Feasibility of Air Target Detection Using GPS as a Bistatic Radar

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Journal of Global Positioning Systems (2006)

Vol. 5, No. 1-2:119-126

Feasibility of Air Target Detection Using GPS as a Bistatic Radar

E. P. Glennon

SigNav Pty Ltd, Unit 2, 59 Tennant St, Fyshwick, ACT 2609, Australia

A. G. Dempster and C. Rizos

University of New South Wales, Sydney, NSW 2052, Australia

Abstract. The feasibility of using GPS as a bistatic radar

illuminator for the purposes of air target detection is

examined. The power budget analysis is first performed

assuming the use of a single satellite, but is followed by a

discussion of the expected improvements when multiple

satellites are employed. The analysis includes the effect

of GPS signal strength dynamic range, also known as the

‘near-far’ problem. The difference between the radar

cross-section (RCS) of a typical air target and ground-

based clutter reflections is discussed, followed by an

estimation of the effect of ground clutter on the operation

of such a system.

Keywords. Bistatic radar, Global Positioning System,

radar detection,

1 Introduction

The Global Positioning System has found widespread

application beyond standard positioning and timing, with

new uses for GPS continually being developed. One of

the more novel concepts is the secondary use of GPS

signals for remote sensing, with the secondary application

considered in this paper concerning the use of GPS

satellite transmissions as the transmitter in a bistatic-radar

for air target detection. Previous publications on this

topic include (Tsui and Shaw, 1993) and (Koch and

Westphal, 1995), although neither of those publications

provides a power budget confirming the feasibility of the

system. (Stolk and Brown, 2003) describes an airborne

GPS remote sensing system capable of detecting large

ocean vessels such as oil-tankers. Another paper by

(Cherniakov et al., 2002) does provide a power budget

estimate for air target detection, but assumes the use of

the higher-powered IRIDIUM satellite system as the

transmission source. Although the methodology of

Cherniakov et-al (2002) has been adapted to the GPS case

by (Mojarrabi et al., 2002), that analysis contained some

errors. This paper duplicates the analysis of original

Mojarrabi paper using a conventional approach and

different parameter selections, resulting in less optimistic

estimates for the maximum detection range.

The paper also estimates the effect of clutter in a GPS

bistatic radar using a different technique to the methods

of (Mojarrabi et al., 2002) and (Cherniakov et al., 2002).

In addition, the effectiveness of using multiple GPS

satellites on the power budget is also examined and

difficulties due to the ‘near-far’ problem are discussed.

2 Bistatic GPS Power Budget

To determine the maximum range of a GPS-based bistatic

radar it is necessary to determine the signal power that

reaches the receiving antenna after being reflected from

the target. For any radar, the power density of the target

echo Sr at the receiver is given by (Skolnik, 1981):

⎟

⎠

⎞

⎜

⎝

⎛

⎟

⎠

⎞

⎜

⎝

⎛

=22 44 ti

rRR

(1)

Here Pt is the transmitted power (W), Gt is the transmitter

antenna gain (dimensionless factor), Ri is the range from

the transmitter (satellite i) to the target (m),

is the radar

cross-section (RCS) of the target (m2) and Rt is the range

of the target from the receiver (m). The RCS is defined

as the fictional area

that produces the observed

reflected power density Sr at a receiver at a range R from

the target that has been illuminated with an incident

power density of Si (Skolnik, 1981).

⎟

⎠

⎞

⎜

⎝

⎛

∞→

4lim

πσ

(2)

120 Journal of Global Positioning Systems

The first term of the product in (1) is the power density of

the direct (transmitted) signal at the target Sdirect prior to

being reflected (units of W/m2).

