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Introduction Motivation and Objectives Array-based acquisition theory Array platform implementation Conclusions

Interference mitigation in GNSS signal acquisition throughantenna arrays

Dr. Javier Arribas

Centre Tecnologic de Telecomunicacions de Catalunya (CTTC)

Interference Management for Tomorrow’s Wireless NetworksNewcom# Summer School Sophia Antipolis - May 28-31, 2013



Overview

Introduction

Motivation and Objectives

Array-based acquisition theory

Array platform implementation

Conclusions


Introduction




Conclusions



Introduction to GNSS• Global Navigation Satellite Systems (GNSS) is the general concept used to

identify those positioning systems that enable the determination of the userposition and time by means of measured distances between the receiver and aset of visible satellites.

Figure: Position determination by GNSSs. Source: Kai Borre, Darius Plausinaitis,Reconfigurable GNSS Receivers, 2007.

(a) GPS (b)Galileo

(c)Glonass

(d)Compass

(e)IRNSS

(f)QZSS



GNSS signal structure

DS-CDMA transmitted signal for the i-th satellite:

sT,i(t) = eI,i(t)+ jeQ,i(t), (1)

where the subindex I and Q denote in-phase and quadrature component respectively,and are defined as:

eI,i(t) =√

2PI,i

∞

∑mI=−∞

bI,i(mI)

NcI

∑uI=1

LcI

∑kI=1

cI,i(kI)gI(t−mITbI −uITPRNI − kITcI ) (2)

with the following definitions for the I component - analogous for the Q component:• PI,i is the transmitted signal power.• bI,i(m) ∈ −1,1 is the sequence of telemetry bits, with TbI being the bit period.• cI,i(k) ∈ −1,1 is the Pseudo Random Noise (PRN) spreading sequence, with

the chip length of the codeword and the chip period defined as LcI and TcI ,respectively. TPRNI = LcI TcI is the codeword period. The number of codeepochs per telemetry bit is NcI .

• gI(t) is the energy-normalized chip shaping pulse.



Simplified receiver signal model

Considering only the LOSS contribution coming from Ms satellites and thepredominant propagation effects:

xRF(t) = ℜ

Ms

∑i=1

αi(t)sT,i(t− τi(t))ej2π(fc+fd,i(t))t

+n(t), (3)

where fc is the carrier frequency, θi = [αi(t), fd,i(t),τi(t)] are the complex amplitude,the Doppler frequency shift, and the time delay, respectively, which are the signalsynchronization parameters for the i-th satellite signal and n(t) is additive whiteGaussian noise plus other undesired terms (such as multipath or interferences).The implicit channel model is defined as Wide-Sense Stationary UncorrelatedScattering (WSSUS).



GNSS receiver block diagram

RFfront-end

ADC

AcquisitionAcquisition

Codetracking

Carriertracking

TLMdemod.

PVT

Userapplication

AGC

Satellite channels

GNSSantenna

Hardware based Hardware or software based

Figure: Simplified GNSS receiver high-level block diagram.



Acquisition operation

Target: provide a coarse estimation of the synchronization parameters vector θi foreach received satellite:

θi = [αi, fd,i, τi︸︷︷︸Grid Search

] (4)

Figure: Acquisition test function output vs. time-delay and Doppler-shift of a noise-free andnoisy Galileo-like MBOC(6,1,1/11) signal.



Acquisition parameters

Acquisition performance indicators

• Sensitivity• TTFFcold = Twarm−up +Tacq +Ttrack +TNAV+GST +TPVT

Performance degradation sources:• Signal attenuation: fading

and low level signalconditions.

• Interferences.

• Navigation message.• Receiver and satellite

movement.• Receiver sample clock drift.



GNSS Interference sourcesAmong the VHF and UHF spurious transmissions (DVB-T, TACAN, and DME), the adjacentfrequencies to GNSS links are populated as:

Band [MHz] Usage1435-1530 Mobile (aeronautical telemetry)1530-1545 Mobile-satellite (space-to-Earth)

Maritime mobile-satellite (space-to-Earth)1545-1549.5 Aeronautical mobile-satellite (space-to-Earth)

Mobile-satellite (space-to-Earth)1549.5-1558.5 Aeronautical mobile-satellite (space-to-Earth)

Mobile-satellite (space-to-Earth)1613.8-1626.5 Mobile-satellite (Earth-to-space)1626.5-1645.5 Mobile-satellite (Earth-to-space)1646.5-1651 Aeronautical mobile-satellite (Earth-to-space)1651-1660 Mobile-satellite (Earth-to-space)1668-1675 Meteorological aids (radiosonde)1700-1710 Meteorological-satellite (space-to-Earth)1710-1755 Mobile communications

Table: Sources and Services of image Interference for single-conversion GPS L1 / Galileo E1front-end [Wil02].

The proposed deployment of Lightsquared’s 4G communication network could create a newinterference situation specially when using the 1552.7 MHz band, as notified for the first timeby the U.S. NTIA to U.S. FCC in January 2011.


Introduction




Conclusions



Problem definition

• New and upgraded GNSSs are being used to provide safety-critical guidance:• Modernized GPS and forthcoming Galileo will provide integrity monitoring

mechanisms: RAIM, SBAS, GBAS, and Galileo embedded integrity concept.• Robust and highly accurate positioning and time dissemination service.• Used for the transport safety of persons and goods, such as in Civil aviation,

Railroad transport, and Commercial maritime.⇒ The acquisition operation can become the bottleneck of GNSS receivers:

• Tracking initialization depends on acquisition results.• Acquisition has the lowest sensitivity of the whole receiver operation.• Strong interferences and jamming signals could increase the acquisition time or

even can make the acquisition fail.



State-of-the-Art

ADC

GNSSAntenna

Interference rejection

-Pulse blanker-Notch filter-Transformed domain excision

ConventionalGNSS receiver

El. maskRF

front-end

El. mask

Figure: Single-antenna receiver interference rejection.

Single-antenna solutions for acquisition interference mitigation

• Time diversity: pulse blanking and Automatic Gain Control (AGC).• Frequency diversity: Continuous Wave Interference (CWI) notch filters.• Spatial diversity: antenna radiation pattern.



Research opportunity

Figure: Array-based GNSS receiver.

• Antenna-array key benefits:• In addition to code, time and frequency diversities, arrays exploit spatial diversity.• Interference and jamming signals rejection.• Sensitivity improvement due to the array gain.

• Acquisition with antenna arrays has not yet received much attention:• Intense research activity on single antenna receivers.• Antenna arrays applied to tracking assuming the success of the acquisition.

⇒ Existing antenna-array solutions suitable for acquisition:• Minimum Variance Distortionless Response (MVDR) beamformer: requires an

estimation of both the signal DOA and the array attitude.• Spatial-domain grid search: requires a calibrated array, but it increases the

dimensions of the search grid.• Blind null-steering beamformers: DOA not necessary, but no array gain.



Research opportunity

• Lack of suitable array-based GNSS real-time receiver commerciallyavailable• Closed implementations with few technical information made public.

Figure: NovAtel GAJT commercial null-steering GNSS array.

• Scientific applications of GNSSs require flexible implementations• The Software Defined Radio (SDR) receiver approach is suitable to test new

algorithms with low development costs.• Interest for a limited-market but highly demanding applications such as reference

stations, geodesy and surveying, among other scientific goals.



Main objectives of the project

Exploit the spatial diversity in acquisition

• Improve the existing GNSS acquisition algorithms performance.• Improve the GNSS interference robustness proposing novel array-based

acquisition algorithms using the statistical detection theory framework.

Demonstrate the implementation feasibility

• Design and implementation of an array-based GNSS receiver platform• Proof-of-concept of array-based acquisition algorithms working in real-time

• Interference mitigation.• Performance measurements in realistic scenarios.

• Tightly coupled with GNSS software receivers.


Introduction




Conclusions



Objectives










Antenna-array signal model

N-elements baseband array signal model for single satellite:

X(t) = hd(t, fd,τ)+N(t), (5)

where• X(t) = [xbb(t− (K−1)Ts) . . .xbb(t)] ∈ CN×K is referred as the space-time data

matrix, where xbb(t) = [x1(t) . . .xN(t)]T is defined as the baseband snapshot,and K is the number of captured snapshots. The acquisition time is defined asTacq = KTs where Fs = 1/Ts is the sampling frequency.

• h = [h1 . . .hN ]T ∈ CN×1 is the non-structured channel model, which includes

both the channel and the array response.• d(t, fd,τ) = [sT,i(t− (K−1)Ts− τi)ej2πfd,i(t−(K−1)Ts), . . . ,sT,i(t− τi)ej2πfd,it] ∈C1×K is the received GNSS baseband signal for the i-th satellite.

• N(t) = [n(t− (K−1)Ts) . . .n(t)] ∈ CN×K is a complex, circularly symmetricGaussian vector process with a zero-mean, temporally white and spatiallycolored with an arbitrary (also unknown) spatial covariance matrixQ ∈ CN×N that models both the noise and other non desirable terms such asinterferences.



Detection theory

Binary hypothesis testing problem:

H1 : X(t) = hd(t, fd,τ)+N(t) (6)

H0 : X(t) = N(t), (7)

where H0 is the null hypothesis, when there is no signal present, and H1 is thealternative hypothesis, when the searched signal is present.



Neymann-Pearson (NP) detector

Likelihood Ratio Test (LRT):

L(X) =p(X;Q,θa,H1)

p(X;Q,H0)=

1πNK det(Q)K exp

−TrQ−1C

1

πNK det(Q)K exp−TrQ−1Rxx

> γ, (8)

where the PDF of a complex multivariate Gaussian vector for K snapshots is used,and

C = Rxx− rxdhH−hrHxd +hRddhH , (9)

with• Rxx =

1K XXH is the autocorrelation matrix estimation

• rxd = 1K XdH is the cross-correlation vector estimation

• Rdd = 1K ddH is the PRN code autocorrelation estimation



Generalized Likelihood Ratio Test (GLRT) detectorGLRT criterion: assume no a priori knowledge of the PDFs parameters and replacethem by their respective Maximum Likelihood Estimators (MLE).

GLRT expression:

L(X) =p(X;QH1

, θa,H1)

p(X;QH0,H0)

=

1πNK det(QH1

)K exp−Tr(Q−1

H1C)

1πNK det(QH0

)K exp−Tr(Q−1

H0Rxx)

> γ, (10)

where (·) is the MLE of the signal and noise parameters.

