advanced signal processing techniques for global navigation satellite...

Carles Fernandez Prades. PhD. Thesis defense: Advanced Signal Processing Techniques For Global Navigation Satellite Systems Receivers 1/ 116

Introduction ML Synchronization Beamforming Search & Rescue Implementation Conclusions Publications

Advanced Signal Processing Techniques ForGlobal Navigation Satellite Systems Receivers

PhD. Thesis Defense

Carles Fernandez Prades

Universitat Politecnica de CatalunyaDept. of Signal Theory and Communications

April 27, 2006



Outline

Introduction to GNSS Synchronization

Maximum Likelihood Synchronization with antenna arrays

Array beamforming algorithms applied to GNSS

Application to satellite-based Search & Rescue systems

Implementation of a GPS antenna array receiver

Conclusions and further research

Research contributions



Introduction to GNSSSynchronization



Navigation

• The art of finding the way from one place to another is callednavigation.

• In the 16 and 17th Century, thousands of sailors were dying atsea because simply they could not find their position, and tonesof goods were lost in maritime accidents.

• The problem was not the latitude, easy to calculate from theSun’s position, but the longitude. The longitude of a location isdirectly related to the difference between the local time and theGreenwich reference time.

• The Board of Longitude offered a reward to obtain a solution thatcould provide longitude to within a half of degree (and usable atsea!)



John Harrison’s timekeepersA number of methods were proposed: the observation of Jupiter’ssatellites by Galileo, the lunar tables by Tobias Mayer or the Newtonianreflecting telescope by John Hardley. None of them worked at sea.Finally, a humble carpenter named John Harrison achieved the reward.

(a) H1 (1730-1735)

(b) H2 (1737-1740)

(c) H3 (1740-1759)

(d) H4 (1755-1759)



How a GNSS works

The Earth is continuallycircled by a constellationof satellites. At least, fourof them are always visiblefrom any location.



GPS: signal structureEach satellite transmits a Direct-Sequence Spread-Spectrum signalwith the following general baseband model:

sT (t)=√

PT

(γ

∞

∑m=−∞

dI(m)pI(t −mTbI )+ j√

1− γ2∞

∑n=−∞

dQ(n)pQ(t −nTbQ )

)(1)

where pI(t)=∑NcI −1u=0 qI(t−uTPRNI ) and qI(t)=∑

LcI −1k=0 cI(k)gT ,I(t−kTcI )

For the sake of simplicity, we can reduce (1) to

sT (t) =1√2

∞

∑m=−∞

d(m)Nc−1

∑u=0

Lc−1

∑k=0

c(k)gT (t − kTc −uTPRN −mTb)

=1√2

∞

∑m=−∞

d(m)p(t −mTb) (2)



GPS spreading codes

• The spreading codes used by GPS are Gold codes.

• They were chosen by their desirable properties ofcross-correlation and easiness of implementation.

• Examples of current codes are:• C/A code. 1 ms in length at a chipping rate of 1023 Kcps.

Allocated in the quadrature component of the L1 band.• P/Y code. 7 days in length at a chipping rate of 10.23 Mcps.

Currently used for precise positioning. When the code isencrypted, we talk about Y code (military reasons). Allocated inthe Inphase component of the L1 band.



GPS frequency bands

• L1 band Centered at fL1 = 1575.42 MHz.

sL1(t) = CP(Y )(t)⊕D(t)+ jCC/A(t)⊕D(t) (3)

• L2 band Centered at fL2 = 1227.6 MHz.

SV Blocks L2 In-Phase L2 Quadrature-Phase (L2CS)CP(Y )(t)⊕D(t),

Block II/IIA/IIR CP(Y )(t), or Not ApplicableCC/A(t)⊕D(t)

CCM(t)⊕D(t) time multiplexed with CCL(t),Block IIR-M CP(Y )(t)⊕D(t), or CCM(t)⊕D′(t) time multiplexed with CCL(t),

CP(Y )(t) CC/A(t)⊕D(t), orCC/A(t)

CCM(t)⊕Dc(t) time multiplexed with CCL(t),Block IIF CP(Y )(t)⊕D(t), or CC/A(t)⊕D(t), or

CP(Y )(t) CC/A(t)



GPS frequency bands

• L5 band. The L5 link will be only available on Block IIF SVs, andthe planned future Block III. Centered at fL5 = 1176.45 MHz.

sL5(t) = CI5(t)⊕D5(t)⊕nh10(t)+ jCQ5(t)⊕nh20(t) (4)

The I5 component contains a synchronization sequencenh10 = 0000110101, a 10 bit Neuman-Hoffman code thatmodules each 100 symbols of D5(t), and the Q5 component hasanother synchronization sequencenh20 = 00000100110101001110 at 20 kbps.