The signal power available at the receiver antenna output

depends on the effective area of the receiving antenna Ae,

which depends on its gain:

A= (3)

where Gr is the receiver antenna gain and λ is the GPS

carrier frequency wavelength of 0.19 m. Using (1) and

(3) the power of the target reflection available at the

receiver antenna output can be calculated as:

⎟

⎠

⎞

⎜

⎝

⎛

⎟

⎠

⎞

⎜

⎝

⎛

directr

SP (4)

(4) permits the attenuation of the reflected signal meas-

ured using a high gain antenna relative to a standard

directly received GPS signal as would be received in an

omni-directional antenna with a gain of G0dBi to be

calculated:

⎟

⎠

⎞

⎜

⎝

⎛

⎟

⎠

⎞

⎜

⎝

⎛

dBi

direct

(5)

To calculate the maximum range of such a system it is

necessary to determine the noise level N0 at the output of

the RF front-end, which can be given in terms of the

equivalent noise temperature Teff and the bandwidth BW

as:

BWTkN eff

0 (6)

(4) and (6) allow the signal-to-noise ratio of the reflected

signal at the RF front-end output to be written as:

()

BWTkR

efft

rdirect

λσ

= (7)

If the subsequent signal processing is then subject to

losses Lsp and processing gain Gsp then the final signal to

noise ratio

is given by:

()

spefft

sprdirect

LBWTkR

GGS

λσ

= (8)

Assuming a minimum value for the detection signal-to-

noise ratio permits an expression for the maximum range

to be given as:

()

speff

sprdirect

tLBWTk

GGS

min

ρπ

λσ

= (9)

Using values for

of 20 m2, a horn antenna with a gain

Gr of 15 dB (31.62) and a range Rt of say 10km, the

reflected signal will be attenuated by about 62 dB, where

this combination of parameters have been selected to

agree with (Mojarrabi et al., 2002). Hence, if the direct

signal has a signal-strength of say 52 dBHz or -152 dBW,

then the reflection from the target will have a signal level

of –10 dBHz or –215.2 dBW. Since the current state of

the art in GPS receiver technology is to detect and track

signals at around 20 dBHz, the detection of such a

reflection is extremely difficult.

However, since such weak signal GPS receivers have

typically been targeted for the E911 cellular application,

some of the constraints present in the E911 case do not

occur in the GPS bistatic radar application thereby

permitting greater sensitivity to be achieved. In particu-

lar, since a bistatic GPS radar has simultaneous access to

both the direct and indirect signals, the data received

from the direct signal can be used to strip the data bits

from the indirect signal, thereby permitting significantly

longer coherent integration than the GPS data bit period

of 20 ms. Appendix A (Van Diggelen, 2001) shows that

for a coherent integration period of 1000 ms a maximum

sensitivity of approximately -190 dBW or 13.2 dBHz is

to be expected, assuming a final SNR of about 9.3 dB.

This represents an attenuation of 38 dB compared to the

typical maximum received signal of 52 dBHz, as is the

case using a typical 3 dBi patch antenna. To calculate the

range that this corresponds to, (4) can be used, setting

Pr/Pdirect to -38 dB (158.48×10-6), G0dBi to 3 dB (2), and

using the previous values for

and Gr, a value for Rt of

398m is obtained.

Alternatively, using (8) with the values given in Table 1

results in a maximum range of 239m. This value is lower

than the previous value because it uses the minimum

specified power spectral density for GPS of

-134 dBW/m2 (Spilker, 1996), whereas GPS satellites

typically exceed the minimum level of performance. If

the value for Gr is increased to 35 dBi (3481), which is

equivalent to an antenna with effective area of

Table 1. Maximum Range Estimation Parameter Values

Parameter Units Values

Sdirect W/m2 39.81×10-15

Sdirect dBW/m2 -134

2 20

Bandwidth Hz 2.4×106

Teff K 344

m 0.19

Gsp n/a 2.046×106

Lsp n/a 2.11

Gr n/a 31.62

k 1.38×10-23

Rmax m 239

Glennon et al.: Feasibility of Air Target Detection Using GPS as a Bistatic Radar 121

3.6m×3.6m (as used in (Cherniakov et al., 2002), then

Rmax increases to 2.51km.

3 Bistatic Radar / Multipath Paradox

The difficulty in detecting an air target reflection occurs

because the power loss following reflection from the

target is extremely high. This fact presents an apparent

contradiction; which is how GPS multipath signals can

ever be detected since in theory they should be signifi-

cantly attenuated. The explanation is that there are

essentially two types of reflections from a surface,

namely specular reflections and diffuse reflections

(Katzberg and Garrison, 1996). Multipath reflections are

generally specular in nature, in which phase coherence is

retained during the reflection process. However, reflec-

tions from an air target are generally diffuse reflections in

which any incident radiation is scattered in multiple

directions and phase coherence is lost.