Maximum Likelihood Estimators [FP06]

QH1= C

∣∣h=h,fd=fd ,τ=τ

(11)

QH0= C

∣∣h=0 = Rxx (12)

h = rxdR−1dd∣∣QH1

=QH1,fd=fd ,τ=τ

(13)

fd, τ = argminfd ,τ

ln(det(W(fd,τ))), (14)

where W(fd,τ) = Rxx− rxd(fd,τ)R−1dd rxd(fd,τ)H = QH1

∣∣h=h,fd ,τ.



GLRT statisticsInserting (11) and (12) in (10), we obtain the test statistic function [Arr12]:

TGL(X) = maxfd ,τ

rH

xd(fd,τ)R−1dd R−1

xx rxd(fd,τ)> γ , (15)

Assuming Rxx ' Rxx, TGL(X) is distributed as:

TGL(X)∼

χ22N(δTGL;H1

), in H1,

χ22N(δTGL;H0

= 0), in H0,(16)

GLRT theoretical performance

Pfa(γ) = exp

−γ

2σ2TGL

N−1

∑k=0

1k!

(γ

2σ2TGL

)k, (17)

Pd(γ) = QN

√

δTGL(Rxx,h)

σTGL

,

√γ

σTGL

, (18)

where σ2TGL

= 12K and QN is the generalized Marcum Q-function of order N. The

detector enjoys a Constant False Alarm Rate (CFAR) condition as Pfa(γ) doesnot depend on X.



GLRT performance

The chi-square non-centrality parameter can be expressed as:

δTGL(Rxx,h) = RddhHR−1xx h' hHR−1

xx h. (19)

Uniformly Most Powerful (UMP) conditionA UMP detector has the highest possible Pd for a given Pfa.Karlin-Rubin Theorem: Suppose that T(X) is a sufficient statistics for θ, and thefamily of PDFs associated to T(X) has a Monotone Likelihood Ratio (MLR). Then,the test that rejects H0 if an only if T(X)> γ is a UMP test.We check TGL(X) against the MLR condition as

p(TGL(X);δ2)

p(TGL(X);δ1)=

p(χ22N(δ2))

p(χ22N(δ1))

, (20)

where δ1 = δTGL(Rxx,h1) and δ2 = δTGL(Rxx,h2) are two possible values for thenon-centrality parameter of the chi-square defied in (19). The ratio is monotonenon-decreasing for all δ2 > δ1. The GLRT for GNSS array-based acquisition is aUMP test.



Simulation results: theoretical PDFs and histograms

RFfront-end

ADC

GNSSAntenna array

X°

H0

H1Array-basedacquisition

T (X )

Figure: Array-based GNSS acquisition concept.

0 100 200 300 400 500 600 700 8000

50

100

150

200

250

TGL(X)

Fre

quen

cy

H0 Histogram.

H1 Histogram.

H0 Theoretical PDF.

H1 Theoretical PDF.

(a) TGL(X)

Figure: Histogram and theoretical PDF in both H1 and H0 acquisition hypotheses for GalileoE1 signal acquisition simulation (CN0=38 dB-Hz, no interferences).



GLRT interference rejection capability

Assume M uncorrelated interferences impinging into the array through a channelmatrix Hi = [hi,1, . . . ,hi,M ] ∈ CN×M and an arbitrary basis function matrixDi = [dT

i,1, . . . ,dTi,M ]T ∈ CM×K . Then, the noise term is modeled as:

N = HiDi +Nw, (21)

where Nw ∼ CN (0,σ2I). The inverse covariance matrix can be approximated as:

Q−1 ' σ−2P⊥Hi

, (22)

where P⊥Hi= (I−Hi(HH

i Hi)−1HH

i ) and RDiDi ' I.Assuming ERxx 'Q, then

δTGL(σ2,h,Hi) =

hHP⊥Hih

σ2 =hHhσ2 −

hPHi hH

σ2 , (23)

where PHi = Hi(HHi Hi)

−1HHi . The SNR can be expressed as ρ = hHh

σ2 = N PsPn

.



GLRT interference rejection capability

(a) N = 2 (b) N = 3 (c) N = 4

(d) N = 8 (e) N = 12 (f) N = 24

Figure: Evolution of δTGL (ρ,N, h, hi) in the presence of an uncorrelated interference impinginginto the array from Az = 45 and El = 45, with ρ = 1.



Existing solutions: Acquisition after beamforming

RFfront-end

ADC

GNSSAntenna array

y = w HXX y

TDBF(y) °

H0

H1

w optR xx

h0

Beamformerprocessor

Single antennaacquisition

Figure: Acquisition after beamforming concept.

Minimum Variance Distortionless Response (MVDR) GLRT test function

TMVDR(X) =rH

xd(R−1xx h0)(R−1

xx h0)H rxd

hH0 R−1

xx h0' 1

σ2

|rHxdP⊥Hi

h0|2

‖hH0 P⊥Hi

‖2, (24)

where h0 ∈ CN×1 is the signal DOA steering vector.

Power Minimization Beamformer: signal DOA unavailable

Minimize the output power establishing a reference antenna

h0 = [10 . . . 0]. (25)



Simulation results: performance in ideal conditions

20 25 30 35 40 450

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

CN0 [dB]

Pd

Cla

irvo

yant

GLRT

Col

oredM

VD

R

PW

RM

in.

Single Antenna GLRTGLRT White

TWh(X)TGL(X)TNP (X)TSingle(X)TPWR(X)TMV DR(X)

Figure: Galileo E1 acquisition Pd vs. satellite CN0 in the presence of an in-band widebandinterference for different algorithms (IN0 = 85 dB-Hz, Pfa = 0.001, fs = 6 MSPS, Tacq = 4ms). No pointing error in TMVDR(X).



Simulation results: performance with pointing error

20 25 30 35 40 450

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

CN0 [dB]

Pd

Cla

irvo

yant

MVD

R

GLRT

Col

ored

PW

RM

in.

GLRT WhiteSingle Antenna GLRT

TWh(X)TGL(X)TNP (X)TSingle(X)TPWR(X)TMV DR(X)

Figure: Galileo E1 acquisition Pd vs. satellite CN0 in the presence of an in-band widebandinterference for different algorithms (IN0 = 85 dB-Hz, Pfa = 0.001, fs = 6 MSPS, Tacq = 4ms). 20 DOA pointing error in TMVDR(X). (array uncalibrated in acquisition)



Realistic conditions

• finite sample size• signal quantization effects• satellite signal synchronization errors

TrackingTracking

AcquisitionAcquisitionAcquisition

S/H

Array-basedAcquisition

Ideal Sample and Hold

Operation

N bits Quantizer

Multichannel coherent RF front-end

LNA

Antenna array IdealAGC

Multichannel ADC

Array-basedTracking

Snapshots Memory buffer

PVT

GNSS Receiver

Act

ive

sate

llite

chan

nels

Figure: GNSS receiver block diagram, as simulated.



A Metric to measure the presence of errors in Rxx

Geodesic distance: For any two points inside S = R ∈ CN×N : RH = R,R 0,the geodesic distance is the length of the geodesic curve that connects them:

distg(R1,R2) = ‖M‖F, (26)

where ‖M‖F =√

(∑i | ln(λi)|2) stands for the logarithmic version of the Frobenius

norm, M = ln(R−12

1 R2R−12

1 ), and λi represents the i-th eigenvalue of matrix

R−12

1 R2R−12

1 . The geodesic distance is able to detect differences both in theeigenvectors and in the eigenvalues of Rxx and Rxx.



Quantization effects in Rxx

1 2 3 4 5 6 70

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Quantization bits

¯dis

t g(R

xx,R

xqxq)Rxx and 85 dB-Hz interference

Rxqxq and 45 dB-Hz. interference





Figure: distg(Rxx, Rxqxq ) vs. different quantization bits and an in-band CW interferenceimpinging into the array with different IN0.



Quantization effects in Rxx

Receiver Operating Characteristic (ROC) curve

0 0.05 0.1 0.15 0.20

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

False Alarm probability (Pfa)

Det

ection

pro

bab

ility

(Pd)

dg = 0

dg = 2

dg = 1

dg = 3

dg = 5

Increase ofdg = distg(Rxx, Rxx)

dg = 4

dg = 6TGL(X) theoretical

Figure: Effect of the distg(Rxx, Rxx) in the acquisition performance of TGL(X), with anin-band CWI impinging into the array with IN0 = 85 dB-Hz.



Acquisition performance vs. ADC resolution

70 80 90 100 110 120 1300.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Interference I/N0

Pd

GLRT white TWh(Xq)

GLRT colored TGL(Xq)

Single antenna MF TMF (Xq)

11.3 dB 23.4 dB

TGL(Xq)Nb = 2 bits

TGL(Xq)Nb = 4 bits

TGL(Xq)Nb = 8 bits

TMF (Xq)Nb = [2, 8]bits

TWh(Xq)Nb = [2, 8]bits

Figure: Pd in an scenario with satellite CN0 = 44 dB-Hz, and an in-band CW interferenceimpinging into the array with IN0 = 70−136 dB-Hz, for Pfa = 0.001 and Nb = 2−8 bits.



Front-end bandwidth effect in acquisition IThe pre-correlation SNR is defined as ρacq =

P′sP′n

, where

P′s = Ps

∫ 12

−12

Gs(f )|HFE(f )|2df , (27)

P′n =N0

2BFE

∫ 12

− 12

|HFE(f )|2df , (28)

with• N0 is the antenna noise density and BFE is the front-end pass-band bandwidth• Gs(f ) = 10

11 GBOC(1,1)+111 GBOC(6,1) is the PSD (for Galileo MBOC(6,1,1/11))

• HFE(f ) is the DTFT of the front-end baseband-equivalent impulse responseConsidering now d′ = d∗hFE, using Wiener-Khinchine, we compute Rd′d as:

Rd′d[τ] =∫ 1

2

−12

Gs(f )HFE(f )ej2πf τdf , (29)

and therefore PsRd′d[0] = Ps∫ 0.5−0.5 Gs(f )HFE(f )df . Now considering HFE(f )

response of an ideal band-pass filter, then

PsRd′d[0] = Ps

∫ BFE2fs

− BFE2fs

Gs(f ) = P′s. (30)



Front-end bandwidth effect in acquisition IIFinally, by inserting P′s and P′n in the non-centrality parameter of the performanceexpressions we can write

δTGL =|µRxd |2

Rxx' P′s

P′n= ρacq, (31)

which implies that the maximization of ρacq maximizes the acquisition performance.

