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Proceedings Articleβ€’DOIβ€’

Performance of a practical two-step detector for non-fluctuating targets

TL;DR: This paper presents the Neyman-Pearson (NP) two-step detection rule for a non-fluctuating target model (Swerling 0), which is non-linear and requires a priori knowledge of the target SNR.
Abstract: In this paper we analyze a two-step detection scheme for use in distributed sensor systems (e.g. statistical MIMO radar). The scheme arises when a data rate restriction forces each of the distributed systems to censor their detection statistics before sharing. We present the Neyman-Pearson (NP) two-step detection rule for a non-fluctuating target model (Swerling 0), which is non-linear and requires a priori knowledge of the target SNR. We then analyze the performance of a practical two-step detection rule under the non-fluctuating target model.

SummaryΒ (2 min read)

Introduction

  • Individual sensors are capable of producing detection statistics at a high data rate.
  • The two-step detection scheme arises when an aggregate data rate restriction is imposed on a distributed sensor system.
  • After being shared, the detection statistics are passed to Stage 2 (second-stage detection) of the two-step detection scheme where they are integrated and compared to a final threshold corresponding to the desired overall probability of false alarm.
  • Thus an individual platform’s data rate is directly proportional to the first-stage probability of false alarm (PFA).

II. TWO-STEP DETECTION RULE

  • In [4] the Neyman-Pearson (NP) two-step detection rule (2SD) for the Swerling 2 (SW2) [5] fluctuating target model was derived and was shown to be clairvoyant [7] because of its dependence on a priori knowledge of the unknown target SNR.
  • [4] presented empirical evidence that the performance of the detector is only weakly dependent on this a priori knowledge.
  • Thus, by assuming a reasonable target SNR, the detector becomes a practical one.
  • Additionally, the detection rule is linear, making threshold selection and performance analysis straightforward.
  • In this section the authors complement the SW2 results in [4] by presenting the NP two-step detection rule for the Swerling 0 (SW0) [5] target model.

A. General NP Two-Step Detection Rule

  • In [4] the general NP two-step detection rule was derived based on the following assumptions: i) Noise at each sensor is independent and identically distributed (IID). ii).
  • The target SNR measured by each sensor is also IID. iii).
  • The detection cells for each platform align exactly (i.e. there are no registration errors).

B. Swerling 0 NP Two-Step Detection Rule

  • The authors now make several important observations: i).
  • The second-stage detection statistic is a non-linear combination the shared first-stage detection statistics. iii).

C. A Practical Two-Step Detection Rule

  • Aside from being clairvoyant, the Swerling 0 NP two-step detector is also non-linear.
  • This not only makes its real-world implementation impractical from a computational and system engineering stand-point, it also makes threshold selection and performance analysis difficult.
  • The major caveat of using the detection rule above is that observation (iii) above is no longer valid, making the process of optimal threshold selection non-obvious.
  • In order to circumvent this issue the authors will select the second-stage thresholds using results from [4] by assuming the target is SW2.

B. Second-Stage Probability of Detection

  • For the SW2 target model the authors were able to derive a closed form for (8) [4].
  • In their analyses the approximation proved comparable to Monte Carlo simulations of the true distribution.

IV. RESULTS

  • Where the second-stage detection thresholds were selected based on the results in [4] by assuming the target is SW2.the authors.
  • In part A the authors present plots illustrating how 𝑃𝑑2 varies with π‘ƒπ‘“π‘Ž1, and in part B they present a series of plots illustrating how 𝑃𝑑2 varies with target SNR.
  • In their analysis the authors consider the Cooperative Networked Radar (CNR) [3] implementation of statistical MIMO radar.
  • In this scenario each platform transmits a single pulse and noncoherently integrates its own pulse plus those transmitted by the other participating platforms prior to first-stage thresholding.

A. 𝑃𝑑2 vs. π‘ƒπ‘“π‘Ž1

  • In the following the authors present two plots (Fig. 2 and 3).
  • The first illustrates how 𝑃𝑑2 varies with π‘ƒπ‘“π‘Ž1 using the practical detector (7) under the SW0 target model.
  • The second plot shows the equivalent SNR loss due to first-stage thresholding .
  • The SNR loss is defined as the additional SNR needed to achieve the single-stage detection performance using the two-step detector.

