is F1
(second) medium pulse length, t is relative time to receiver
start-up, ∆ is gap among pulses for spectrum control, T is receiver start-up time after complete of transmission and c is the
speed of light. RL1, RL2, RM1, RM2, are range of reflected signals for
first LP, second LP, first MP and second MP, respectively.
For land clutter backscattering coefficient σ0, we adopt the
constant-γ model which is in excellent agreement with most
measurements at grazing angles not too close to 90° or 0° [5],
and the model for range R is:
σ °(R ) = γ sinψ (R )
(7)
cτ  2
λ
2 
C L1 (t ) =
4
i =0
(4π )3  RL1(t ) − i cτ 
2 

cτ 2
N L1 −1
Pt Gt Gr γθ B
λ
2
=
3
i =0
(4π )3  RL1 (t ) − i cτ 
2 



N L1 −1 Pt Gt Grσ  RL1 (t ) − i
∑
(10)
∑
where Pt is peak transmitted power, Gt and Gr are respectively
the transmit and receive antenna gains, λ is radar wavelength
and NL1 is the pulse compression ratio for the first long pulse. It
is worth noting that integration over the uncompressed pulse
length is important for the estimation of land clutter strength.
This integration, often neglected, shows the correlation between
different range cells in order to provide this land clutter strength
estimate. In a similar way we can obtain the clutter power received from the other pulses:
cτ 2
N L 2 −1
Pt Gt Gr γθ B
λ
2
C L 2 (t ) =
(11)
3
cτ 
3
i =0
(4π )  RL 2 (t ) − i 
2 

∑
N M 1 −1
C M 1 (t ) =
∑
i =0
cτ 2
λ
2
3
(4π )3  RM 1 (t ) − i cτ 
2 

Pt Gt Gr γθ B
(12)
cτ 2
λ
2
C M 2 (t ) =
(13)
3
cτ 
3
i =0
(4π )  RM 2 (t ) − i 
2 