2 4 6 8 10 12x 10

6

−41

−40

−39

−38

−37

−36

−35

−34

−33

−32

Acquisition Baseband Bandwidth [Hz]

Bas

eban

d S

NR

[dB

]

Simulated SNRTheoretical SNR

Best Baseband SNR

C/N0=34 dB−Hz.

(a) SNR vs. BW

0 0.02 0.04 0.06 0.08 0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Pfa

Pd

2MHz.

2MHz.

3MHz.

3MHz.

4MHz.

4MHz.

6MHz.

6MHz.

8MHz.

8MHz.

10MHz.

10MHz.

13MHz.

13MHz.Bbb

(b) ROC vs. BW

Figure: Theoretical and simulated Galileo E1 MBOC(6,1,1/11) SNR and ROC curves vs. thebaseband BW.



Front-end bandwidth effect in acquisition III

−1 −0.5 0 0.5 1

−8

−6

−4

−2

0

Delay τ (Code chips)

Nor

mal

ized

|Rd’

d L(τ)|

2 (dB

)

3MHz.4MHz.5MHz.6MHz.7MHz.8MHz.9MHz.10MHz.11MHz.12MHz.2MHz.

Increase of theautocorrelationpeakwidth.

Despreading gainreduction.

Figure: Autocorrelation of Galileo E1 MBOC(6,1,1/11) signal with the local replica versus τ fordifferent baseband bandwidths.


Introduction




Conclusions



Objectives










Generic GNSS array-based receiver platform

RF front-end

LNA

ADCAcquisition

&Beamformer

FPGA

RF front-end

LNA

Local Oscillator

SDR GNSSReceiver

PC

Multichannel phase-coherent front-end FPGA platform

Antenna array

RF

IF

Figure: Simplified system block diagram.

RF BPF

RF

LNA1

Local Oscillator

Single-channel front-end detail

Antenna

array

element

IF BPF IF VGA

IF

ADC

i-th CH

Beamforming

platform

LNA2

Figure: Simplified front-end for each antenna element.



Front-end requirements overview

Parameter Effect in Acquisition Effect in Tracking↑ Bandwidth (BW) ↓ sensitivity ↑ τ precision

if BW exceeds the main lobe (see RMSE CRB)(SNR loss)

↑ Noise Figure (NF) ↓ sensitivity ↓ τ precision(↓ CN0) (↓ CN0)

↑ ADC active bits (Nb) ↑ sensitivity ↑ sensitivity(No CN0 ↓ if Nb ≥ 4) (No CN0 ↓ if Nb ≥ 4)

↑ Linearity ↑ interference robustness ↑ interference robustness



Receiver performance bounds

30 35 40 45 50 55 600

0.5

1

1.5

2

2.5

3

3.5

Carrier-to-Noise density Ratio (C/N0) [dB]

RM

Sco

de

trac

kin

ger

ror

[m]

Bbb = 1MHz

Bbb = 2MHz

Bbb = 3MHz

Bbb = 4MHz

Bbb = 6MHz

Bbb = 8MHz

Bbb = 10MHz

Bbb = 12MHz

1 2 3 4 5 6 7 8 9 10 11 12 13 14 150

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Front-end Noise Figure [dB]

RM

Sco

de

trac

kin

ger

ror

[m]

Bbb = 1MHz

Bbb = 2MHz

Bbb = 3MHz

Bbb = 4MHz

Bbb = 6MHz

Bbb = 8MHz

Bbb = 10MHz

Bbb = 12MHz

Figure: GPS L1 C/A code tracking Cramer-Rao Bound (CRB) minimum RMSE vs. front-endNF, BW, and signal CN0 [Wei94].

ADC resolution CN0 degradation fs ≥ 2Bs CN0 degradation fs = 2Bp1 bit 1.96 dB 3.5 dB2 bits 0.55 dB 1.2 dB3 bits 0.16 dB 0.6 dB4 bits or more ≤ 0.16 ≤ 0.6 dB

Table: GPS L1 C/A CN0 degradation vs. ADC resolution assuming Gaussian noise [Par96].



Front-end specifications

• Bandwidth, fs, and Noise Figure (NF): set by the desired GNSS performance.• Gain: the thermal noise excites the ADC, thus:

GFE ≥ PADC−Pn,

GFE ≥ 10log

((VLSB2Nbits−1)2

ZADC

)kTaBp

, (32)

where VLSB is the Least Significant Bit voltage (RMS), Nbits is the number ofactive bits and Pn = kTaBp is the noise power where k = 1.3806×10−23 J/Kand Ta is the antenna sky temperature, and Bp is the passband bandwidth.

• Linearity Parameters: Compression Point (CP) and Third Order InterceptionPoint (IP3) are set by the maximum admissible input power

Pint max = PFSR−GFE. (33)

where PFSR is the ADC full-scale input power. The front-end should behavelinear for an input signal power Pin ≤ Pint max.

ADC Particular case: VFSR = 2 Vpp, ZADC = 50 Ω, PFSR = 19.1 dBm, and Nb = 12.FE Specifications: Nb ≥ 4, PADC ≥−35 dBm, Pn =−107.8 dBm, GFE ≥ 72.8 dBPint max = PFSR−GFE =−53.7 dBm, PCP ≥ Pint max and PIP3 ≥ (Pint max +9.6).



Proposed front-end channel architecture and specifications

RF BPF

LNA1

Local Oscillator

Antenna array element

IF BPF IF VGA

ADCi-th CH

LNA2LNA

MIXER

antG 1LNAG 2LNAGRFBPFL VGAG

cable

MIXG

IFBPFLcableL

1LNAF 2LNAF VGAFantF

MIXF, 1CP LNAP , 2CP LNAP ,CP MIXP ,CP VGAP FSRP

,p IFB

,s IFB,p RFB

,s RFB

,CP antP

By applying the Friis formula we obtain the overall NF as:

FFE = Fant +Lcable−1

Gant+

FLNA1−1Gant

Lcable

+LRF BPF−1

GantGLNA1Lcable

+FLNA2−1GantGLNA1

LcableLRF BPF

+

+FMIX−1

GantGLNA1GLNA2LcableLRF BPF

+LIF BPF−1

GantGLNA1GLNA2GMIXLcableLRF BPF

+FVGA−1

GantGLNA1GLNA2GMIXLcableLRF BPFLIF BPF

, (34)

and

Component Compression point Computed min. valueAntenna LNA PCP,ant ≥ PCP,LNA1−Gant +Lcable −55.9 dBm

LNA1 PCP,LNA1 ≥ PCP,LNA2−GLNA1 +LRF BPF −44.9 dBmLNA2 PCP,LNA2 ≥ PCP,MIX−GLNA2 −25.9 dBmMixer PCP,MIX ≥ PCP,VGA−GMIX +LIF BPF −10.9 dBmVGA PCP,VGA ≥ PFSR−GVGA −15.9 dBm



Antenna array elements

Figure: Garmin GA27c active antenna.

−8.9

−7.8

−6.7

−5.6

−4.5

−3.4

−2.3

−1.2

−0.1

1 dB

0o

30o

60o

90o

60o

30o

0o

PATCH 1PATCH 2PATCH 3PATCH 4PATCH 5

Figure: Antenna array prototype and differences between radiation patterns of some antennaelements in elevation.



Local Oscillator distribution network

Figure: Eight ports Wilkinson PCB layout and prototype.

1.4

1

1.4

2

1.4

3

1.4

4

1.4

5

1.4

6

1.4

7

1.4

8

1.4

9

1.5

0

1.5

1

1.5

2

1.5

3

1.5

4

1.5

5

1.5

6

1.5

7

1.5

8

1.5

9

1.6

0

1.6

1

1.6

2

1.6

3

1.6

4

1.6

5

1.6

6

1.6

7

1.6

8

1.6

9

1.4

0

1.7

0

-8

-6

-4

-2

-10

0

f req, GHz

unw

rap(p

hase(S

(2,1

)))-

unw

rap(p

hase(S

(2,1

)))

unw

rap(p

hase(S

(4,3

)))-

unw

rap(p

hase(S

(2,1

)))

unw

rap(p

hase(S

(6,5

)))-

unw

rap(p

hase(S

(2,1

)))

unw

rap(p

hase(S

(8,7

)))-

unw

rap(p

hase(S

(2,1

)))

unw

rap(p

hase(S

(10,9

)))-

unw

rap(p

hase(S

(2,1

)))

unw

rap(p

hase(S

(12,1

1))

)-unw

rap(p

hase(S

(2,1

)))

unw

rap(p

hase(S

(14,1

3))

)-unw

rap(p

hase(S

(2,1

)))

unw

rap(p

hase(S

(16,1

5))

)-unw

rap(p

hase(S

(2,1

)))

Figure: Measured output signal phase differences [].