B. 𝑃𝑑2 vs. Target SNR

  • The focus of each plot is the comparison of a practical detector that can be easily implemented, to the optimal, yet unrealizable one, for the SW0 case.
  • Hence, each plot displays two series: one series shows the performance of the practical 2SD (7) where the second-stage thresholds are fixed and were selected based on an assumed SNR yielding a PD of 0.5 for the single-stage detector (2.3 dB and -1.4 dB per pulse per platform for 𝑁 = 4 and 𝑁 = 8 respectively).
  • The second series shows the performance of the Swerling 0 NP two-step detector (4) in which the second-stage thresholds were selected assuming prior knowledge of the target SNR.
  • For reference, these plots also include an upper curve for the unrestricted case and a lower curve for the single platform case.

V. CONCLUSION

  • The authors have examined the two-step detection scheme that arises when practical data-rate limits are imposed on the Cooperative Networked Radar implementation of statistical MIMO radar.
  • The authors results echo those in [4] and indicate that the data rates in a distributed detection system can be reduced by several orders of magnitude using the two-step detection scheme without fully compromising the detection capability of the distributed sensor system.
  • Additionally, the results presented in Subsection B indicate that the performance of the linear detector is very close to optimal.
  • Thus, the authors should expect the linear detector (with thresholds selected by assuming the target is SW2), to perform close to optimal over a range of fluctuating target models.

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Performance of a Practical Two-Step Detector for
Non-Fluctuating Targets
Max Scharrenbroich
βˆ—
, Michael Zatman
βˆ—
, and Radu Balan
†
βˆ—
QinetiQ North America
Reston, Virginia
†
Department of Mathematics
University of Maryland, College Park
Abstractβ€”In this paper we analyze a two-step detection scheme
for use in distributed sensor systems (e.g. statistical MIMO
radar). The scheme arises when a data rate restriction forces
each of the distributed systems to censor their detection statistics
before sharing. We present the Neyman-Pearson (NP) two-step
detection rule for a non-fluctuating target model (Swerling 0),
which is non-linear and requires a priori knowledge of the target
SNR. We then analyze the performance of a practical two-step
detection rule under the non-fluctuating target model.
I. INTRODUCTION
Individual sensors are capable of producing detection statis-
tics at a high data rate. When individual sensor platforms are
aggregated to improve sensitivity, such as in statistical MIMO
radar [1], [2], [3], the aggregate data rate can saturate both the
communication and computational capacity of the system.
The two-step detection scheme arises when an aggregate
data rate restriction is imposed on a distributed sensor system.
One approach to restricting the aggregate data rate is to ini-
tially censor, or equivalently, threshold the detection statistics
at each platform and share only those statistics that pass
an initial threshold test (see Fig. 1). We refer to this initial
threshold test as Stage 1 (first-stage detection) of the two-step
detection scheme. After being shared, the detection statistics
are passed to Stage 2 (second-stage detection) of the two-step
detection scheme where they are integrated and compared to a
final threshold corresponding to the desired overall probability
of false alarm.
Under the assumption that the number of actual targets
is small compared to the number of detection cells, most
of the first-stage detection statistics are due to false alarms
from noise. Thus an individual platform’s data rate is directly
proportional to the first-stage probability of false alarm (PFA).
By reducing each platform’s first-stage PFA the aggregate data
rate is reduced.
To illustrate, if a single platform is producing detection
statistics at a data rate of 100 Mb/s, by initially thresholding
the detection statistics such that the Stage 1 PFA is 10
βˆ’3
,the
data rate into Stage 2 is reduced to approximately 100 Kb/s.
This work was sponsored by the Office of Naval Research under contract
number N00178-04-D-4030-EH02. All views in this paper are those of the
authors, and are not necessarily endorsed by the U.S. Navy.
Fig. 1. Two-Step Detection Scheme
II. TWO-STEP DETECTION RULE
In [4] the Neyman-Pearson (NP) two-step detection rule
(2SD) for the Swerling 2 (SW2) [5] fluctuating target model
was derived and was shown to be clairvoyant [7] because of its
dependence on a priori knowledge of the unknown target SNR.
Despite being clairvoyant, [4] presented empirical evidence
that the performance of the detector is only weakly dependent
on this a priori knowledge. Thus, by assuming a reasonable
target SNR, the detector becomes a practical one. Additionally,
the detection rule is linear, making threshold selection and
performance analysis straightforward.
In this section we complement the SW2 results in [4] by
presenting the NP two-step detection rule for the Swerling 0
(SW0) [5] target model.
A. General NP Two-Step Detection Rule
In [4] the general NP two-step detection rule was derived
based on the following assumptions:
i) Noise at each sensor is independent and identically dis-
tributed (IID).
ii) The target SNR measured by each sensor is also IID.
iii) The detection cells for each platform align exactly (i.e.
there are no registration errors).