This means that the RCS in the direction corresponding

to a specular reflection is significantly greater than in the

other directions, which are diffuse. This observation

applies to both targets and clutter reflectors and is

apparent on plots of RCS versus angle of incidence

(Skolnik, 1981). Hence when a standard GPS receiver

observes a multipath signal it generally corresponds to a

specular reflection.

4 Clutter Power Estimate

The clutter power that is observed in a GPS bistatic radar

system is dependent on the operating environment and

the system characteristics. One factor under control of

the designer is the receiving antenna. For this case, a

suitable antenna is one in which there is high directivity

and gain in a particular direction, but has small antenna

sidelobes and gain in all other directions. The polariza-

tion of the antenna should be tuned to best match the

polarization of the reflections and as such, will probably

be left hand circular polarized (LHCP) which is opposite

to the RHCP of the direct GPS signal. Clutter power is

assumed to enter the system via the antenna sidelobes

only, an assumption that is also made in (Cherniakov et

al., 2002). The effect of observing the direct signal in the

antenna main lobe is a more difficult issue that is

separately considered in a subsequent section.

This analysis employs a simple antenna model in which

the boresight gain Gr and beamwidth

bw are constant and

the sidelobe gain Grsl is constant and omni-directional.

The model does not include realistically-shaped antenna

sidelobes and is only intended for a first order analysis.

When calculating the clutter for a GPS bistatic radar,

recall that GPS is a spread spectrum system with a

chipping rate of fc (1.023 MHz) and hence has a range

resolution dRc of c/ fc, where c is the speed of light. For

this reason, the clutter will generally be range limited by

the GPS range resolution of 293m. Assuming that all

clutter is due to diffuse ground reflection, the power

received at the antenna within a particular range cell Rt

can be calculated as the power reflected by the area

between the isorange contours on the ground starting at a

range Rt and ending at R+dRc and adjusted for the free

space loss of 1/(4

2). Using this procedure, the clutter

power density at the receiving antenna can be given as

⎟

⎠

⎞

⎜

⎝

⎛+=

edirectC R

SS 1log

(10)

where

0 is the RCS of the clutter per unit area and which

is typically a function of the grazing angle, although for

this analysis is taken to be constant. A derivation of this

result is given in Appendix B.

The power of the clutter at the receiver antenna output

can now be given as:

⎟

⎠

⎞

⎜

⎝

⎛

⎟

⎠

⎞

⎜

⎝

⎛+=

1log

rsl

edirectC

SP (11)

This permits the clutter-to-target power ratio at the

receiver antenna output to be given as:

rsl

dRR

⎟

⎠

⎞

⎜

⎝

⎛

≈

⎟

⎠

⎞

⎜

⎝

⎛+

⎟

⎠

⎞

⎜

⎝

⎛

σπ

1log

(12)

Table 2 gives the clutter-to-target power ratio for various

values of

0, Rt and Grsl. The

0 values of -20 dB and

-2 dB are taken from (Willis, 1995) and correspond to

data for “out-of-plane, horizontally polarized,

0 data for

tall weeds and scrub trees” measured at a frequency of

1.3 GHz, a value that is close to the GPS carrier fre-

quency of 1.57542 GHz. The maximum value for this

parameter is about -2 dB corresponding to a specular

reflection, while the typical value is about -20 dB. The

minimum value is about -30 dB. All data is for bistatic

mode of operation. The sidelobe gain values for Grsl are

Table 2. Clutter-to-Target Power Ratio

σ0(α)(dB) Grsl (dB) Rt (m) PC/ Pr (dB)

-20 0 1,000 -0.36

-20 -10 1,000 -10.36

-20 -10 5,000 -3.37

-20 -10 10,000 -0.36

-2 -10 1,000 7.64

-2 0 1,000 17.64

122 Journal of Global Positioning Systems

estimates only. Values for Gr and

have been chosen as

30 dB and 20 m2 respectively to match the previous

section and dRc has been set at 293m.