Galileo signal structure: introducing the BOC modulation

• A Binary Offset Carrier modulation, BOC(fs,rc) is generated inbaseband by the product of two signal components: a non-filteredPRN code with a chip rate rc and values ±1 and a non-filteredsquare signal with frequency fs (equal or higher than rc) acting asa carrier. In general:

xBOC(t) = x(t)sign (sin(2πfst)) (5)

• The Alternative BOC (AltBOC) allows the allocation of differentchannels. Intuitively, the idea is to perform the same process thanin the BOC modulation but multiplying the baseband signal for acomplex square signalv(t) = sign (cos(2πfst))+ jsign (sin(2πfst)). Then:

xAltBOC(t) = x1(t)v(t)+ x2(t)v∗(t) (6)



Galileo frequency bands

Galileo will provide 10 navigation RHCP signals:• E5 band 1164−1215 MHz, final election between:

• Two QPSK(10) signals transmitted on a carrier frequency offE5A = 1176.45 MHz and fE5B = 1207.14 MHz.

• One AltBOC(15,10) signal transmitted at fE5 = 1191.795 MHz

• E6 band 1215−1300 MHz. It contains three channels inHexaphase modulation.

SE6(t) = [CE6A(t)DE6A

(t)ScE6 (t)cos(m)−CE6C(t)sin(m)]+ (7)

+j[CE6B(t)DE6B

(t)cos(m)+CE6A(t)DE6A

(t)ScE6 (t)CE6B(t)DE6B

(t)CE6C(t)sin(m)]

where ScE6(t) is the sub-carrier for generating the BOC(10,5).

• E2-L1-E1 1559−1610 MHz. Same structure than E6, usingBOC(1,1) and BOC(15,2.5)



Autocorrelation functions

−2 −1.5 −1 −0.5 0 0.5 1 1.5 2−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

Delay in code chips

Nor

mal

ized

aut

ocor

rela

tion

func

tion

(a) BPSK(1)

−2 −1.5 −1 −0.5 0 0.5 1 1.5 2−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

Delay in code chips

Nor

mal

ized

aut

ocor

rela

tion

func

tion

(b) BOC(1,1)

−2 −1.5 −1 −0.5 0 0.5 1 1.5 2−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

Delay in code chips

Nor

mal

ized

aut

ocor

rela

tion

func

tion

(c) BOC(10,5)

−2 −1.5 −1 −0.5 0 0.5 1 1.5 2−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

Delay in code chips

Nor

mal

ized

aut

ocor

rela

tion

func

tion

(d) BOC(15,2.5)

Normalized autocorrelation functions of navigation signals, filtered at20 MHz.



Power spectral density

−10 −8 −6 −4 −2 0 2 4 6 8 10−50

−45

−40

−35

−30

−25

−20

−15

−10

−5

0

Frequency [MHz]

Nor

mal

ized

spe

ctru

m [d

B]

(a) BPSK(1)

−10 −8 −6 −4 −2 0 2 4 6 8 10−50

−45

−40

−35

−30

−25

−20

−15

−10

−5

0

Frequency [MHz]

Nor

mal

ized

spe

ctru

m [d

B]

(b) BOC(1,1)

−10 −8 −6 −4 −2 0 2 4 6 8 10−50

−45

−40

−35

−30

−25

−20

−15

−10

−5

0

Frequency [MHz]

Nor

mal

ized

spe

ctru

m [d

B]

(c) BOC(10,5)

−10 −8 −6 −4 −2 0 2 4 6 8 10−50

−45

−40

−35

−30

−25

−20

−15

−10

−5

0

Frequency [MHz]