The general NP two-step detection rule is to decide 𝐻
1
(the
hypothesis that a target is present) if:
ξ˜‚
π‘₯
π‘˜
>𝑇
1
{ln(𝑝(π‘₯
π‘˜
∣𝐻
1
)) βˆ’ ln(𝑝(π‘₯
π‘˜
∣𝐻
0
))}
+(𝑁 βˆ’ 𝐿)ln
ξ˜ƒ
1 βˆ’ 𝑃
𝑑1
1 βˆ’ 𝑃
π‘“π‘Ž1
ξ˜„
𝐻
1
> ln(πœ†),
(1)
where 𝑝(π‘₯
π‘˜
∣𝐻
𝑖
) is the PDF of platform π‘˜β€™s shared detection
statistic, π‘₯
π‘˜
, conditioned on either 𝑖 =0(noise only), or
𝑖 =1(target present), 𝑁 is the total number of par-
ticipating platforms, 𝐿, the detection level, is the number
of sensors passing along their first-stage detection statistics
(𝐿 =Σ
𝑁
π‘˜=1
1{π‘₯
π‘˜
>𝑇
1
}), 𝑃
π‘“π‘Ž1
is the first-stage PFA, 𝑃
𝑑1
is
the first-stage probability of detection (PD), 𝑇
1
is the first-stage
threshold associated with 𝑃
π‘“π‘Ž1
and πœ† is a detection threshold.
B. Swerling 0 NP Two-Step Detection Rule
In the case of the SW0 target model, the return pulse has
a Rician power distribution, and the non-coherent integration
(using a square law detector) of 𝑀 such pulses yields a
noncentral πœ’
2
distribution:
𝑝(π‘₯
π‘˜
∣𝐻
1
,πœ‰)=
ξ˜ƒ
π‘₯
π‘˜
π‘€πœ‰
ξ˜„
(𝑀 βˆ’1)
2
𝑒
βˆ’(π‘₯
π‘˜
+π‘€πœ‰)
×𝐼
π‘€βˆ’1
ξ˜…
2
ξ˜†
π‘€πœ‰π‘₯
π‘˜
ξ˜‡
,
(2)
where πœ‰ is the target SNR and 𝐼
𝜈
(β‹…) is the modified Bessel
function of the first kind.
As πœ‰ β†’ 0, (2) becomes the noise-only case which is an
Erlang density (or Ξ“(𝑀,1)):
𝑝(π‘₯
π‘˜
∣𝐻
0
)=
π‘₯
(π‘€βˆ’1)
π‘˜
𝑒
βˆ’π‘₯
π‘˜
(𝑀 βˆ’ 1)!
. (3)
After inserting (2) and (3) into (1) we have the Swerling
0 NP two-step detection rule: decide that a target is present
(𝐻
1
)if
ξ˜‚
π‘₯
π‘˜
β‰₯𝑇
1
𝛼(π‘₯
π‘˜
,πœ‰)
𝐻
1
>πœ‚+ πΏπœ…(πœ‰) ≑ 𝑇
2,𝐿
(πœ‰) (4)
where πœ‚ is a threshold parameter (implicitly) dependent on
πœ‰ and the desired overall (second-stage) probability of false
alarm (𝑃
π‘“π‘Ž2
),
𝛼(π‘₯
π‘˜
,πœ‰) ≑ 𝑙𝑛
ξ˜…
𝐼
π‘€βˆ’1
ξ˜…
2
ξ˜†
π‘€πœ‰π‘₯
π‘˜
ξ˜‡ξ˜‡
βˆ’
(𝑀 βˆ’ 1)
2
𝑙𝑛(π‘₯
π‘˜
),
(5)
πœ…(πœ‰) ≑ ln
ξ˜ƒ
1 βˆ’ 𝑃
𝑑1
1 βˆ’ 𝑃
π‘“π‘Ž1
ξ˜„
βˆ’ 𝑙𝑛((𝑀 βˆ’ 1)!)
+
(𝑀 βˆ’ 1)
2
𝑙𝑛(π‘€πœ‰)+π‘€πœ‰,
(6)
and 𝑇
2,𝐿
(πœ‰) is the second-stage threshold for the 𝐿
π‘‘β„Ž
detection
level. To be concise, the explicit dependence of 𝑃
𝑑1
on πœ‰ and
𝑃
π‘“π‘Ž1
is omitted.
We now make several important observations:
i) The NP detector is a clairvoyant detector since it is
dependent on an unknown parameter πœ‰, the target SNR.
ii) The second-stage detection statistic is a non-linear com-
bination the shared first-stage detection statistics.
iii) Assuming knowledge of πœ‰ there is only a single threshold
parameter πœ‚ that needs to be found based on the desired
𝑃
π‘“π‘Ž2
.
C. A Practical Two-Step Detection Rule
Aside from being clairvoyant, the Swerling 0 NP two-step
detector is also non-linear. This not only makes its real-world
implementation impractical from a computational and system
engineering stand-point, it also makes threshold selection and
performance analysis difficult.
In the performance analysis that follows we will use the
Swerling 2 NP t wo-step detection rule derived in [4]:
ξ˜‚
π‘₯
π‘˜
β‰₯𝑇
1
π‘₯
π‘˜
𝐻
1
>𝑇
2,𝐿
(πœ‰), (7)
where 𝑇
2,𝐿
is defined as in [4].
The major caveat of using the detection rule above is that
observation (iii) above is no longer valid, making the process
of optimal threshold selection non-obvious. In order to cir-
cumvent this issue we will select the second-stage thresholds
using results from [4] by assuming the target is SW2.
III. A
NALYSIS OF PERFORMANCE
A. Second-Stage Probability of False Alarm
We refer the reader to [4] where we presented an expression
for computing the overall probability of false-alarm (𝑃
π‘“π‘Ž2
)
given a set of second-stage thresholds for the linear detector
in (7).
B. Second-Stage Probability of Detection
For the linear detector in (7) the second-stage probability
of detection (𝑃
𝑑2
) takes the following form:
𝑃
𝑑2
=
𝑁
ξ˜‚
𝐿=1
ξ˜ƒ
𝑁
𝐿
ξ˜„
(1 βˆ’ 𝑃
𝑑1
)
(π‘βˆ’πΏ)
(𝑃
𝑑1
)
𝐿
𝐹
𝐿
(𝑇
2,𝐿
), (8)
where
𝐹
𝐿
(𝑇
2,𝐿
) β‰‘π‘ƒπ‘Ÿ