Multichannel PCB implementation

PAC101PAC102COC1

PAC201 PAC202COC2

PAC301PAC302COC3

PAC401

PAC402COC4

PAC502

PAC501COC5

PAC60CH102

PAC60CH101

COC60CH1

PAC60CH202PAC60CH201

COC60CH2

PAC60CH302

PAC60CH301

COC60CH3

PAC60CH402

PAC60CH401

COC60CH4

PAC60CH502

PAC60CH501

COC60CH5PAC60CH602

PAC60CH601

COC60CH6

PAC60CH702

PAC60CH701

COC60CH7

PAC60CH802

PAC60CH801

COC60CH8


COC70CH1PAC70CH201

PAC70CH202

COC70CH2


COC70CH3


COC70CH4


COC70CH5

PAC70CH601

PAC70CH602

COC70CH6PAC70CH701PAC70CH702

COC70CH7


COC70CH8

PAC80CH101

PAC80CH102

COC80CH1

PAC80CH201

PAC80CH202

COC80CH2PAC80CH301

PAC80CH302

COC80CH3

PAC80CH401

PAC80CH402

COC80CH4

PAC80CH501

PAC80CH502

COC80CH5

PAC80CH601

PAC80CH602

COC80CH6

PAC80CH701

PAC80CH702

COC80CH7

PAC80CH801

PAC80CH802

COC80CH8

PAC90CH102PAC90CH101COC90CH1 PAC90CH202

PAC90CH201 COC90CH2 PAC90CH302

PAC90CH301 COC90CH3PAC90CH402

PAC90CH401COC90CH4 PAC90CH502




PAC90CH801 COC90CH8

PAC100CH102


PAC100CH201COC100CH2

PAC100CH302


PAC100CH401

COC100CH4 PAC100CH502


PAC100CH601

COC100CH6 PAC100CH702PAC100CH701 COC100CH7

PAC100CH802PAC100CH801 COC100CH8

PAC110CH102

PAC110CH101

COC110CH1PAC110CH202

PAC110CH201


PAC110CH301


PAC110CH401


PAC110CH501


PAC110CH601


PAC110CH701

COC110CH7PAC110CH802PAC110CH801COC110CH8

PAC120CH102

PAC120CH101COC120CH1PAC120CH202

PAC120CH201


PAC120CH301


PAC120CH401


PAC120CH501


PAC120CH601


PAC120CH701


COC120CH8


COC130CH1

PAC130CH201

PAC130CH202

COC130CH2

PAC130CH301

PAC130CH302


PAC130CH402

COC130CH4

PAC130CH501

PAC130CH502


PAC130CH602

COC130CH6

PAC130CH701

PAC130CH702

COC130CH7

PAC130CH801

PAC130CH802

COC130CH8

PAC140CH102 PAC140CH101COC140CH1 PAC140CH202 PAC140CH201 COC140CH2

PAC140CH302 PAC140CH301 COC140CH3 PAC140CH402 PAC140CH401 COC140CH4PAC140CH502 PAC140CH501COC140CH5 PAC140CH602 PAC140CH601 COC140CH6 PAC140CH702 PAC140CH701 COC140CH7

PAC140CH802 PAC140CH801 COC140CH8PAC150CH102 PAC150CH101 COC150CH1 PAC150CH202 PAC150CH201 COC150CH2

PAC150CH302 PAC150CH301 COC150CH3 PAC150CH402 PAC150CH401 COC150CH4 PAC150CH502 PAC150CH501 COC150CH5 PAC150CH602 PAC150CH601

COC150CH6PAC150CH702 PAC150CH701

COC150CH7

PAC150CH802 PAC150CH801COC150CH8

PAC160CH102 PAC160CH101


COC160CH2


COC160CH3


COC160CH4



COC160CH6



COC160CH8

PAC170CH102PAC170CH101COC170CH1



PAC170CH402

PAC170CH401 COC170CH4 PAC170CH502PAC170CH501COC170CH5

PAC170CH602




PAC180CH102




PAC180CH401

COC180CH4 PAC180CH502



PAC180CH701




COC190CH1 PAC190CH202PAC190CH201

COC190CH2 PAC190CH302PAC190CH301COC190CH3 PAC190CH402

PAC190CH401


PAC190CH501


PAC190CH601 COC190CH6PAC190CH702PAC190CH701 COC190CH7

PAC190CH802

PAC190CH801





PAC200CH401



PAC200CH601COC200CH6PAC200CH702PAC200CH701COC200CH7

PAC200CH802

PAC200CH801

COC200CH8


COC210CH1PAC210CH202 PAC210CH201COC210CH2

PAC210CH302 PAC210CH301 COC210CH3 PAC210CH402 PAC210CH401 COC210CH4 PAC210CH502 PAC210CH501 COC210CH5 PAC210CH602 PAC210CH601 COC210CH6 PAC210CH702 PAC210CH701 COC210CH7PAC210CH802 PAC210CH801

COC210CH8

PAC220CH102

PAC220CH101

COC220CH1



PAC220CH301

COC220CH3

PAC220CH402

PAC220CH401


PAC220CH501

COC220CH5

PAC220CH602

PAC220CH601

COC220CH6





COC230CH1PAC230CH202 PAC230CH201 COC230CH2 PAC230CH302 PAC230CH301 COC230CH3 PAC230CH402 PAC230CH401 COC230CH4 PAC230CH502 PAC230CH501 COC230CH5 PAC230CH602 PAC230CH601

COC230CH6PAC230CH702 PAC230CH701 COC230CH7 PAC230CH802 PAC230CH801

COC230CH8



PAC240CH302 PAC240CH301 COC240CH3 PAC240CH402 PAC240CH401 COC240CH4 PAC240CH502 PAC240CH501COC240CH5 PAC240CH602 PAC240CH601 COC240CH6 PAC240CH702 PAC240CH701 COC240CH7 PAC240CH802 PAC240CH801

COC240CH8

PAC250CH102



PAC250CH301 COC250CH3PAC250CH402PAC250CH401

COC250CH4


COC250CH5

PAC250CH602PAC250CH601COC250CH6

PAC250CH702PAC250CH701 COC250CH7 PAC250CH802


PAC260CH101

COC260CH1

PAC260CH202

PAC260CH201

COC260CH2


COC260CH3

PAC260CH402PAC260CH401COC260CH4 PAC260CH502

PAC260CH501

COC260CH5


COC260CH6


COC260CH7

PAC260CH802


PAC270CH102

PAC270CH101

COC270CH1


COC270CH2

PAC270CH302

PAC270CH301

COC270CH3


COC270CH4

PAC270CH502

PAC270CH501

COC270CH5


COC270CH6


COC270CH7


COC270CH8

PAJ101 PAJ102

PAJ103 PAJ104

PAJ105 PAJ106

PAJ107 PAJ108

COJ1

PAJ20CH101

PAJ20CH102COJ20CH1 PAJ20CH201

PAJ20CH202

COJ20CH2

PAJ20CH301

PAJ20CH302

COJ20CH3

PAJ20CH401

PAJ20CH402

COJ20CH4

PAJ20CH501

PAJ20CH502

COJ20CH5

PAJ20CH601

PAJ20CH602

COJ20CH6

PAJ20CH701

PAJ20CH702

COJ20CH7

PAJ20CH801

PAJ20CH802

COJ20CH8

PAL10CH102 PAL10CH101 COL10CH1 PAL10CH202PAL10CH201 COL10CH2 PAL10CH302PAL10CH301 COL10CH3 PAL10CH402 PAL10CH401 COL10CH4 PAL10CH502PAL10CH501 COL10CH5 PAL10CH602 PAL10CH601 COL10CH6 PAL10CH702 PAL10CH701 COL10CH7 PAL10CH802 PAL10CH801COL10CH8

PAL20CH102

PAL20CH101

COL20CH1 PAL20CH202PAL20CH201 COL20CH2 PAL20CH302

PAL20CH301 COL20CH3PAL20CH402

PAL20CH401 COL20CH4 PAL20CH502

PAL20CH501 COL20CH5 PAL20CH602PAL20CH601 COL20CH6 PAL20CH702


PAL20CH801COL20CH8

PAL30CH102PAL30CH101COL30CH1 PAL30CH202PAL30CH201COL30CH2 PAL30CH302PAL30CH301COL30CH3

PAL30CH402PAL30CH401COL30CH4 PAL30CH502PAL30CH501COL30CH5 PAL30CH602PAL30CH601COL30CH6 PAL30CH702PAL30CH701COL30CH7PAL30CH802PAL30CH801