At a given receiver time t, STC may be required due to the following reason(s):
1) To prevent the land clutter power from saturating the receiver. The receiver saturation happens when the maximum
signal power received Psa causes a LNA gain compression
of one dB. STC has to be applied at the RF front end. The
STC required for this purpose is*:
N M 2 −1
∑
Pt Gt Gr γθ B
STC LLC
1 (t ) = C L1 (t ) − Psa + δ
STC LLC
2 (t ) = C L 2 (t ) − Psa + δ
STC MLC1 (t ) = CM 1 (t ) − Psa + δ
(14)
where δ is the margin to protect the LNA from saturation.
2) To prevent A/D converter saturation, STC can be applied at
any point prior to the A/D converter. This is because in
general the A/D converter has a smaller dynamic range than
the analog receiver and sets more aggressive requirements
on STC. The STC required for this purpose is:
STC LAD
1 (t ) = C L1 (t ) − N fl − Dr + δ n
N fl − Dr + δ n
STC MAD1 (t ) = CM 1 (t ) − N fl − Dr + δ n
STC can be applied either at the RF stage, IF stage and/or digital section of the system. Due to the complexity of concatenated waveforms, a combination of these STCs is proposed.
The proposed scheme works ideally for the situation where the
most demanding requirement is for angel clutter control, and
least demanding requirement is for amplifier saturation. If this
situation does not exist, the designer has to be aware of the
possible integration loss and diversity loss for close in targets.
This might not be an issue for low flying targets, but might be a
concern for close-in height coverage especially with cosecantsquared beampattern, such as air traffic control radars.
A
STC MLC2 (t ) = CM 2 (t ) − Psa + δ
STC LAD
2 (t ) = C L 2 (t ) −
IV. STC SCHEMES FOR CONCATENATED WAVEFORMS
At the RF front end, RF STC is required to prevent amplifier
saturation. At this stage, all pulses are non-separable, and only
one STC can be applied. The STC is determined as:
STC RF (t ) =
(
LC
LC
LC
max STC LLC
1 (t ), STC L 2 (t ), STC M 1 (t ) , STC M 2 (t ), 0
STC LBC
2 (t ) = S L 2 (t ) − N fl − Vx
STC MBC1 (t ) = S M 1 (t ) − N fl − Vx
IF STC
(
(
(
(
RF
STC LIF1 (t ) = max STC LAD
(t ), 0
1 (t ) − STC
STC LBC
1 (t ) = S L1 (t ) − N fl − Vx
(16)
STC MBC2 (t ) = S M 2 (t ) − N fl − Vx
where the Vχ is visibility factor which can be determined
based on the system requirements for false alarm rate and
probability of detection for the largest birds of interest.
SL1(t), SL2(t), SM1(t), and SM2(t), are respectively the received
power from the largest birds of interest at different pulses.
More than often, receiver (LNA) requires the least STC attenuation, and angel clutter requires the most STC attenuation. This is
at lease the case in the later example.
(17)
The IF STC should be applied prior to A/D converter. At this
stage data from different pulses have been separated. Individual
STC can be applied. The required IF STC is as follows:
STC MAD2 (t ) = CM 2 (t ) − N fl − Dr + δ n
where Nfl is the system noise floor, δn is the margin required
to protect A/D converter from clipping, and Dr is the A/D
converter dynamic range.
3) To prevent angel clutter (birds) from saturating radar. This
is especially required for air traffic control radars. STC can
be applied in analog or in digital sections. The required
STC is:
)
As shown in Equation (17), amplifier saturation is avoided by
selection of the largest STCRF(t) value over the long and medium
pulses.
B
(15)
RF STC
)
)
)
)
RF
STC LIF2 (t ) = max STC LAD
(t ), 0
2 (t ) − STC
IF
AD
RF
STC M 1 (t ) = max STC M 1 (t ) − STC (t ), 0
STC MIF2 (t ) = max STC MAD2 (t ) − STC RF (t ), 0
(18)
The IF STC can be applied anywhere between the data
separation and A/D converter. However special consideration
has to be given if Constant False Alarm Rate (CFAR) techniques
are adopted in the later detection stage in that the IF STC can
alter the noise floor.
The combination of RF STC and IF STC helps to prevent
the A/D converter from clipping due to any of the pulses. When
RF STC sets a higher attenuation value, there will be no need to
have an IF STC.
C
Digital STC
Individual digital STC can be applied anywhere after A/D converter. The STC required is as follows:
RF
STC LD1 (t ) = STC LBC
(t ) − STC LIF1 (t )
1 (t ) − STC
RF
STC LD2 (t ) = STC LBC
(t ) − STC LIF2 (t )
2 (t ) − STC
STC MD 1 (t ) = STC MBC1 (t ) − STC RF (t ) − STC MIF1 (t )
(19)
STC MD 2 (t ) = STC MBC2 (t ) − STC RF (t ) − STC MIF2 (t )
*
In this paper, the positive STC value means attenuation; zero and
negative STC values means no STC required. All units are in dB.
The digital STC can bring artefacts to the noise floor in a similar way to that of the IF STC. When CFAR is employed, the
threshold has to be carefully designed to obtain a real constant
false alarm rate. A feasible design is to apply a minimum
threshold map during the detection process, which will regulate
the detection of the smallest target of interest under the consideration of combined IF and digital STC effects.
The application of digital STC is flexible in that it can be
combined and applied together with IF STC. Another way to
apply digital STC is to incorporate it into the detection process
instead of physically applying the attenuation, which avoids the
side effects on noise floor.