Ξ£
𝐿
𝑙=1
π‘₯
(𝑙)
>𝑇
2,𝐿
∣ (9)
π‘₯
(1)
>𝑇
1
,...,π‘₯
(𝐿)
>𝑇
1
,𝐻
1
ξ˜‰
is the complementary cumulative distribution function of the
second-stage detection statistic given that 𝐿 of the first-stage
detection statistics are greater than 𝑇
1
and a target is present
(𝐻
1
).
For the SW2 target model we were able to derive a closed
form for ( 8) [4]. Because of the complexity of the left-
truncated distributions that (8) involves under the SW0 target
model we resorted to an approximation using a shifted Gamma
density and moment-matching:
𝐹
𝐿
(𝑇
2,𝐿
) β‰ˆ
1 βˆ’ Ξ“(𝑇
2,𝐿
/πœƒ, π‘˜)
Ξ“(π‘˜)
,𝑇
2,𝐿
β‰₯ 𝐿𝑇
1
, (10)

where π‘˜πœƒ =(π‘š
1,𝐿
βˆ’πΏπ‘‡
1
) and π‘˜πœƒ
2
=(π‘š
2
2,𝐿
βˆ’ π‘š
2
1,𝐿
)
1/2
, with
π‘š
1,𝐿
≑ πΏπ‘š
1
and π‘š
2,𝐿
≑ 𝐿(π‘š
2
βˆ’ (𝐿 βˆ’ 1)π‘š
2
1
), where π‘š
1
and π‘š
2
are the first and second moments of the left-truncated
density shown in (2) and were computed using results from
[8]. In our analyses the approximation proved comparable to
Monte Carlo simulations of the true distribution.
IV. R
ESULTS
In this section we present two parts each covering a different
analysis of the practical 2SD (7) detection performance under
the SW0 target model, where the second-stage detection
thresholds were selected based on the results in [4] by assum-
ing the target is SW2. In part A we present plots illustrating
how 𝑃
𝑑2
varies with 𝑃
π‘“π‘Ž1
, and in part B we present a series
of plots illustrating how 𝑃
𝑑2
varies with target SNR.
In our analysis we consider the Cooperative Networked
Radar (CNR) [3] implementation of statistical MIMO radar. In
this scenario each platform transmits a single pulse and non-
coherently integrates its own pulse plus those transmitted by
the other participating platforms prior to first-stage threshold-
ing.
A. 𝑃
𝑑2
vs. 𝑃
π‘“π‘Ž1
In the following we present two plots (Fig. 2 and 3). The
first illustrates how 𝑃
𝑑2
varies with 𝑃
π‘“π‘Ž1
using the practical
detector (7) under the SW0 target model. The second plot
shows the equivalent SNR loss due to first-stage thresholding
(censoring). The SNR loss is defined as the additional SNR
needed to achieve the single-stage detection performance using
the two-step detector.
We analyze two CNR cases where the number of platforms,
𝑁, is 4 and 8, respectively. In both cases each platform trans-
mits a single pulse (thus the number of pulses integrated at
each platform, 𝑀, is 4 and 8, respectively) and 𝑃
π‘“π‘Ž2
=10
βˆ’6
.
The target SNR for each case is selected based on a PD of