COL30CH8

PAL40CH102PAL40CH101 COL40CH1

PAL40CH202


PAL40CH301 COL40CH3 PAL40CH402PAL40CH401 COL40CH4



PAL40CH702PAL40CH701 COL40CH7 PAL40CH802

PAL40CH801 COL40CH8

PAL50CH102

PAL50CH101

COL50CH1 PAL50CH202

PAL50CH201COL50CH2

PAL50CH302PAL50CH301 COL50CH3 PAL50CH402

PAL50CH401COL50CH4 PAL50CH502

PAL50CH501 COL50CH5PAL50CH602PAL50CH601 COL50CH6 PAL50CH702

PAL50CH701 COL50CH7PAL50CH802

PAL50CH801 COL50CH8

PAL60CH102

PAL60CH101

COL60CH1 PAL60CH202


PAL60CH301COL60CH3 PAL60CH402PAL60CH401

COL60CH4PAL60CH502PAL60CH501COL60CH5

PAL60CH602

PAL60CH601COL60CH6PAL60CH702


PAL60CH801 COL60CH8PAL70CH102PAL70CH101COL70CH1 PAL70CH202PAL70CH201COL70CH2 PAL70CH302PAL70CH301COL70CH3

PAL70CH402PAL70CH401COL70CH4PAL70CH502PAL70CH501COL70CH5 PAL70CH602PAL70CH601COL70CH6 PAL70CH702PAL70CH701COL70CH7

PAL70CH802PAL70CH801COL70CH8

PAP101 PAP102 COP1 PAP201PAP202 COP2

PAP301 PAP302COP3

PAP401PAP402 COP4

PAP501 PAP502COP5

PAP602PAP601

COP6

PAP701PAP702

COP7

PAP801PAP802 COP8

PAP901 PAP902COP9

PAP1001PAP1002 COP10

PAP1101 PAP1102COP11

PAP1201PAP1202

COP12 PAP1301PAP1302

COP13





PAP1801PAP1802


COP19





PAP2401PAP2402


COP25

PAR101 PAR102 COR1PAR201 PAR202 COR2PAR301 PAR302 COR3PAR401 PAR402 COR4

PASAW10CH1013

PASAW10CH1012 PASAW10CH1011

PASAW10CH106PASAW10CH105

PASAW10CH1010

PASAW10CH109

PASAW10CH107


PASAW10CH104

PASAW10CH102

PASAW10CH101

COSAW10CH1

PASAW10CH2013



PASAW10CH2010

PASAW10CH209

PASAW10CH207


PASAW10CH204

PASAW10CH202

PASAW10CH201

COSAW10CH2

PASAW10CH3013



PASAW10CH3010

PASAW10CH309

PASAW10CH307


PASAW10CH304

PASAW10CH302

PASAW10CH301

COSAW10CH3

PASAW10CH4013



PASAW10CH4010

PASAW10CH409

PASAW10CH407


PASAW10CH404

PASAW10CH402

PASAW10CH401

COSAW10CH4

PASAW10CH5013



PASAW10CH5010

PASAW10CH509

PASAW10CH507


PASAW10CH504

PASAW10CH502

PASAW10CH501

COSAW10CH5

PASAW10CH6013



PASAW10CH6010

PASAW10CH609

PASAW10CH607


PASAW10CH604

PASAW10CH602

PASAW10CH601

COSAW10CH6

PASAW10CH7013



PASAW10CH7010

PASAW10CH709

PASAW10CH707


PASAW10CH704

PASAW10CH702

PASAW10CH701

COSAW10CH7

PASAW10CH8013



PASAW10CH8010

PASAW10CH809

PASAW10CH807


PASAW10CH804

PASAW10CH802

PASAW10CH801

COSAW10CH8

PAT10CH101

PAT10CH106

PAT10CH102PAT10CH103

PAT10CH104COT10CH1

PAT10CH201

PAT10CH206


PAT10CH204COT10CH2

PAT10CH301

PAT10CH306


PAT10CH304COT10CH3

PAT10CH401

PAT10CH406


PAT10CH404 COT10CH4

PAT10CH501

PAT10CH506


PAT10CH504 COT10CH5PAT10CH601

PAT10CH606


PAT10CH604COT10CH6

PAT10CH701

PAT10CH706


PAT10CH704COT10CH7

PAT10CH801

PAT10CH806


PAT10CH804COT10CH8

PAT20CH101

PAT20CH106

PAT20CH102 PAT20CH103

PAT20CH104COT20CH1 PAT20CH201

PAT20CH206


PAT20CH204COT20CH2 PAT20CH301

PAT20CH306


PAT20CH304COT20CH3

PAT20CH401

PAT20CH406


PAT20CH404COT20CH4

PAT20CH501

PAT20CH506


PAT20CH504COT20CH5

PAT20CH601

PAT20CH606


PAT20CH604COT20CH6

PAT20CH701

PAT20CH706


PAT20CH704COT20CH7

PAT20CH801

PAT20CH806


PAT20CH804COT20CH8

PAU103 PAU101PAU102

COU1

PAU205

PAU204PAU203PAU202

PAU201COU2 PAU30CH102

PAU30CH101PAU30CH103

PAU30CH104COU30CH1PAU30CH202


PAU30CH204 COU30CH2PAU30CH302












PAU30CH804 COU30CH8

PAU40CH104 PAU40CH101


COU40CH1PAU40CH204 PAU40CH201


COU40CH2PAU40CH304 PAU40CH301

PAU40CH302PAU40CH303COU40CH3


PAU40CH402PAU40CH403COU40CH4 PAU40CH504 PAU40CH501



PAU40CH602PAU40CH603COU40CH6 PAU40CH704 PAU40CH701




PAU50CH104PAU50CH105 PAU50CH106PAU50CH101PAU50CH103PAU50CH102 COU50CH1 PAU50CH204PAU50CH205 PAU50CH206

PAU50CH201PAU50CH203PAU50CH202 COU50CH2 PAU50CH304PAU50CH305PAU50CH306



PAU50CH501PAU50CH503PAU50CH502 COU50CH5 PAU50CH604PAU50CH605 PAU50CH606PAU50CH601PAU50CH603PAU50CH602 COU50CH6 PAU50CH704PAU50CH705 PAU50CH706

PAU50CH701PAU50CH703PAU50CH702 COU50CH7 PAU50CH804 PAU50CH805PAU50CH806PAU50CH801PAU50CH803 PAU50CH802 COU50CH8

PAU60CH106PAU60CH105PAU60CH104PAU60CH103 PAU60CH102PAU60CH101

COU60CH1 PAU60CH206PAU60CH205PAU60CH204

PAU60CH203 PAU60CH202 PAU60CH201COU60CH2PAU60CH306PAU60CH305PAU60CH304

PAU60CH303 PAU60CH302 PAU60CH301

COU60CH3 PAU60CH406PAU60CH405PAU60CH404


COU60CH4PAU60CH506PAU60CH505PAU60CH504

PAU60CH503PAU60CH502 PAU60CH501

COU60CH5

PAU60CH606PAU60CH605PAU60CH604






COU60CH8


PAU70CH104

PAU70CH105PAU70CH106PAU70CH107PAU70CH108


PAU70CH1013


COU70CH1


PAU70CH205



PAU70CH2012


COU70CH2


PAU70CH304PAU70CH305PAU70CH306PAU70CH307PAU70CH308


PAU70CH3013PAU70CH3012PAU70CH3011PAU70CH3010PAU70CH309

COU70CH3


PAU70CH403PAU70CH404PAU70CH405PAU70CH406PAU70CH407PAU70CH408



COU70CH4





COU70CH5





COU70CH6





COU70CH7





COU70CH8

PAJ102 PAR101

PAU70CH103 PAU70CH203PAU70CH303 PAU70CH403 PAU70CH503 PAU70CH603 PAU70CH703 PAU70CH803PAJ104 PAR201 PAU70CH104

PAU70CH204

PAU70CH304 PAU70CH404 PAU70CH504 PAU70CH604 PAU70CH704 PAU70CH804

PAJ106 PAR301


PAU70CH305 PAU70CH405 PAU70CH505 PAU70CH605 PAU70CH705 PAU70CH805

PAJ108 PAR401

PAU70CH106 PAU70CH206 PAU70CH306 PAU70CH406 PAU70CH506 PAU70CH606 PAU70CH706 PAU70CH806

PAC101

PAC201

PAC301

PAC401

PAC501

PAC60CH101PAC60CH201 PAC60CH301 PAC60CH401 PAC60CH501 PAC60CH601 PAC60CH701 PAC60CH801


PAC80CH101 PAC80CH201 PAC80CH301 PAC80CH401 PAC80CH501 PAC80CH601 PAC80CH701 PAC80CH801

PAC120CH101 PAC120CH201 PAC120CH301 PAC120CH401 PAC120CH501 PAC120CH601 PAC120CH701PAC120CH801

PAC130CH101 PAC130CH201 PAC130CH301 PAC130CH401 PAC130CH501 PAC130CH601 PAC130CH701PAC130CH801


PAC140CH301 PAC140CH401PAC140CH501 PAC140CH601 PAC140CH701


PAC150CH801

PAC210CH101 PAC210CH201 PAC210CH301PAC210CH401 PAC210CH501 PAC210CH601 PAC210CH701

PAC210CH801


PAC220CH301 PAC220CH401 PAC220CH501 PAC220CH601PAC220CH701

PAC220CH801

PAC230CH101 PAC230CH201 PAC230CH301 PAC230CH401 PAC230CH501PAC230CH601 PAC230CH701 PAC230CH801

PAC240CH101 PAC240CH201 PAC240CH301 PAC240CH401 PAC240CH501PAC240CH601 PAC240CH701 PAC240CH801

PAC270CH102 PAC270CH202 PAC270CH302 PAC270CH402 PAC270CH502 PAC270CH602 PAC270CH702 PAC270CH802

PAJ101

PAJ103

PAJ105

PAJ107

PAL70CH101PAL70CH201 PAL70CH301

PAL70CH401

PAL70CH501 PAL70CH601 PAL70CH701PAL70CH801

PAP101 PAP202

PAP302

PAP402

PAP502

PAP602

PAP702

PAP802

PAP902

PAP1002

PAP1102

PAP1202 PAP1302

PAP1402

PAP1502

PAP1602

PAP1702

PAP1802 PAP1902

PAP2002

PAP2102

PAP2202

PAP2302

PAP2402 PAP2502

PASAW10CH101

PASAW10CH102

PASAW10CH103

PASAW10CH104

PASAW10CH106

PASAW10CH107

PASAW10CH108

PASAW10CH109

PASAW10CH1010

PASAW10CH1012


PASAW10CH202

PASAW10CH203

PASAW10CH204

PASAW10CH206

PASAW10CH207

PASAW10CH208

PASAW10CH209

PASAW10CH2010

PASAW10CH2012


PASAW10CH302

PASAW10CH303

PASAW10CH304

PASAW10CH306

PASAW10CH307

PASAW10CH308

PASAW10CH309

PASAW10CH3010

PASAW10CH3012


PASAW10CH402

PASAW10CH403

PASAW10CH404

PASAW10CH406

PASAW10CH407

PASAW10CH408

PASAW10CH409

PASAW10CH4010

PASAW10CH4012


PASAW10CH502

PASAW10CH503

PASAW10CH504

PASAW10CH506

PASAW10CH507

PASAW10CH508

PASAW10CH509

PASAW10CH5010

PASAW10CH5012


PASAW10CH602

PASAW10CH603

PASAW10CH604

PASAW10CH606

PASAW10CH607

PASAW10CH608

PASAW10CH609

PASAW10CH6010

PASAW10CH6012


PASAW10CH702

PASAW10CH703

PASAW10CH704

PASAW10CH706

PASAW10CH707

PASAW10CH708

PASAW10CH709

PASAW10CH7010

PASAW10CH7012


PASAW10CH802

PASAW10CH803

PASAW10CH804

PASAW10CH806

PASAW10CH807

PASAW10CH808

PASAW10CH809

PASAW10CH8010

PASAW10CH8012

PASAW10CH8013

PAT10CH102

PAT10CH104

PAT10CH202

PAT10CH204

PAT10CH302

PAT10CH304

PAT10CH402

PAT10CH404

PAT10CH502

PAT10CH504

PAT10CH602


PAT10CH704

PAT10CH802

PAT10CH804

PAT20CH102


PAT20CH206

PAT20CH302

PAT20CH306

PAT20CH402

PAT20CH406

PAT20CH502

PAT20CH506

PAT20CH602

PAT20CH606

PAT20CH702

PAT20CH706

PAT20CH802

PAT20CH806

PAU102

PAU202 PAU30CH102








PAU30CH804


PAU40CH402 PAU40CH502 PAU40CH602 PAU40CH702PAU40CH802

PAU50CH101PAU50CH102PAU50CH201PAU50CH202 PAU50CH301PAU50CH302 PAU50CH401PAU50CH402 PAU50CH501PAU50CH502 PAU50CH601PAU50CH602 PAU50CH701PAU50CH702