Nor

mal

ized

spe

ctru

m [d

B]

(d) BOC(15,2.5)



Signals coming from the sky

• Channel model: Wide Sense Stationary with UncorrelatedScattering (WSSUS)

h(t;ξ) =M−1

∑m=0

am(t)ejθm(t)δ(ξ− τm(t)) (8)

• Signal after LNA and downconversion

zM(t) =M−1

∑m=0

αmej2π(fdm−fd0 )tLc−1

∑k=0

c(k)gT (t−τm−kTc)+w(t) (9)



Generic GNSS receiver block diagram

RF Low Noise Amplifier

Down converter

A/D converter Digital receiver

channel 1

2 N

RHCP Antenna

Receiver processing

Navigation processing

User interface

Analog FI

Digital FI

Reference oscillator

Phase Locked Loop

Synthesiser

Automatic Gain Control

Power control



The Delay Locked Loop (DLL)

In DS-SS terminology, the matched filter is often referred as correlator,while the processing it performs is called despreading.Synchronization algorithms can be classified in:

• Non-Data Aided τ0NDA = arg maxτ0

N

∑n=0

|y(nTs + τ0)|2

• Data Aided or Decision Directed

τ0DD/DA = arg maxτ0

ℜ

N

∑n=0

d∗(n)y(nTs + τ0)e−jθ0

In both cases, maximization of y(τ0) ⇒ Derivative ⇒ Finitedifferences: Early E = y(τ+ δ

2 Tc), Prompt P = y(τ) and LateL = y(τ− δ

2 Tc).



DLL discriminators• Early minus late power

Deml−p(τ) =(I2E +Q2

E

)−(I2L +Q2

L

)(10)

• Early minus late envelope

Deml−e(τ) =√(

I2E +Q2

E

)−√(

I2L +Q2

L

)(11)

• Dot product power

Ddot(τ) = (IE − IL) IP +(QE −QL)QP (12)

• Coherent

Dc(τ) =[(IE − IL)cos(θ)+(QE −QL)sin(θ)

]sign (IP) (13)

The expected value of the discriminator output η = ED(τ) in termsof the trial value τ is called S-curve.



A classical synchronization architecture: the DLL

Integration & Dump

Integration & Dump

Integration & Dump

Integration & Dump

Integration & Dump

Integration & Dump

Shift register

COS map

SIN map

Carrier NCO

Code generator Code NCO

Receiver baseband processor

Carrier cycle counter

Code phase counter

Digital IF

I E

I P

I L

Q E

Q P

Q L

E P L



S-curves for different DLL implementations

−2 −1.5 −1 −0.5 0 0.5 1 1.5 2

−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

S−curve for different DLL implementations (BPSK signal)

Tracking error [chips]

Dis

crim

inat

or o

utpu

t

EML powerDot productCoherentEML normalized envelope

−2 −1.5 −1 −0.5 0 0.5 1 1.5 2

−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

S−curve for different DLL implementations (BOC(1,1) signal)

Tracking error [chips]

Dis

crim

inat

or o

utpu

t

EML powerDot productCoherentEML normalized envelope



Problem identification

Receiver

Line Of Sight Signal

Secondarypath

Multipath with the direct path (Line-Of-Sight Signal or LOSS) and onesingle echo.



Multipath produces bias

-1 -0.5 0 0.5 1-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4LOSS signal

Delayed and attenuated replica

LOSS+Delayed and attenuated replica

Norm

aliz

edco

rrel

ator

outp

ut

Delay error / Tc

-0.01 0 0.01 0.02 0.03 0.04

1.42

1.425

1.43

1.435

1.44

1.445

1.45

1.455




-1.5 -1 -0.5 0 0.5 1 1.5-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

=0.1

=0.5

-0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

Bias

Dif

fere

nce

betw

een

late

and

earl

yre

plic

as

S-curve for non-coherent DLL (with multipath)

Delay error / Tc




0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2−0.25

−0.2

−0.15

−0.1

−0.05

0

0.05

0.1

0.15

0.2

0.25

Reflection Delay [chips]