0.5 for the single-stage detector (the unrestricted case where
𝑃
π‘“π‘Ž1
=1) where the total number of pulses integrated is
𝑀 ×𝑁 =16and 𝑀 ×𝑁 =64for the 𝑁 =4and 𝑁 =8cases
respectively, and the overall PFA is 10
βˆ’6
.Inthe𝑁 =4and
𝑁 =8cases this translates into a target SNR of 2.3 dB and
-1.4 dB per pulse per platform respectively. Note that going
from the 𝑁 =4to the 𝑁 =8case we are able to maintain
a PD of 0.5 with a lower target SNR since we are integrating
over more platforms.
Fig. 2 shows the performance of the practical 2SD versus
𝑃
π‘“π‘Ž1
and also includes two curves as references for each CNR
case: an upper curve for the unrestricted case where 𝑃
π‘“π‘Ž1
=1
(equivalent to a single-stage detector), labelled as 1S and a
lower curve for the single platform case with a PFA of 10
βˆ’6
(best possible single platform performance given the same
overall PFA), labelled as 1P.
In Fig. 2 we see that 𝑃
𝑑2
suffers steeper losses versus 𝑃
π‘“π‘Ž1
with decreasing target SNR because with a lower SNR the
first-stage censors actual targets more often. In the 𝑁 =4case
a 𝑃
π‘“π‘Ž1
=10
βˆ’3
translates into a reduction of 𝑃
𝑑2
by about 0.3
which is equivalent to an SNR loss of approximately 1.1 dB.
βˆ’3 βˆ’2.5 βˆ’2 βˆ’1.5 βˆ’1 βˆ’0.5 0
0
0.1
0.2
0.3
0.4
0.5
log10(P
fa1
)
P
d2
1S (single stage)
1P (N=4)
2SD (N=4)
1P (N=8)
2SD (N=8)
Fig. 2. 2SD detection performance curves illustrating how 𝑃
𝑑2
varies with
𝑃
π‘“π‘Ž1
for 𝑁 =4and 𝑁 =8and a target SNR of 2.3 dB and -1.4 dB per
pulse per platform respectively.
In the 𝑁 =8case the same 𝑃
π‘“π‘Ž1
reduces 𝑃
𝑑2
by slightly less
than 0.4 which is equivalent to an SNR loss of approximately
1.8 dB.
βˆ’3 βˆ’2.5 βˆ’2 βˆ’1.5 βˆ’1 βˆ’0.5
0
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
log10(P
fa1
)
SNR LOSS (dB)
N=4
N=8
Fig. 3. Equivalent SNR loss as a function of 𝑃
π‘“π‘Ž1
.
B. 𝑃
𝑑2
vs. Target SNR
In this subsection we present two plots (Fig. 4 and 5)
illustrating how 𝑃
𝑑2
varies with target SNR for the same two
previous CNR cases (𝑁 = 4 and 8), with several values of
𝑃
π‘“π‘Ž1
∈{10
βˆ’1
, 10
βˆ’2
, 10
βˆ’3
} and 𝑃
π‘“π‘Ž2
=10
βˆ’6
.
The focus of each plot is the comparison of a practical
detector that can be easily implemented, to the optimal, yet
unrealizable one, for the SW0 case. Hence, each plot displays
two series: one series shows the performance of the practical
2SD (7) where the second-stage thresholds are fixed and were
selected based on an assumed SNR yielding a PD of 0.5