PAU60CH102 PAU60CH202 PAU60CH302PAU60CH402 PAU60CH502 PAU60CH602 PAU60CH702 PAU60CH802

PAU70CH102

PAU70CH1012


PAU70CH2012


PAU70CH3012


PAU70CH4012


PAU70CH5012


PAU70CH6012


PAU70CH7012


PAU70CH8012

PAU70CH8015

PAL50CH102

PAT10CH106

PAL50CH202

PAT10CH206

PAL50CH302

PAT10CH306

PAL50CH402

PAT10CH406

PAL50CH502

PAT10CH506

PAL50CH602

PAT10CH606

PAL50CH702

PAT10CH706

PAL50CH802

PAT10CH806

PAC202

PAP102

PAU101

PAC502

PAU205

PAC80CH102PAC270CH101PAJ20CH101 PAL10CH102 PAC80CH202 PAC270CH201PAJ20CH201 PAL10CH202 PAC80CH302 PAC270CH301PAJ20CH301 PAL10CH302 PAC80CH402 PAC270CH401PAJ20CH401PAL10CH402 PAC80CH502 PAC270CH501

PAJ20CH501PAL10CH502 PAC80CH602 PAC270CH601PAJ20CH601 PAL10CH602 PAC80CH702 PAC270CH701PAJ20CH701

PAL10CH702 PAC80CH802 PAC270CH801PAJ20CH801PAL10CH802

PAC90CH101

PAU30CH101

PAC90CH102

PAU50CH106

PAC90CH201

PAU30CH201

PAC90CH202

PAU50CH206

PAC90CH301

PAU30CH301

PAC90CH302

PAU50CH306

PAC90CH401

PAU30CH401

PAC90CH402

PAU50CH406

PAC90CH501

PAU30CH501

PAC90CH502

PAU50CH506

PAC90CH601

PAU30CH601

PAC90CH602

PAU50CH606

PAC90CH701

PAU30CH701

PAC90CH702

PAU50CH706

PAC90CH801

PAU30CH801

PAC90CH802

PAU50CH806

PAC100CH101

PAU40CH101

PAC100CH102

PAU30CH103

PAC100CH201

PAU40CH201

PAC100CH202

PAU30CH203

PAC100CH301

PAU40CH301

PAC100CH302

PAU30CH303

PAC100CH401

PAU40CH401

PAC100CH402

PAU30CH403

PAC100CH501

PAU40CH501

PAC100CH502

PAU30CH503

PAC100CH601

PAU40CH601

PAC100CH602

PAU30CH603

PAC100CH701

PAU40CH701

PAC100CH702

PAU30CH703

PAC100CH801

PAU40CH801

PAC100CH802

PAU30CH803

PAC110CH101

PAL10CH101

PAP201

PAC110CH102

PAL20CH101

PAC110CH201

PAL10CH201

PAP801

PAC110CH202

PAL20CH201

PAC110CH301

PAL10CH301

PAP1401

PAC110CH302

PAL20CH301

PAC110CH401

PAL10CH401

PAP2001

PAC110CH402

PAL20CH401

PAC110CH501

PAL10CH501

PAP401

PAC110CH502

PAL20CH501

PAC110CH601

PAL10CH601

PAP1001

PAC110CH602

PAL20CH601

PAC110CH701

PAL10CH701

PAP1601

PAC110CH702

PAL20CH701

PAC110CH801

PAL10CH801

PAP2201

PAC110CH802

PAL20CH801

PAC160CH101 PAP601PAC160CH102

PAU60CH101PAC160CH201 PAP1201PAC160CH202

PAU60CH201PAC160CH301 PAP1801PAC160CH302

PAU60CH301PAC160CH401 PAP2401PAC160CH402PAU60CH401 PAC160CH501 PAP701PAC160CH502PAU60CH501 PAC160CH601 PAP1301PAC160CH602PAU60CH601 PAC160CH701 PAP1901PAC160CH702PAU60CH701

PAC160CH801 PAP2501PAC160CH802PAU60CH801

PAC170CH101

PAL40CH101

PAC170CH102

PAL30CH101

PAU60CH104

PAC170CH201

PAL40CH201

PAC170CH202

PAL30CH201

PAU60CH204

PAC170CH301

PAL40CH301

PAC170CH302

PAL30CH301

PAU60CH304

PAC170CH401

PAL40CH401

PAC170CH402

PAL30CH401

PAU60CH404

PAC170CH501

PAL40CH501

PAC170CH502

PAL30CH501

PAU60CH504

PAC170CH601

PAL40CH601

PAC170CH602

PAL30CH601

PAU60CH604

PAC170CH701

PAL40CH701

PAC170CH702

PAL30CH701

PAU60CH704

PAC170CH801

PAL40CH801

PAC170CH802

PAL30CH801

PAU60CH804

PAC180CH101

PAL60CH102

PAC180CH102

PAU60CH103

PAC180CH201

PAL60CH202

PAC180CH202

PAU60CH203

PAC180CH301

PAL60CH302

PAC180CH302

PAU60CH303

PAC180CH401

PAL60CH402

PAC180CH402

PAU60CH403

PAC180CH501

PAL60CH502

PAC180CH502

PAU60CH503

PAC180CH601

PAL60CH602

PAC180CH602

PAU60CH603

PAC180CH701

PAL60CH702

PAC180CH702

PAU60CH703

PAC180CH801

PAL60CH802

PAC180CH802

PAU60CH803

PAC190CH101

PAU70CH1016

PAC190CH102

PAT10CH101

PAC190CH201

PAU70CH2016

PAC190CH202

PAT10CH201

PAC190CH301

PAU70CH3016

PAC190CH302

PAT10CH301

PAC190CH401

PAU70CH4016

PAC190CH402

PAT10CH401

PAC190CH501

PAU70CH5016

PAC190CH502

PAT10CH501

PAC190CH601

PAU70CH6016

PAC190CH602

PAT10CH601

PAC190CH701

PAU70CH7016

PAC190CH702

PAT10CH701

PAC190CH801

PAU70CH8016

PAC190CH802

PAT10CH801

PAC200CH101

PAU70CH101

PAC200CH102

PAT10CH103

PAC200CH201

PAU70CH201

PAC200CH202

PAT10CH203

PAC200CH301

PAU70CH301

PAC200CH302

PAT10CH303

PAC200CH401

PAU70CH401

PAC200CH402

PAT10CH403

PAC200CH501

PAU70CH501

PAC200CH502

PAT10CH503

PAC200CH601

PAU70CH601

PAC200CH602

PAT10CH603

PAC200CH701

PAU70CH701

PAC200CH702

PAT10CH703

PAC200CH801

PAU70CH801

PAC200CH802

PAT10CH803

PAC230CH102PAU70CH1010PAC230CH202PAU70CH2010 PAC230CH302PAU70CH3010 PAC230CH402

PAU70CH4010

PAC230CH502PAU70CH5010 PAC230CH602PAU70CH6010 PAC230CH702PAU70CH7010

PAC230CH802PAU70CH8010

PAC240CH102PAU70CH1011 PAC240CH202

PAU70CH2011PAC240CH302

PAU70CH3011






PAC250CH101

PAT20CH103

PAC250CH102

PAU70CH109

PAC250CH201

PAT20CH203

PAC250CH202

PAU70CH209

PAC250CH301

PAT20CH303

PAC250CH302

PAU70CH309

PAC250CH401

PAT20CH403

PAC250CH402

PAU70CH409

PAC250CH501

PAT20CH503

PAC250CH502

PAU70CH509

PAC250CH601

PAT20CH603

PAC250CH602

PAU70CH609

PAC250CH701

PAT20CH703

PAC250CH702

PAU70CH709

PAC250CH801

PAT20CH803

PAC250CH802

PAU70CH809

PAC260CH101

PAT20CH101

PAC260CH102

PAU70CH108

PAC260CH201

PAT20CH201

PAC260CH202

PAU70CH208

PAC260CH301

PAT20CH301

PAC260CH302

PAU70CH308

PAC260CH401

PAT20CH401

PAC260CH402

PAU70CH408

PAC260CH501

PAT20CH501

PAC260CH502

PAU70CH508

PAC260CH601

PAT20CH601

PAC260CH602

PAU70CH608

PAC260CH701

PAT20CH701

PAC260CH702

PAU70CH708

PAC260CH801

PAT20CH801

PAC260CH802

PAU70CH808

PAL20CH102

PAU50CH103

PAL20CH202

PAU50CH203

PAL20CH302

PAU50CH303

PAL20CH402

PAU50CH403

PAL20CH502

PAU50CH503

PAL20CH602

PAU50CH603

PAL20CH702

PAU50CH703

PAL20CH802

PAU50CH803

PAL40CH102

PASAW10CH1011

PAL40CH202

PASAW10CH2011

PAL40CH302

PASAW10CH3011

PAL40CH402

PASAW10CH4011

PAL40CH502

PASAW10CH5011

PAL40CH602

PASAW10CH6011

PAL40CH702

PASAW10CH7011

PAL40CH802

PASAW10CH8011

PAL50CH101

PASAW10CH105

PAL50CH201

PASAW10CH205

PAL50CH301

PASAW10CH305

PAL50CH401

PASAW10CH405

PAL50CH501

PASAW10CH505

PAL50CH601

PASAW10CH605

PAL50CH701

PASAW10CH705

PAL50CH801

PASAW10CH805

PAP301

PAT20CH104

PAP501

PAT20CH504

PAP901

PAT20CH204

PAP1101

PAT20CH604

PAP1501

PAT20CH304

PAP1701

PAT20CH704

PAP2101

PAT20CH404

PAP2301

PAT20CH804

PAL60CH101PAL70CH102

PAU40CH103

PAL60CH201

PAL70CH202

PAU40CH203

PAL60CH301

PAL70CH302

PAU40CH303

PAL60CH401

PAL70CH402

PAU40CH403

PAL60CH501

PAL70CH502

PAU40CH503

PAL60CH601

PAL70CH602

PAU40CH603

PAL60CH701

PAL70CH702

PAU40CH703

PAL60CH801

PAL70CH802

PAU40CH803

PAC402



PAU204

PAU50CH104PAU50CH105 PAU50CH204PAU50CH205 PAU50CH304PAU50CH305 PAU50CH404PAU50CH405 PAU50CH504PAU50CH505 PAU50CH604PAU50CH605 PAU50CH704PAU50CH705PAU50CH804 PAU50CH805