Tim

e D

elay

Bia

s [c

hips

]

Conventional and Narrow DLL bias produced by a single reflection for BPSK(1)

Conventional DLL, δ=1 Narrow Correlator, δ=0.1

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2−0.25

−0.2

−0.15

−0.1

−0.05

0

0.05

0.1

0.15

0.2

0.25


Tim

e D

elay

Bia

s [c

hips

]

Conventional and Narrow DLL bias produced by a single reflection for BOC(1,1)

Conventional DLL, δ=1 Narrow Correlator, δ=0.1



State-of-the-art in GNSS synchronization• Multipath Estimating Delay Locked Loop (MEDLL): robust

statistical approach. ML applied to a signal model where thenumber of reflections is considered known.

τi = arg maxτ

ℜ

Ry(τ)−

M−1

∑m=0m 6=i

amR(τ− τm)e−jθm

e−jθi

(14)

ai = ℜ

Ry(τi)−

M−1

∑m=0m 6=i

amR(τi − τm)e−jθm

e−jθi

(15)

θi = ∠

Ry(τi)−M−1

∑m=0m 6=i

amR(τi − τm)e−jθm

(16)

where Ry(τ) is the I/Q downconverted correlation function andR(τ) is the reference correlation function.



State-of-the-art in GNSS synchronization

• Double Delta Correlators• Multipath Elimination Technology (MET)

∆TMET =(E1−E2)+ δ

2 (a1 +a2)

a1−a2(17)

• High Resolution Correlator (HRC), Strobe correlator, PulseAperture Correlator (PAC)

DPAC(τ) = 2∗ (E1−L1)− (E2−L2) (18)



Performance of the PAC correlator

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2−0.025

−0.02

−0.015

−0.01

−0.005

0

0.005

0.01

0.015

0.02

0.025


Tim

e D

elay

Bia

s [c

hips

]

(a) BPSK(1)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2−0.025

−0.02

−0.015

−0.01

−0.005

0

0.005

0.01

0.015

0.02

0.025


Tim

e D

elay

Bia

s [c

hips

]

(b) BOC(1,1)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2−0.025

−0.02

−0.015

−0.01

−0.005

0

0.005

0.01

0.015

0.02

0.025


Tim

e D

elay

Bia

s [c

hips

]

(c) BOC(10,5)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2−0.025

−0.02

−0.015

−0.01

−0.005

0

0.005

0.01

0.015

0.02

0.025


Tim

e D

elay

Bia

s [c

hips

]

(d) BOC(15,2.5)



Maximum LikelihoodSynchronization with antenna

arrays



Approach justification

• Why ML? Because its desirable properties: asymptoticalefficiency, invariance

• Why antenna arrays? Among code, time and frequencydiversities, arrays exploit spatial diversity. The application ofantenna arrays to GNSS was pioneered by Dr. Gonzalo Seco.

We will consider an N-element antenna array receiving Mtime-delayed and Doppler-shifted signals with known structure.



Structured array modelBaseband model for a single antenna:

x(t) =M

∑i=1

aisi(t − τi)expj2πfi t+w(t) (19)

Antenna array signal model:

x = GAd+n (20)

where• x(t) ∈ CN×1 is the observed signal vector,• G ∈ CN×M is the spatial signature matrix,• A = diag(a) ∈ CM×M is a diagonal matrix with the elements of

the amplitude vector a along its diagonal,• d = [s1(t − τ1)expj2πf1t . . .sM(t − τM)expj2πfM t]T ∈ CM×1

the delayed and Doppler–shifted narrowband signals envelopes,• n(t) ∈ CN×1 represents additive noise and all other disturbing

terms.



Assumptions

• Narrowband array assumption: the time required for the signal topropagate along the array is much smaller than the inverse of itsbandwidth.

• Narrowband signal assumption: the Doppler effect can bemodeled by a frequency shift.

• We consider the baseband functions s(t) as band-limitedfinite-average-power signals.

• Synchronization parameters and statistical properties of the noiseare piecewise constants during the observation window.