for the single-stage detector (2.3 dB and -1.4 dB per pulse
per platform for 𝑁 =4and 𝑁 =8respectively). The
second series shows the performance of the Swerling 0 NP
two-step detector (4) in which the second-stage thresholds
were selected assuming prior knowledge of the target SNR.
Because of the complexity of the Swerling 0 NP two-step
detector, the second-stage thresholds and overall probability
of detection were computed numerically using Monte-Carlo
(MC) techniques and importance sampling.
For reference, these plots also include an upper curve for
the unrestricted case and a lower curve for t he single platform
case.
βˆ’2 0 2 4 6 8
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
SNR (dB)
P
d2
1S (single stage)
1P (single platform)
2SD
SW0 NP 2SD (MC)
P
fa1
= 1eβˆ’3
P
fa1
= 1eβˆ’2
P
fa1
= 1eβˆ’1
Fig. 4. Detection performance curves for a practical 2SD and the SW0 NP
2SD illustrating how 𝑃
𝑑2
varies with target SNR for the 𝑁 =4case.
βˆ’5 βˆ’4 βˆ’3 βˆ’2 βˆ’1 0 1 2 3
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
SNR (dB)
P
d2
1S (single stage)
1P (single platform)
2SD
SW0 NP 2SD (MC)
P
fa1
= 1eβˆ’1
P
fa1
= 1eβˆ’2
P
fa1
= 1eβˆ’3
Fig. 5. Detection performance curves for a practical 2SD and the SW0 NP
2SD illustrating how 𝑃
𝑑2
varies with target SNR for the 𝑁 =8case.
It is interesting to note that in both the 𝑁 =4and 𝑁 =8
cases the performance of the sub-optimal linear detector is
close to that of the optimal one.
V. C
ONCLUSION
We have examined the two-step detection scheme that arises
when practical data-rate limits are imposed on the Cooperative
Networked Radar implementation of statistical MIMO radar.
We have complimented our Swerling 2 NP two-step detection
results presented in [4] and derived the Neyman-Pearson two-
step detection rule in the case when the underlying target
model is Swerling 0 (4), which is non-linear and requires a
priori knowledge of the target SNR.
Due to the complexity of implementing the Swerling 0 NP
two-step detector our SW0 performance results are based on a
practical linear detector (7), where the thresholds are selected
by assuming the target is Swerling 2 [4] .
We have presented an approximation for the overall proba-
bility of detection for the Swerling 0 target model when using
a linear two-step detection rule by using a shifted Gamma
density and moment matching.
Our results echo those in [4] and indicate that the data rates
in a distributed detection system can be reduced by several
orders of magnitude using the two-step detection scheme
without fully compromising the detection capability of the
distributed sensor system.
Additionally, the results presented in Subsection B indicate
that the performance of the linear detector is very close to
optimal. Thus, we should expect the linear detector (with
thresholds selected by assuming the target is SW2), to perform
close to optimal over a range of fluctuating target models.
In future work we plan to compliment the SNR sensitivity
results in [4] by investigating the loss in detection capability
from using the linear detection scheme over the true optimal
NP detection rule for the Swerling 0 target model.
A
CKNOWLEDGMENT
The third author was partially supported by NSF DMS
0807896 and DMS 1109498.
R
EFERENCES
[1] J. Li and P. Stoica, Signal Processing for MIMO Radar, New Jersey:
Wiley, 2008.
[2] Haimovich, A.M., Blum, R.S., and Cimini, L.J., ”MIMO Radar with
widely Separated Antennas”, IEEE Signal Processing Magazine,Jan
2008.
[3] M.A. Zatman, ”Cooperative Networked Radar,” in Proc. Tri-Service
Radar Symposium, July 2008.
[4] Scharrenbroich, M.F., Zatman, M.A., Balan, R.V., ”Cooperative Radar
Techniques: The Two-Step Detector”, Asilomar Conf. Signals, Systems,
Computers, Asilomar, 2011
[5] Swerling, P., ”Probability of detection for fluctuating targets,” Information
Theory, IRE Transactions on, vol.6, no.2, pp.269-308, April 1960.
[6] Richards, M., Fundamentals of Radar Signal Processing, McGraw-Hill,
New York 2005.
[7] S.M. Kay, Fundamentals of Statistical Signal Processing-II, Prentice-Hall,
New Jersey 1998.
[8] Marchand, E., 1996, ”Computing the Moments of a Truncated Noncentral
Chi-Square Distribution”, Journal of Statistical Computation and Simu-
lation, 55: 1, 23-29.
Citations
More filters
Book Chapterβ€’DOIβ€’
29 Jan 2008