PAC102

PAC302

PAC60CH102PAC60CH202 PAC60CH302 PAC60CH402 PAC60CH502 PAC60CH602 PAC60CH702

PAC60CH802



PAC140CH302 PAC140CH402PAC140CH502 PAC140CH602 PAC140CH702


PAC150CH802

PAC210CH102 PAC210CH202 PAC210CH302PAC210CH402 PAC210CH502 PAC210CH602 PAC210CH702

PAC210CH802

PAC220CH102PAC220CH202 PAC220CH302 PAC220CH402 PAC220CH502 PAC220CH602 PAC220CH702

PAC220CH802

PAJ20CH102 PAJ20CH202 PAJ20CH302 PAJ20CH402 PAJ20CH502 PAJ20CH602 PAJ20CH702 PAJ20CH802

PAL30CH102 PAL30CH202 PAL30CH302 PAL30CH402 PAL30CH502PAL30CH602 PAL30CH702

PAL30CH802

PAR102

PAR202

PAR302

PAR402

PAU103

PAU201

PAU203


PAU40CH404 PAU40CH504 PAU40CH604 PAU40CH704PAU40CH804

PAU60CH105PAU60CH106 PAU60CH205 PAU60CH206 PAU60CH305 PAU60CH306PAU60CH405 PAU60CH406 PAU60CH505 PAU60CH506 PAU60CH605 PAU60CH606 PAU60CH705 PAU60CH706 PAU60CH805 PAU60CH806

PAU70CH107

PAU70CH1013

PAU70CH1014

PAU70CH207

PAU70CH2013

PAU70CH2014

PAU70CH307

PAU70CH3013

PAU70CH3014

PAU70CH407


PAU70CH507


PAU70CH607


PAU70CH707


PAU70CH807


Figure: PCB design and prototype.

RF inputs LO inputs IF outputsAGC control

Front-end PCBLO inputs

LO Wilkinson divider

LO synthesizer

Power Supply

PLL ref. clock

LO output

Figure: Front-end housing and setup on the antenna-array frame.



Front-end channel design specifications and prototype performance summary

Parameter Simulated Value Measured Value SpecificationRF frequency 1575.42 MHz 1575.42 MHz 1575.42 MHzIF frequency 70 MHz 69.9988 MHz 70 MHz (*)

Passband bandwidth (Bp) 17.8 MHz 17.5 MHz ≥ 12 MHzStopband bandwidth (Bs) 20 MHz 22 MHz ≤ 20 MHz (*)

GFE 73.9 dB 58+Gant = 73 dB ≥ 72.8 dBNFFE 2.178 dB 2.18 dB ≤ 4 dBPCP,FE — −65.3 dBm >−44.9 dBm (*)PIP3,FE — −65.3+9.6 =−54.7 dBm >−35.3 dBm (*)

Image rejection 60.2 dB 57 dB ≥ 40 dBPhase noise (10 kHz) −75.65 dBc −82 dBc —

Table: Simulated and measured front-end performance compared to design specifications.

• Out-of-specs linearity: considering an in-band interference signal present at the antennaterminals with Pint = PCP,FE, the front-end linearity is sufficient to test the algorithmsinterference mitigation capability for IN0≤ 113 dB-Hz considering Ta = 100 K.



FPGA Digital processing detailed block diagram

XILINX ML605 FPGA BOARD

8 CHADC

RF

8 C

HFR

ON

T-EN

D

SAMPLECLOCK

DOWNCONVERTERS&

DECIMATING FILTERS

ADCINTERFACE

SPATIALFILTER

Gb ETHMAC

CPUuBLAZE

HARDWARE ACCELERATOR

AC

QU

ISIT

ION

CO

NTR

OL

BEAMFORMERCONTROL

FPGACLOCK

MMCMADV

USB TO UART

BRIDGE

SNAPSHOTSRAM

UART

CH1

CH8

8 C

H B

US SDR GNSS

Receiver

PC

CALIBRATIONCORRECTION

GNSS FPGA PLATFORM

PLL REF

12 bits x IF channel

(22+22) bits x BB channel

(22+22) bits x BB channel (16+16) bits BB

(32+32) bits

Fs=40 Msps Fs=5 Msps

(22+22) bits x BB channel



Autocorrelation matrix estimation implementation

Rxx =1K

XXH =

=1K

[K

∑k=1

x(k)x∗1(k), . . . ,K

∑k=1

x(k)x∗N(k)

]=

=1K

K

∑k=1

x1(k)x∗1(k) . . .K

∑k=1

x1(k)x∗N(k)

.... . .

...K

∑k=1

xN(k)x∗1(k) . . .K

∑k=1

xN(k)x∗N(k)

.(35)

Rxx(1,j)

Rxx(2,j)

Rxx(3,j)

Rxx(4,j)

Rxx(5,j)

Rxx(6,j)

Rxx(7,j)

Rxx(8,j)

Column (j)Processor time

multiplexing

MU

LTIPLICATIO

N P

HA

SEIN

TEGR

ATION

PHAS

E



Real-time logic for Rxx.S

NA

PS

HO

TSR

AM

C

B

ACPL MULT 8

C

B

ACPL ADD 1

MUXC

B

ACPL MULT 1

Dout_bAddr_a

Addr_b

Dout_a

WR

Din_a

DUAL PORT

RAM

C

B

ACPL ADD 8

Rxx(1,j)[k]

Rxx(8,j)[k]

Rxx(1,j)[k-1]Rxx(2,j)[k-1]Rxx(3,j)[k-1]Rxx(4,j)[k-1]Rxx(5,j)[k-1]Rxx(6,j)[k-1]Rxx(7,j)[k-1]Rxx(8,j)[k-1]Rxx(1,j)[k-1]

Dout

Rxx(8,j)[k-1]

ACQ CTLRxx_AddrRxx_Data

FSMLOGIC

RAM_wr

RAM_Addr

StartEnd

Start_Rxx_calcEnd_Rxx_calc

Addr

Snapshots_Addr=k

Column_sel=j

Rxx estimator

)(1 kx

)(8 kx

(18+18)b

(32+32)b

(16+16)b(32+32)b

(22+22)b

)(1* kx

)(8* kx



Cross-correlation vector estimation implementation

rxd(fd, τ ) =1K

Xd(fd, τ)H =

=

[K

∑k=1

x1(k)e−j2πfd d∗(k, τ), . . . ,K

∑k=1

xN(k)e−j2πfd d∗(k, τ)

]. (36)

Rxd(1)[t]

Rxd(1)[t-1]

Rxd(1)[t-1]

Rxd(1)[t]

Rxd(1)[t-1]

Rxd(1)[t]

Rxd(1)[t-1]

Rxd(1)[t]

Rxd(1)[t-1]

Rxd(1)[t]

Rxd(1)[t-1]

Rxd(1)[t]

Rxd(1)[t-1]

Rxd(1)[t]

Rxd(1)[t-1]

Rxd(1)[t]

MU

LTIPLIC

ATIO

N

PH

AS

EIN

TEG

RA

TION

PHA

SE



Real-time logic for rxd.

DopplerWipe-off

SN

APS

HO

TSR

AM

Dout_bAddr_a

Addr_b

Dout_a

WR

Din_a

DUAL PORT

RAM

Rxd(1)[k-1]Rxd(2)[k-1]Rxd(3)[k-1]Rxd(4)[k-1]Rxd(5)[k-1]Rxd(6)[k-1]Rxd(7)[k-1]Rxd(8)[k-1]

Dout

ACQ CTL

Rxd_Addr

Rxd_Data

Start_Rxd_calc

End_Rxd_calc

Addr

Rxd estimator

C

B

ACPL MULT 1

C

B

ACPL ADD 1

C

B

A

BPSK

MOD 1

reset

Parallel load

Count

COUNTER FSMLOGIC

RAM_wr

RAM_Addr

StartEndReset

Code Delay

reset

SV

PRN_out

GPS C/A

PRN

Rxd(1)[k]

C

B

ACPL MULT 8

C

B

ACPL ADD 8

C

B

A

BPSK

MOD 8

Rxd(8)[k]

Rxd(1)[k-1]

Rxd(8)[k-1]

SVNUM

Doppler

(22+

22)b

)(1 kx

)(8 kx

(8+8)b

(31+

31)b

(31+

31)b

(32+32)b

1 b



High-level operations: FPGA embedded software-defined processor

EMBEDDED PROCESSOR RESET

INITPLATFORM

WAITFOR

COMMAND

SET SAT ID,

SET ACQUISION

COMPUTE

COMPUTE

GLRTCOLORED

COMPUTEACQUISITION

GLRTWHITE

SINGLEANTENNA

MF

SENDRESULTS

UART AXI LITE

AXI LITE

ACQUISITIONCONTROL

FSL

FSL

FSL

FSL

FSLYOUR

ACQUISITIONALGORITHM

FSL

SDR GNSSReceiver

PC



Calibration process1. Generate a reference carrier fcal = fc + fref, capture X, and estimate the amplitudes

vector acal = [ 1√P1, . . . , 1√

PN] ∈ R1×N , where Pi =

1K ∑

K−10 xix∗i

2. Estimate the phase shifts between the reference channel and rest of the channels using

the ML estimator and compute φcal =

[e−j2π

ˆ∆k1 freffs , . . . ,e−j2π

ˆ∆ki freffs

]∈ C1×N .

3. Compute Gcal = diag(acal)diag(φcal) and apply it to the snapshots as Xcal = GcalX.

Figure: Calibration setup in an anechoicchamber.

0 500 1000 1500 2000

−1000

−500

0

500

1000

Sample index k

Am

plitu

de

0 500 1000 1500 2000−1.5

−1

−0.5

0

0.5

1

1.5

Sample index k

Am

plitu

te

Figure: Uncalibrated and calibrated snapshotsplots for fref = 10 kHz.



Calibration validation IA spectral Multiple Signal Classification (MUSIC) algorithm was used to estimate atest signal DOA and verify the array calibration:

(θ, ψ) = argmaxθ,ψ

1v(θ,ψ)H(I−uuH)v(θ,ψ)

, (37)

where v(θ,ψ) ∈ CN×1 is the signal steering vector, u ∈ CN×1 is the eigenvectorassociated with the most powerful eigenvalue of Rxx, and I ∈ RN×N is the identity.

10 20 30 40 50 60 70 80 900

2

4

6

8

10

12

14

Elevation ψ []

MU

SIC

DO

Aes

tim

atio

nR

oot

squar

eer

ror

[]

Calibrated DOAθ = 180

θ = 0

Figure: DOA elevation estimation pointing error for θ = 0 and θ = 180 (The array wascalibrated in the broadside direction ψ = 90).