This data shows that even for relatively short ranges, the

clutter contains almost as much power as the target radar

return. The situation can be improved by reducing the

magnitude of the antenna sidelobe gain. However,

occasionally it will be possible that ‘specular’ type clutter

will occur that will completely dominate over the target

reflection.

One factor that has not been taken into account is the

clutter Doppler frequency, where the analysis assumes

that the clutter will have the same Doppler offset as the

target. This is not realistic for air targets thereby enabling

the option of using Moving Target Indicator (MTI) to

separate the target from the clutter. The use of MTI is

consistent with the use of long coherent integration and

its associated narrow bandwidths required for the

detection of very weak signals. Proper analysis of the

MTI improvement is beyond the scope of this paper and

in the case of GPS, care must be taken since the Doppler

frequency return varies with distance from the receiver.

5 GPS ‘Near-Far’ Problem

Cross-correlation or the ‘near-far’ problem occurs when

trying to detect weak GPS signals in the presence of other

strong GPS signals. Due to the use of 10-bit Gold codes,

the dynamic range of the GPS C/A code is normally

limited to signal levels that are no more than 21.6 dB

weaker than the strongest signal present (Spilker, 1996).

Since the target signal reflections that need to be detected

by a GPS-based bistatic-radar are significantly weaker

than the strongest signals present, this presents a clear

limitation that must be addressed. There are several

methods that could be used to suppress the strong GPS

signals. One method is to employ a highly directional

high-gain antenna that has very low-gain sidelobes,

although this will probably result in the strong signal

suppression of between 30 to 40 dB, assuming the

antenna gain is about 30 to 40 dB above the sidelobes.

However, it has already been shown that target echoes

could easily be attenuated by approximately 60 dB

compared to the main signal, so unless additional cross-

correlation mitigation techniques are employed reliable

detection of the reflections is unlikely. Such techniques

range from cancellation to subspace projection techniques

(Madhani et al., 2003; Glennon and Dempster, 2004;

Glennon and Dempster, 2005), although no commercial-

off-the-shelf GPS chipsets currently implement cross-

correlation mitigation therefore leaving software correla-

tion as the only viable alternative. Cross-correlation

mitigation represents a challenging problem and has

applications for weak signal GPS receivers in general,

although since these techniques are not in widespread use

it is difficult to estimate their effectiveness.

One interesting case that can arise is when the target

happens to lie in the line-of-sight of a GPS satellite.

Clearly the receiving antenna offers no protection against

cross-correlation since the both reflection and direct

signal are amplified equally. However, from a bistatic

radar point of view this case is significant for another

reason, namely the forward scatter RCS of the target

experiences significant enhancement compared to the

typical value. The forward-scatter RCS

F for a target is

given by (Willis, 1995):

F= (13)

where A is the target shadow area. If (13) is substituted

into (4), then the power reflected by the target and

received by the receiver can be expressed as:

directr GA

SP2

⎟

⎠

⎞

⎜

⎝

⎛

(14)

Assuming that the direct signal is not significantly

attenuated due to blockage by the target, then the direct

received signal power at the antenna output is:

⎟

⎠

⎞

⎜

⎝

⎛

directdirect

SP (15)

and the ratio of the reflected to the direct signal is:

direct

P= (16)

It should also be noted that according to (Koch and

Westphal, 1995) this assumption about the direct signal

not being attenuated may not be entirely true. This is

because the target size could be comparable to the size of

the first Fresnel zone, this being the size at which

significant RF blockage becomes apparent. If this is the

case then it means that better results than the above

analysis predicts may be expected.

The other difficulty with this particular scenario is that

the path difference between the direct path and the

reflection will be smaller and unless it exceeds one GPS

chip (293m), separation of the two signals will be

difficult. The geometry of this scenario also means that

the velocity of the target cannot be determined since the

Doppler difference between the direct and indirect path is

small.

Using a value for A of 5 m2 and a value for Rt of say

10km, the attenuation of the reflection compared to the

direct signal comes out at about 51.6 dB. As a result,

although the forward scatter enhancement of the RCS is

Glennon et al.: Feasibility of Air Target Detection Using GPS as a Bistatic Radar 123

quite significant (

is 26 dB), the benefit is partially

cancelled by the loss of the antenna directivity and gain

in reducing the direct signal.