Spatially colored noise

The term n gathers noise, multipath and interferences in a complex,circularly symmetric Gaussian vector process with a zero–mean,temporally white and arbitrary unknown spatial correlation matrix Q:

E n[n]= 0 (21)

E

n[n]nT [m]

= 0 (22)

E

n[n]nH [m]

= Qδn,m (23)

ClaimThis is a key statistical assumption for multipath mitigation withantenna arrays



Working with blocks of dataTaking K snapshots with a sampling interval satisfying Nyquistcriterion:

• X ∈ CN×K , the spatiotemporal data matrix

• The basis function matrix:

D =

s1(t0 − τ1)ej2πf1 t0 · · · s1(tK−1 − τ1)ej2πf1 tK−1

......

sM(t0 − τM)ej2πfM t0 · · · sM(tK−1 − τM)ej2πfM tK−1

∈ CM×K

• N =(

n(t0) · · · n(tK−1))∈ CN×K

X = GAD+N (24)



Unstructured array model

• The a priori knowledge of DOAs and the location of the antennaelements is a reasonable assumption in GNSS applications.

• In practice, this assumption implies a considerable technicalcomplexity (calibration, phase reference).

Solution: we can define a channel matrix H which assumes the role ofGA but does not impose any structure. This matrix implicitly modelsunknown phenomenons: errors in measured gain, mutual coupling,variations in temperature and humidity, drift in hardware behavior...

X = HD+N (25)



Cramer-Rao Bound definitionWe denote the covariance matrix of the estimation errors of a vectorparameter ξ by

C(ξ) = E

[ξ−ξ

][ξ−ξ

]T

. (26)

The multiple-parameter Cramer-Rao Bound states that, for anyunbiased estimate of ξ,

C(ξ)≥ J−1, (27)

where J is the Fisher Information Matrix or FIM.

DefinitionThe FIM elements are defined by

Juv =−E

[∂2Λx(ξ)

∂ξu∂ξv

]. (28)



CRB matrix partitioningComputation

Juv = 2ℜ

K−1

∑k=0

∂(µx(tk ,ξ))H

∂ξuQ−1 ∂µx(tk ,ξ)

∂ξv

(29)

µx(t,ξ) = G(θ,φ)Ad(t,τ , f).ξ =

[ℜaT ℑaT θT φT τ T fT

]T• Amplitude parameters: α =

[ℜaT ℑaT

]T• Spatial parameters: Ψ =

[θT φT

]T• Synchronization parameters: Υ =

[τ T fT

]TJ=

Jαα JT

Ψα JTΥα

JΨα JΨΨ JTΥΨ

JΥα JΥΨ JΥΥ

, J∈R6M×6M



Computation of the FIM elements

The FIM elements can becomputed analytically usingequation (29) and the definition of

• amplitude α,

• space Ψ, and

• synchronization Υ

vector parameters.

J =

Jαα JTΨα JT

Υα

JΨα JΨΨ JTΥΨ

JΥα JΥΨ JΥΥ

Jαu αv = 2ℜ

K−1

∑k=0

d(tk )H ∂AH

∂αuGH Q−1G

∂A∂αv

d(tk )

JΨu αv = 2ℜ

K−1

∑k=0

d(tk )H AH ∂GH

∂ΨuQ−1G

∂A∂αv

d(tk )

JΥu αv = 2ℜ

K−1

∑k=0

∂d(tk )H

∂ΥuAH GH Q−1G

∂A∂αv

d(tk )

JΨuΨv = 2ℜ

K−1

∑k=0

d(tk )H AH ∂GH

∂ΨuQ−1 ∂G

∂ΨvAd(tk )

JΥuΨv = 2ℜ

K−1

∑k=0

∂d(tk )H

∂ΥuAH GH Q−1 ∂G

∂ΨvAd(tk )

JΥuΥv = 2ℜ

K−1

∑k=0

∂d(tk )H

∂ΥuAH GH Q−1GA

∂d(tk )∂Υv



CRB of navigation signals

0 10 20 30 40 5010−11

10−10

10−9

10−8

10−7

10−6

10−5

10−4

10−3

CN0 [dB−Hz]

CR

B o

f Tim

e D

elay

est

imat

ion

/ Tc2

BPSK(1)BOC(1,1)BOC(10,5)BOC(15,2.5)

Cramer-Rao Bounds for time delay estimation applied to BPSK(1),BOC(1,1), BOC(10,5) and BOC(15,2.5)



Discussion about the results

ClaimThe DOA and the synchronization parameters are decoupled.