Calibration validation II

Figure: MUSIC signal DOA estimation forθ = 0, ψ = 45.






Interference scenario setup

• A GPS L1 C/A satellite signal is transmitted using a horn antenna, with θ = 0

and ψ = 90, simulating a realistic situation were a high elevation satellite isreceived with C/N0 = 44 dB-Hz.

• An interference signal is transmitted using an auxiliary monopole antenna withan approximated DOA of θ = 45 and ψ = 45, which simulates a moderateelevation jammer or a communication signal coming from nearbycommunication tower.

• The interference signal and the satellite signal were generated by two AgilentE4438C generators. The latter was equipped with GPS Personality.

• The test functions were executed using Tacq = 1 ms of captured snapshots.



Interference scenario setup

Satellite antenna

Jammer antenna

45º

Antenna array receiver prototype

Reference receiver



Implemented acquisition functions

• GLRT colored

T1(X) = maxfd ,τ

rH

xd(fd,τ)R−1dd R−1

xx rxd(fd,τ)> γ. (38)

• GLRT white

T2(X) = maxfd ,τ

rxd(fd,τ)H rxd(fd,τ)

Tr(Rxx)

> γ. (39)

• Single antenna MF

T3(X, i) = maxfd ,τ

K−1

∑t=0‖xi(t)e−j2πfd d∗(t,τ)‖2

> γ, (40)

where i is the selected antenna element.



Acquisition results for CW interferenceA Continuous Wave (CW) jammer impinges into the array with fint = 1575.43MHz and J/N0 = 133 dB-Hz.

5.5 5.75 6 6.25 6.5 6.75 7 7.25 7.5 7.75 8 8.25 8.5

x 107

−70

−60

−50

−40

−30

−20

−10

0

10

Frequency [Hz]

Pow

er[d

Bm

]in-band CWinterference

GPS L1 C/A

(a) IF spectrum. (b) TSingle(x(t, fd , τ)).

(c) TGL White(X(t, fd , τ)). (d) TGL Colored(X(t, fd , τ)).



Acquisition results for 4G/LTEA possible Lightsquared interference was simulated using a Long Term Evolution(LTE) downlink signal with 5 MHz of bandwidth, impinging into the array withfint = 1575.42 MHz and J/N0 = 133 dB-Hz.

5.5 5.75 6 6.25 6.5 6.75 7 7.25 7.5 7.75 8 8.25 8.5

x 107

−70

−60

−50

−40

−30

−20

−10

Frequency [Hz]

Pow

er[d

Bm

]

in-band 4G/LTEinterference

GPS L1 C/A

(e) IF spectrum. (f) TSingle(t, fd , τ)).

(g) TGL White(t, fd , τ)). (h) TGL Colored(t, fd , τ)).



Deflection coefficient

The deflection coefficient is defined as

d2 =(ET(X;H1)−ET(X;H0))2

varT(X;H0). (41)

In the measurements, the expectations operators and the variance operator weresubstituted by its sample mean and sample variance respectively.

90 100 110 120 130 140 1500

2000

4000

6000

8000

10000

12000

14000

CW interference I/N0 [dB-Hz]

Defl

ecti

onco

effici

ent

GLRT Colored (T1(X))

GLRT White (T2(X))

Single antenna MF (T3(X))

33 dB

(i) CW interference scenario.

90 100 110 120 130 140 1500

2000

4000

6000

8000

10000

12000

14000

LTE interference I/N0 [dB-Hz]

Defl

ecti

onco

effici

ent

GLRT Colored (T1(X))

GLRT White (T2(X))

Single antenna MF (T3(X))

25 dB

(j) LTE interference scenario.


Introduction




Conclusions



Theoretical analysis

Done:

! GLRT extension to the GNSS array signal model assuming an arbitrary andunknown covariance noise matrix. The obtained detector is able to mitigatetemporally uncorrelated interferences even if the array is unstructured andmoderately uncalibrated.

! The performance and the interference rejection capability were modeled andcompared to their theoretical bound. The detector was proven to be a UMP testdetector and has CFAR properties.

! The proposed acquisition algorithm was compared to conventional acquisitionafter the MVDR beamformer. The MVDR is severely affected by moderatepointing errors and/or array miss-calibration, while the GLRT detectorremains insensible to this situation.

! Analysis of realistic conditions to obtain preliminary hardware requirementsfor an implementation of the algorithm.

! The effect of the signal bandwidth in the acquisition has been modeled: anincrease of the bandwidth beyond the main spectrum lobe reduces the SNR,and, consequently, reduces also the performance of the acquisitionalgorithms.



Theoretical analysis

To Do:

f Explore the application of the Bayesian approach to the acquisition problem; itmight be possible to estimate a prior PDF for the synchronizationparameters and integrate them in the GLRT detector.

f Integration of inertial sensors in the receiver at acquisition stage.

f Ultimately, an hybridization between array-based acquisition and trackingmight be possible, since both algorithms are related in the sense that acquisitioncontains prior information suitable for tracking initialization and vice-versa.



Design and implementation of a real-time array-based GNSS receiver platform

Done:

! A novel real-time array-based GNSS receiver platform was developed:! A complete signal reception chain, including the antenna array and the multichannel

RF front-end for the GPS L1/ Galileo E1 was designed, implemented and tested.! The FPGA digital processing section of the platform, such as the array signal

statistics extraction modules were also implemented.! Coupled with a software defined receiver.

! Design trade-offs and implementation complexities were carefully analyzed andtaken into account.

! Proof-of-concept prototype: the array-based acquisition algorithm introducedin this Dissertation was implemented and tested under realistic conditions.

! Harsh in-band interference scenarios were tested, including narrow/wideband interferers and communication signals. The performance results werealigned with the theoretical and simulated ones, thus, completing thealgorithm validation.



Design and implementation of a real-time array-based GNSS receiver platform

To Do:

f The platform can be enhanced by integrating an IMU.

f Design and implementation of dual-band antenna elements patches to coverboth the GPS L1 / Galileo E1 and the GPS L5 Galileo E5a links, which providea complete SoL signals coverage of two of the most evolved GNSS.

f Explore the integration of array elements and front-end calibrationprocedures.

f Explore the application of open source soft processors such as the AeroflexGaisler LEON3 to replace the Microblaze implementation. Ultimately, it shouldbe possible to integrate the GNU Radio framework and the GNSS-SDRsoftware receiver in the soft processor.



Interference mitigation in GNSS signal acquisition through antenna arrays

Dr. Javier Arribas([email protected])

Interference Management for Tomorrow’s Wireless NetworksNewcom# Summer School Sophia Antipolis - May 28-31, 2013

Thank you for your attention!


Existing solutions: Acquisition after beamforming

RFfront-end

ADC

GNSSAntenna array

y = w HXX y

TDBF(y) °

H0

H1

w optR xx

h0

Beamformerprocessor

Single antennaacquisition

Figure: Acquisition after beamforming concept.

Beamformer output signal model and GLRT test function:

y = wHX, (42)

TDBF(X) = maxfd ,τ

RHyd(fd,τ)Ryd(fd,τ)

Ryy> γ, (43)

where w ∈ CN×1 is the beamformer weights vector, and

Ryd =1K

ydH = wH 1K

XdH = wH rxd (44)

Ryy =1K

yyH = wHRxxw. (45)


Existing solutions: Acquisition after beamformingTest function distribution

TDBF(X)∼

χ22(δTDBF;H1

), in H1,

χ22(δTDBF;H0

= 0), in H0,(46)

where σ2TDBF

= 12K and

δTDBF;H1=‖µRyd

‖2

Ryy=

wHRddhhHR∗ddwwHRxxw

. (47)

Performance expressions

Pd(γ) = Q1

√

δTDBF;H1

σTDBF

,

√γ

σTDBF

, (48)

Pfa(γ) = exp

−γ

2σ2TDBF

, (49)

where Q1 is the generalized Marcum Q-function of order 1. The acquisition teststatistic is CFAR.


Existing solutions: MVDR beamformer

Minimum Variance Distortionless Response (MVDR) optimum weights

minw

wHRxxw

s.t wHh0 = 1,(50)

where h0 ∈ CN×1 is the DOA steering vector. Then,

wopt =R−1

xx h0

hH0 R−1

xx h0. (51)

MVDR GLRT test function

TMVDR(X) =rH

xd(R−1xx h0)(R−1

xx h0)H rxd

hH0 R−1

xx h0' 1

σ2

|rHxdP⊥Hi

h0|2

‖hH0 P⊥Hi

‖2. (52)


Existing solutions: Power minimization beamformerDesign condition: the DOA is unavailable. The beamformer minimizes the outputpower while not weighting a reference antenna (h0 = [10 . . . 0]).

Performance in absence of interferences (P⊥Hi= I)

TPWR(X) = σ−2‖rH

xdh0‖2 = TGL(x1, fd,τ). (53)

0 50 100 1500

100

200

300

400

500

600

700

TDBF (X)

Fre

quen

cy

H0 Histogram.

H1 Histogram.

H0 Theoretical PDF.

H1 Theoretical PDF.

Figure: TPWR(X) histogram and theoretical PDF in both H1 and H0 acquisition hypotheses forGalileo E1 signal acquisition simulation.


J. Arribas, GNSS Array-based Acquisition: Theory and Implementation, PhDThesis, Universitat Politecnica de Catalunya (UPC), Barcelona, Spain, June2012.

C. Fernandez-Prades, Advanced Signal Processing Techniques for GNSSReceivers, PhD Thesis, Universitat Politecnica de Catalunya (UPC), Barcelona,Spain, May 2006.

B.W. Parkinson, and J.J. Spilker (eds.), Global Positioning System: Theory andApplications, vol. I, II, Progress in Astronautics and Aeronautics, AmericanInstitute of Aeronautics, Inc., Washington DC, 1996.

L. Weill, “C/A Code Pseudoranging Accuracy-How Good Can it Get?”,Proceedings of ION GPS-94, the 7th International Technical Meeting of theSatellite Division of the Institute of Navigation, pp. 133–141, Salt Lake City,UT, 1994.

J. R. Williams, “U.S. Spectrum Allocations 300 - 3000 MHz”, Tech. rep.,OPP/FCC, 2002.

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