This analysis shows that the forward scatter RCS

enhancement advantage may not be as beneficial as

expected and is still very much dependent on the proper-

ties of the receiving antenna system. This is because the

forward scatter RCS effect typically takes place when the

bistatic angle is within 10° of the 180° ideal angle. This

means that for an extremely narrow antenna beam-width

it would still be possible to gain some of the advantage of

the enhanced RCS while still gaining the benefit of some

reduction in the direct signal. However trying to analyze

a case such as this using the simple antenna model

employed in this paper clearly represents a limitation of

this approach, with a proper analysis of this particular

case requiring a particular antenna and target RCS profile

be employed.

The GPS front-end chip may also fail to operate correctly

if the input signal levels exceed its design parameters.

6 Use of Multiple Satellites

Up to this point the analysis has assumed the use of a

single GPS satellite and a single GPS receiver. However,

the number of visible satellites varies from a minimum of

about four to a maximum of about twelve satellites and

this presents an opportunity to improve performance.

Figure 1 shows the system geometry for a GPS bistatic

radar as well as an illustration of one of the correlations

that could be expected (neither to scale). The difficulty in

using multiple satellites arises because although the range

from the target to the receiver is the same for all satel-

lites, the multipath delay between the direct path and the

reflected path is not. For the example, the multipath

delay for SVi would be expected to be larger than for SVj

which is closer to the line-of- sight (LOS).

If the range vectors from the receiver to satellite i, the

target to satellite i and the receiver to the target are

denoted by Rrsi, Rtsi and Rrt respectively and the bistatic

angle is given by βi, then the multipath delay c

∆

t between

the direct path and the reflected path is given by:

)2(cos2

)cos(

irt

rtirt

rtrsitsi

dtc

⋅⋅=

+⋅=

+−=

+=∆

RRR

(17)

(17) makes it possible to predict the multipath delay for a

given target range and bistatic angle (the angle between

the transmitter and receiver measured at the target).

Since the range from the target to the receiver is fixed

across all satellites and the bistatic angle is constant for a

given satellite on a particular target LOS vector, it is

possible to scale the correlation outputs for each satellite

so that the target delays are the same for all satellites.

Provided this is done after removal of the direct signal (to

remove the effect of local correlation peaks and cross-

correlations), it should be possible to accumulate the

scaled correlation outputs from all satellites together.

The most straightforward method of accumulating

correlations across multiple satellites is to do so non-

coherently by first taking magnitudes of the complex

correlation outputs. The improvement that is to be

expected can be approximated by assuming that use of

Nsv satellites each with power spectral density Sdirect is

equivalent to the use of a single satellite with power

spectral density Nsv×Sdirect. Unfortunately this approach

suffers from the problem of non-linear integration loss

(Barton, 1969; Lin et al., 2002), where the magnitude of

the loss depends on the signal detectability-factor (signal-

to-noise ratio) as well as the number of non-coherent

integrations performed. A plot of integration loss versus

number of integrations for different output single-pulse

detectability factors D0(1) can be found in (Barton, 1969)

and is reproduced below in Figure 3.

tsi

Direct Path

rsi

Indirect Path

Receiver r

Target t

Fig. 2 Delay Path Length

GPS SVi

GPS SVj

Rtsi

Direct Path

Rrsi

Indirect Path

Rrt

Receiver

Target

Rrsj

Rtsj

Correlation

Delay

(Chips)

Direct

Correlation

Target

Correlation

Rrsj

Fig. 1. System Geometry & Correlation Curves

124 Journal of Global Positioning Systems

To obtain the integration loss Li, the detectability factor

D0(1) that provides required probability of false-alarm Pfa

and probability of detection Pd for a single pulse detector

is determined using Rayleigh-Rice probability distribu-

tion curves. The loss caused by obtaining this quantity

through integration of multiple pulses can then be

determined by interpolating the curves given in Figure 4

for the given value of D0(1) and then reading the loss

corresponding to the number of non-coherent integrations

n. For the multiple GPS satellite case, the value of n will

range from between 4 and 12, while for a Pfa of less than

10-6 and a Pd of greater than 0.9 a D0(1) value of greater

then 13 dB is required (Barton, 1969). These combina-

tions of parameters imply an integration loss of less than

2 dB.