Proof. Using partitioned matrix theory:(CRBΨΨ CRBT

ΥΨCRBΥΨ CRBΥΥ

)=(

JΨΨ−JΨαJ−1ααJT

Ψα JTΥΨ−JΨαJ−1

ααJTΥα

JΥΨ−JΥαJ−1ααJT

Ψα JΥΥ−JΥαJ−1ααJT

Υα

)−1

If M = 1...

JΥΨ−JΥαJ−1ααJT

Ψα = 0 ⇒ CRBΥΨ = 0

Complete proof provided in the Dissertation.



Consequences of CRBΥΨ = 0

• The CRB for synchronization parameters CRBΥΥ remains thesame whether or not the spatial parameter vector Ψ is known.

• We do not need aprioristic estimates of the DOA to asymptoticallyachieve the minimum variance in the estimation of thesynchronization parameters when an unbiased estimator isconsidered.

• The same accuracy in parameter estimation can be theoreticallyachieved with the structured and the unstructured signal model.



ML estimation of time delays and Doppler shiftsThe PDF of a complex multivariate Gaussian vector x is:

p(x) =exp[−(x−Hd)HQ−1(x−Hd)

]πN det(Q)

(30)

The negative log-likelihood function for K observations of x is:

Λ1(Q,H, f,τ ) = ln(det(Q))+TrQ−1 1K

(X−HD)(X−HD)H (31)

Using the following cross-correlation estimation matrix definitions:

RXX = 1K XXH RXD = 1

K XDH

RDX = RHXD RDD = 1

K DDH (32)

Computing gradient of Λ1 with respect to Q and equalling to zero:

QML =(RXX− RXDHH −HRDX +HRDDHH)∣∣∣H=HML,f=fML,τ=τML

(33)



ML estimation of time delays and Doppler shifts

Replacing QML in Λ1:

Λ2(H, f,τ ) = lndet(W)+ lndet

(I+ B

)(34)

whereW = RXX− RXDR−1

DD RHXD = QML (35)

andB = RDD

(H− RXDR−1

DD

)HW−1 (H− RXDR−1

DD

)(36)

The value of the channel matrix H which nulls B and thereforeminimizes Λ2 is the ML estimator HML = RXDR−1

DD . Therefore:

fML, τML = argminf,τ

lndet(W). (37)



Thinking in the obtained estimator

• It does not depend on the estimation of the channel matrix H.Therefore, it does not depend on DOAs (as predicted in the CRBanalysis).

• With some matrix algebra manipulations, the obtained estimatoris equivalent to

fML, τML = argminf,τ

ln(det(I−PXH PDH )) (38)

where PDH = DH(DDH)−1D is the projection matrix over thesubspace spanned by the columns of DH , and PXH definedequally.



ML cost function shapes

(a) BPSK(1) (b) BOC(10,5)

Plots of ΛML for BPSK and BOC signals. In all the cases, it has beenconsidered a circular array with N = 8 antennas, M = 1, a DOA ofφ = 80o and θ = 80o, CN0 = 30 dBHz, fs = 40 MHz, τ = 50 samplesand fd = 1 kHz



ML cost function shapes

Representation of ΛML using the signal structure of a Search &Rescue beacon.



Line-Of-Sight Signal delay and carrier phase estimation

In the particular case of structured array, M = 1 and fd = 0

X = agsT (τ)+N, (39)

the ML approach [G. Seco] leads to

aML =gHW−1(τ)rXs(τ)

PsgHW−1(τ)g

∣∣∣∣τ=τML

(40)

and

τML = argmaxτ

∣∣gHR−1XX rXs(τ)

∣∣2Ps − rH

Xs(τ)R−1XX rXs(τ)

(41)

which are the recommended estimators for implementation in a realreceiver.



Other suboptimal estimators• Steepest descent. It does not ensure finding the global minimum,

must be initialized within a convergence region.