24Β citations

Journal Articleβ€’DOIβ€’
TL;DR: It is proved that the proposed detection algorithm has 2 dB signal-to-interference-plus-noise power ratio improvement on average in detection performance at a low computation and communication cost over conventional detection algorithms.
Abstract: In this study, a constant false alarm rate (CFAR) decision scheme is devised for frequency diversity multiple-input-multiple-output (MIMO) radar. Under the assumption that there exists not only the unstructured disturbance but also the structured interference, a double threshold detector (DT-MGLRT) based on the modified generalised likelihood ratio test (MGLRT) algorithm is proposed, of which the first stage deals with the unknown parameters and the second stage determines the final decision. It is proved that the proposed detector possesses a CFAR with respect not only to the unknown spectral properties of the unstructured disturbance but also to the structured interference distribution. Finally, some experiment results indicate that the proposed detection algorithm has 2 dB signal-to-interference-plus-noise power ratio improvement on average in detection performance at a low computation and communication cost over conventional detection algorithms.

3Β citations

Patentβ€’
23 Mar 2016
TL;DR: In this paper, a radar target detection method under the constraint of the data transmission rate is proposed, and the method comprises that echo data of a multistatic radar system is obtained, and observation vectors of all space diversity channels are obtained; self-adaptive coupling filtering is carried out on the observation vectors to obtain local examination statistics of each space diversity channel, the local false alarm probability is calculated, and if the global examination statistics are greater than the second threshold, the multi-system system determines a target exists in a detection unit.
Abstract: The invention discloses a radar target detection method under the constraint of the data transmission rate, and belongs to the technical field of radars. The method comprises that echo data of a multistatic radar system is obtained, and observation vectors of all space diversity channels are obtained; self-adaptive coupling filtering is carried out on the observation vectors to obtain local examination statistics of each space diversity channel; the data transmission rate of each space diversity channel is obtained, the local false alarm probability of each space diversity channel is calculated, and a first threshold is determined; the local examination statistics of each local examination statistics is compared with the first threshold, and local examination statistics greater and lower than the first threshold are determined; the global examination statistics are obtained; the global false alarm probability is obtained, and a second threshold is determined according to the global false alarm probability; and if the global examination statistics are greater than the second threshold, the multistatic radar system determines a target exists in a detection unit. The radar target detection method can reduce the data transmission amount between local radar stations and a fusion center.

3Β citations

Journal Articleβ€’DOIβ€’
TL;DR: In this paper , a low-communication-rate spatial alignment in range-Doppler domain is proposed for networked radars without the prior spatial information (positions and attitudes) of radars, which is different from the existing methods in the trajectory domain or echo domain for alignment.
Abstract: Abstract An important prerequisite for the radar network detection is that the measurements from local radars are transformed to a common reference frame without systematic or registration errors. For the signal level alignment, only partial signals are available for global decision-making due to power and bandwidth limitations. In this paper, a low-communication-rate spatial alignment in range-Doppler domain is proposed for networked radars without the prior spatial information (positions and attitudes) of radars, which is different from the existing methods in the trajectory domain or echo domain for alignment. To reduce the radar-to-fusion-center communication-rate, the method of initial constant false alarm rate detection is used to censor the signals in range-Doppler domain from local radars. Based on the spatial alignment model for the networked radars in geometry, a maximization problem is formulated. The objective function is the cross-correlation between the range-Doppler domain signals from different local radars. The optimization problem is solved by a genetic algorithm. Simulation results show that the rotation matrix and translation vector are estimated, and the detection probability of the proposed algorithm is improved after alignment and fusion compared with state-of-art methods.

1Β citations

Journal Articleβ€’DOIβ€’
TL;DR: In this article , a low-communication-rate spatial alignment in range-Doppler domain is proposed for networked radars without the prior spatial information (positions and attitudes) of radars, which is different from the existing methods in the trajectory domain or echo domain for alignment.
Abstract: Abstract An important prerequisite for the radar network detection is that the measurements from local radars are transformed to a common reference frame without systematic or registration errors. For the signal level alignment, only partial signals are available for global decision-making due to power and bandwidth limitations. In this paper, a low-communication-rate spatial alignment in range-Doppler domain is proposed for networked radars without the prior spatial information (positions and attitudes) of radars, which is different from the existing methods in the trajectory domain or echo domain for alignment. To reduce the radar-to-fusion-center communication-rate, the method of initial constant false alarm rate detection is used to censor the signals in range-Doppler domain from local radars. Based on the spatial alignment model for the networked radars in geometry, a maximization problem is formulated. The objective function is the cross-correlation between the range-Doppler domain signals from different local radars. The optimization problem is solved by a genetic algorithm. Simulation results show that the rotation matrix and translation vector are estimated, and the detection probability of the proposed algorithm is improved after alignment and fusion compared with state-of-art methods.
References
More filters
Bookβ€’
16 Mar 2001