Depending on the signal strength of the target reflection,

this accumulation across multiple satellites should result

in improved detectability. More importantly however,

with the use of multiple satellites the bistatic angle for

one of the satellites may be more favourable, leading to a

better RCS, also improving the probability of detection.

It is probably not possible to perform a fully coherent

integration across multiple satellites since the phase

coherence of the signal is unlikely to be retained during

the diffuse reflection process. As a result, the integration

losses of the non-coherent process probably cannot be

eliminated.

7 Conclusions

This analysis has shown that due to the extreme weakness

of the transmitted GPS signal, detection of targets with

small RCS using receive antennas of gain 15 dB is

probably not feasible. Other problems that need to be

overcome involve the ‘near-far’ problem caused by the

dynamic range of the received GPS signals and the

problem of the received ground clutter power having a

greater power level than the target reflection. Given

these difficulties, the following recommendations are

suggested if construction of such a system is to be

undertaken.

Firstly, the gain of the receive antenna should be as large

as possible. The worked example used a horn antenna

with a gain of 15 dB, however it should be possible to

achieve a gain of say 25 dB which would increase the

maximum range by a factor of 3. Secondly extremely

long coherent integration periods of approximately 1 to 2

seconds using full data-wiping should be employed.

Thirdly, the method of non-coherently combining the

output from all the available satellites should be imple-

mented. Since there are generally at least 6 satellites

visible and sometimes as many as 12, this would proba-

bly increase the maximum range by a further factor of 1.5

to 3, depending on the squaring loss. GPS signal

cancellation techniques need to be developed in order of

mitigate against the ‘near-far’ problem.

Use of the system could also be limited to detection of

larger targets (with larger RCS) thereby also increasing

the detection range, although if a sufficient number of

satellites are present then some may have a more favour-

able geometry than others resulting in a better RCS in

these circumstances.

In conclusion, it has been shown that implementing a

GPS-based bistatic radar for the purposes of target

detection is significantly constrained by the available

power budget. These constraints explain why the patent

(Tsui and Shaw, 1993) and early-published papers (Koch

and Westphal, 1995) do not appear to have resulted in

any follow-on work. However, it is possible that use of

the suggestions outlined above and the availability and

use of new GNSS signals could permit construction of a

workable system, albeit one with limited maximum

range.

Appendix A: Maximum GPS Sensitivity

To estimate the maximum sensitivity of a GPS receiver it

is first necessary to estimate the noise figure of the RF

front-end (Figure 4) using the Friss formula (Van

Dierendonck, 1996). Table 3 shows the resulting noise

figure and effective temperature at each stage of the

process with typical values for the gain, loss and noise

figures. The end result is a total noise figure NFT of

2.4 dB and effective temperature Teff of 344 K assuming

an antenna source temperature TA of 130 K.

Using the effective temperature of the front-end (FE) and

assuming availability of the full GPS navigation message

to enable data wiping on the detected signal and hence

enabling long coherent integration, the ability to detect

various signal levels can be established. Table 4 (Van

Diggelen, 2001) shows that with a very weak input signal

of -160 dBm at the antenna output and using a 1 second

No Of Integrated Pulses n

Integration Loss Li (dB)

Integration Loss Li (dB) vs No of Integrated Pulses n (given D0(1))

20 dB

18 dB

16 dB

14 dB

12 dB

10 dB

08 dB

06 dB

04 dB

00 dB

Fig 3. Non-coherent integration loss for a given number of

integration periods.

Glennon et al.: Feasibility of Air Target Detection Using GPS as a Bistatic Radar 125

coherent integration period with full data wipe, the output

signal to noise ratio is 9.3 dB and therefore at the limit of

detectability.