When the combination of RF STC and IF STC sets a higher
attenuation value, there is no requirement for digital STC.
For the four sub-pulses concatenated waveform or similar
waveform which requires integrating the sub-pulses, it is recommended to apply the digital STC prior to any video or binary
integrator.
The combination of RF, IF and digital STC helps to control
the angel clutter breakthrough from any of the pulses.
The other curves in Fig. 5 represent the STC requirements
for angel clutter control with a maximum RCS of 0.01m2. If the
STC required for the second medium pulse was applied at the
RF stage, then we would be applying the correct STC for the
second medium pulse but too much for the other three pulses.
For example at receiver time 1µs, we would have the correct
STC for the second medium pulse but 35 dB too much for the
echo from the second long pulse which is coming back from a
range of 13.77 nmi at the same time. This would result in the
sensitivity loss, which can not be made up for later in the system. To circumvent this problem we should defer the required
STC for angel clutter control to digital stage, but only apply the
RF STC determined by the amplifier saturation.
STCs Required for the Four Pulse Waveform
In this section the STC is designed for the waveform shown in
Fig. 4 with parameters that are typical for modern L band air
surveillance radars.
Both long pulses have a length of 120µs and effective
length of 110µs with tapering at the start and end of each pulse.
Both medium pulses have a length of 22µs and effective length
of 20µs with tapering. The gap in any two neighbouring pulses
is 5µs. All pulses will be compressed into 1µs.
The transmitter peak power is 50 kW and the carrier frequency is 1.3 GHz. The antenna has a gain of 34 dB. A typical
limit level for the receiver protector is -10 dBm and a 10 dB
margin has been added during the calculation. The receiver is
gated on at 1µs after the completion of transmission. The instrumental coverage is from 5 nmi to 200 nmi. Land clutter
backscattering coefficient σ0 is set to -10 dB (m2/m2 ) which is a
severe clutter scenario [5] for a rural environment.
The analysis has shown that at the RF stage the second medium pulse requires the most attenuation and determines the RF
STC according to Eq. (17). The RF STC is shown in Fig. 5 as
the star-labeled curve. The abscissa indicates the range of the
second medium pulse’s returns at receiver time t. For example,
at receiver time 1µs, the radar returns of second medium pulse
is from 1.78 nmi, while the returns of first medium pulse, second long pulse and first long pulse are actually from 3.97 nmi,
13.77 nmi and 23.89 nmi, respectively.
Fig. 4 – Example of the 4-pulses waveforms with specific timing and
reflection range.
STC (dB)
V. EXAMPLE ANALYSIS
85
80
75
70
65
60
55
50
45
40
35
30
25
20
15
10
5
0
-25 -20 -15 -10 -5 0
2nd Med Pls
1st Med Pls
2nd Lng Pls
1st Lng Pls
RF STC for all
5
10 15 20 25 30 35 40 45 50 55 60 65 70
Range (nmi)
Fig. 5 – RF STC and the individual STCs required by angel clutter
control
There is no need for the IF STC in that the A/D converter
has 16 bits which provides sufficient dynamic range. The digital
STC is then determined by the difference of the applied RF STC
and the desired STC for angel clutter control according to Eq.
(19). The digital STC curves are presented in Fig. 6 for each
pulse, respectively.
Except for the early receiver time (before 4µs), the RF STC
is less demanding than all the other angel clutter STCs. Therefore there is an optimal solution for most of the receiver time
(after 4µs), which is to apply RF STC at the RF front end and
apply the difference in as digital STCs according to Eq. (19).
VI. SUMMARY
In this paper we analyze and propose a multi-stage STC
scheme for complex concatenated waveforms. The principle is
to apply minimum STC at the RF front end to satisfy the receiver saturation protection from close in clutter. Additional
pulse-specific STCs are applied at the IF and/or digital stages
where the pulses have been split and extra flexibility exists.
When the STC required by receiver saturation is least demanding, our proposed scheme can provide an optimal solution
as if all pulses could be separated at the RF front end. If this is
not the case, a loss in sensitivity is unavoidable.
Digital STCs Required for the Four Pulse Waveform
45
40
35
STC (dB)
30
2nd Med Pls
1st Med Pls
2nd Lng Pls
1st Lng Pls
25
20
15
10
5
0
0
5
10
15
20
25
30
35
40
45
50
55
60
65
70
Range (nmi)
Fig. 6 – Digital STCs for each of the pulses
ACKNOWLEDGMENT
The first author would like to thank Dr. A. M. Ponsford for his
valuable comments.
REFERENCES
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McGraw-Hill Press, 2001.
[2] M. I. Skolnik, Radar Handbook. New York, McGraw-Hill Press, 1990.
[3] A. W. Rihaczek, Principles of High-Resolution Radar. Peninsula Publishing, 1985.
[4] T. M. Chan, M. Gerecke, “Method and System for Concatenation of Radar
Pulses”, US Patent Application # 11/832,973 filed August 2, 2007.
[5] D. Barton, Radar System Analysis and Modeling, Norwood, US, Artech
House, 2005.
[6] F. E. Nathanson, Radar Design Principles, Second Edition, New York,
McGraw-Hill Press, 1991.