7,058Β citations

Journal Articleβ€’DOIβ€’
TL;DR: It is shown that with noncoherent processing, a target's RCS spatial variations can be exploited to obtain a diversity gain for target detection and for estimation of various parameters, such as angle of arrival and Doppler.
Abstract: MIMO (multiple-input multiple-output) radar refers to an architecture that employs multiple, spatially distributed transmitters and receivers. While, in a general sense, MIMO radar can be viewed as a type of multistatic radar, the separate nomenclature suggests unique features that set MIMO radar apart from the multistatic radar literature and that have a close relation to MIMO communications. This article reviews some recent work on MIMO radar with widely separated antennas. Widely separated transmit/receive antennas capture the spatial diversity of the target's radar cross section (RCS). Unique features of MIMO radar are explained and illustrated by examples. It is shown that with noncoherent processing, a target's RCS spatial variations can be exploited to obtain a diversity gain for target detection and for estimation of various parameters, such as angle of arrival and Doppler. For target location, it is shown that coherent processing can provide a resolution far exceeding that supported by the radar's waveform.

1,927Β citations


Additional excerpts

  • ...When individual sensor platforms are aggregated to improve sensitivity, such as in statistical MIMO radar [1], [2], [3], the aggregate data rate can saturate both the communication and computational capacity of the system....

    [...]

Bookβ€’
01 Jan 2005
TL;DR: This revised edition of Fundamentals of Radar Signal Processing provides in-depth coverage of radar digital signal processing fundamentals and applications and has been updated to include coverage of measurement accuracy and target tracking.
Abstract: This detailed guide clearly and concisely presents radar digital signal processing for both practicing engineers and engineering students. This revised edition of Fundamentals of Radar Signal Processing provides in-depth coverage of radar digital signal processing (DSP) fundamentals and applications. It has been updated to include coverage of measurement accuracy and target tracking. Additionally, to make it more useful as a teaching tool, it now includes end-of-chapter problems and a solutions manual. New to this Edition: New chapter on Measurement Accuracy and Target Tracking Two new appendices--Important Digital Signal Processing Facts; Important Probability Density Function and Their Relationships Addition of 20 to 30 problems to ends of chapters Solutions manual

1,765Β citations

Journal Articleβ€’DOIβ€’
TL;DR: The investigation shows that, for these fluctuation models, the probability of detection for a fluctuating target is less than that for a non-fluctuating target if the range is sufficiently short, and is greater if therange is sufficiently long.
Abstract: This report considers the probability of detection off a target by a pulsed search radar, when the target has a fluctuating cross section. Formulas for detection probability are derived, and curves off detection probability vs, range are given, for four different target fluctuation models. The investigation shows that, for these fluctuation models, the probability of detection for a fluctuating target is less than that for a non-fluctuating target if the range is sufficiently short, and is greater if the range is sufficiently long. The amount by which the fluctuating and non-fluctuating cases differ depends on the rapidity of fluctuation and on the statistical distribution of the fluctuations. Figure 18, p. 307, shows a comparison between the non-fluctuating case and the four fluctuating cases considered.

633Β citations


"Performance of a practical two-step..." refers methods in this paper

  • ...In this section we complement the SW2 results in [4] by presenting the NP two-step detection rule for the Swerling 0 (SW0) [5] target model....

    [...]

  • ...In [4] the Neyman-Pearson (NP) two-step detection rule (2SD) for the Swerling 2 (SW2) [5] fluctuating target model was derived and was shown to be clairvoyant [7] because of its dependence on a priori knowledge of the unknown target SNR....

    [...]

Book Chapterβ€’DOIβ€’
29 Jan 2008

24Β citations

Frequently Asked Questions (2)
Q1. What contributions have the authors mentioned in the paper "Performance of a practical two-step detector for non-fluctuating targets" ?

In this paper the authors analyze a two-step detection scheme for use in distributed sensor systems ( e. g. statistical MIMO radar ).Β The authors present the Neyman-Pearson ( NP ) two-step detection rule for a non-fluctuating target model ( Swerling 0 ), which is non-linear and requires a priori knowledge of the target SNR.Β The authors then analyze the performance of a practical two-step detection rule under the non-fluctuating target model.Β 

In future work the authors plan to compliment the SNR sensitivity results in [ 4 ] by investigating the loss in detection capability from using the linear detection scheme over the true optimal NP detection rule for the Swerling 0 target model.Β