NF1

Ta2 bit

digital

Loss

NF3

NF2

Fig. 4 RF Front-End

Table 3. Front-End Noise Figure

L1 G1 L2a L2b G2 FE

Gain (dB) 0.10 19.0 6.0 3.00 19.0

Gain 0.98 79.4 0.3 0.50 79.4

Total Gain 0.98 77.6 19.5 9.8 776

NF (dB) 0.10 1.9 6.0 3.0 1.9 9.0

F = 10NF (db) / 10 1.02 1.6 4.0 2.0 1.6 7.9

Total FT 1.02 1.6 1.6 1.7 1.7 1.7

Total NFT (dB) 0.10 2.0 2.1 2.3 2.4 2.4

Teff =TA+

(FT-1) T0

137 300 311 326 342 344

Table 4. Maximum GPS Sensitivity

Parameter Value Notes

Antenna OP (dBm) -160.0 Signal at Antenna Output

Antenna OP (dBHz) 13.23 AntOP–30+10 log10(kTeff)

IF Bandwidth (MHz) 2.40 Typical RF FE is 2.4 MHz

within 3dB.

Teff (K) 344.40 FE effective temperature

Noise power (dBm) -109.43 10 log10 (k Teff BW) + 30

IF SNR (dB) -50.57 Ant OP - Noise power

Input Bandwidth (MHz) 2.046

Coherent Period (ms) 1000.0 Coherent integration

Output Bandwidth (Hz) 1.00 1/Coherent Integration

Coherent Gain 1430.4 √(Input BW/Output BW)

Coherent Gain (dB) 63.1 20 log10(Coherent Gain).

Mistuning Loss (dB) 2.0 Correlation&Mistuning loss

Quantization Loss (dB) 1.25 2-bit quantization Loss

Actual Gain (dB) 59.9 Coherent Gain – Losses

Final SNR (dB) 9.3 IF SNR + Actual Gain

Final SNR ( ratio) 2.91 Peak/sigma ratio = 10(dB/20)

Appendix B: Clutter Power Density Estimation

The clutter power density affecting a target at range Rt

can be estimated by integrating the power reflected from

the ground between the isorange contours, starting from

Rt and ending at Rt+dRc with a free-space loss-factor

weighting of 1/(4

2). This isorange contour can be

obtained for a given multipath delay c

∆

t using the

relationship (Stolk and Brown, 2003)

cos

rtrt

irtrt

kRR

⋅−=∆

where Rrt is the range vector from the receiver to the

target (clutter) , ki is the unit line-of-sight vector to the

satellite and βi is the (bistatic) angle between Rrt and ki.

Assuming a flat earth model with the receiver at the

origin, the multipath delay can be written as:

(

)

()

cos()cos()cos()sin()sin( )

cossin 0

coscos()cos()sincos()sin()

1cos()cos()

cc c

eaea e

ct RReaRea

ReaR

θθ

∆= −−

=− −=

where e is the satellite elevation, a is the satellite azimuth

and Rc and

are the range and angle from the receiving

antenna to the clutter respectively. Hence the isorange

clutter contour Iso(Rt) for a target at a range Rt occurs at a

clutter range Rc is defined by:

(

)

(

)

)cos()cos(1 aeRRIsoR ttc−

−

A clutter element at Rrt contributes dSC to the total clutter

power density, where

0 is the clutter RCS per unit area.

ddRR

dS cc

direct

Applying a change of variables from clutter range to

target range and then integrating dSc over the full

range

and a target range with the applicable range resolution

yields the total clutter power density as required:

()

⎟

⎠

⎞

⎜

⎝

⎛+=

∫

−−

∫∫

)(

1log

)cos()cos(1

cdirect

direct

dRR

direct

dRRIso

RIso

direct

dRS

dRR

Rae

dRae

ddRR

πθ

Note that the total clutter power density is independent of

satellite position despite the fact that this is not the case

for the isorange contours. A cross check for the case

where the bistatic illuminator is directly overhead can be

performed since in this case the isorange contours are

126 Journal of Global Positioning Systems

concentric circles around the antenna, yielding approxi-

mation (12).

Acknowledgement

This research was supported by the Australian Research

Council Discovery Project DP0556848. Comments by

Rod Bryant on the use of multiple satellites are also

gratefully acknowledged.

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