Υ(i+1) = Υ(i)−λ(i)∇ΥΛML(Υ(i)) (42)

• Slow convergence• Problematic choosing of the weight term λ(i) (dependence of the

scenario)

• Newton-Raphson method. Local method with faster convergence.

Υ(i+1) = Υ(i)−(

HΥΛML(Υ(i)))−1

∇ΥΛML(Υ(i)). (43)

• Numerically unstable• Heavy computational load



Time delay estimation bias

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.510−5

10−4

10−3

10−2

10−1

100

Delay of second path / Tc

Bia

s of

tim

e de

lay

estim

atio

n / T

c

ML unstructuredML white noiseML structured

Circular array with N = 8 antennas, a DOA of φ = 80o and θ = 80o , M = 1, CN0 = 30 dBHz, fs = 40 MHz, τ = 50 samples and

fd = 1 kHz. Reflection 3 dB below the LOSS, impinging from φ = 70o , θ = 70o .



MSE of time delay estimation

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 210−10

10−9

10−8

10−7

10−6

10−5

10−4

10−3

10−2

10−1

Delay of second path / Tc

MS

E o

f tim

e de

lay

estim

atio

n / T

c

CRB

CRB detailed model

ML unstructured

ML white noise

ML structured

Parameters of direct signal: CN0d = 30 dB-Hz, φd = 80o , θd = 80o . Parameters of the reflection: CNOm = 27 dB-Hz, φ = 70o ,

θ = 70o . Relative Doppler: 1 kHz.



Consistency of the estimator

0 5 10 15 20 25 30 35 40 45 5010−11

10−10

10−9

10−8

10−7

10−6

10−5

Number of pulses

MS

E o

f tim

e de

lay

estim

atio

n / T

c

CRB

ML unstructured

ML white noise

ML structured

MSE of time delay estimation when a secondary path is present, expressed as a function of the number of pulses used in thecomputation. Parameters of direct signal: CN0d = 30 dB-Hz, φd = 80o , θd = 80o . Parameters of the reflection: CNOm = 27

dB-Hz, φ = 70o , θ = 70o . Relative delay: Tc4 . Relative Doppler: 1 kHz.



Array beamforming algorithmsapplied to GNSS



Concept of beamforming

DefinitionBeamforming with antenna arrays is a technique that consists ofseveral antennas which outputs are controlled in phase and gain, i.e.,multiplied by complex weights, in order to achieve a gain pattern thatcan be manipulated electronically.

• The ML approach was based in the statistical properties of theincoming signals (arbitrary covariance matrix).

• The spatial filtering provided by array beamforming allows moreintuitively interpretation. No need of statistical assumptions.

• In GNSS, we have information about the DOA thanks to thenavigation message.



Temporal Reference Beamforming

A possible criterion: minimization of the mean square error,understanding error as the mismatch between the actual output signaland a reference signal. ⇒ Temporal diversity.

wTE = argminw

E∣∣wHX−aT D

∣∣2 (44)

A straightforward gradient computation leads to

wTE = R−1XX RXDa∗ (45)



Space Reference Beamforming

Another possible criterion: minimizing the total output power whileforcing the beamformer to always point to the desired sources.⇒ Spatial Diversity

wMVB = argminw

[E∣∣wHX

∣∣2= E

wHXXHw

= wHRXX w]

(46)

subject to wHG = 11×M (47)

Applying the Lagrange multipliers method, the beamvector results in

wMVB = R−1XX G

(GHR−1

XX G)−1

1M×1 (48)



Hybrid Beamforming

Objective: to minimize the MSE but constraining the system to alwayspoint towards the desired signals. Space-Time diversity

minw

J1(w) =1K

wwwHX−aT Dww2

(49)

subject to wHG = 1 (50)

This is a well-known M linear–constrained (50) quadratic–form (49)optimization problem. Applying Lagrange’s multipliers technique:

wMHB = R−1XX RXDa∗+ R−1

XX G(GHR−1

XX G)−1 (

1−GHR−1XX RXDa∗

)(51)



Interpretation of the result

wMHB = R−1XX RXDa∗+ R−1

XX G(GHR−1

XX G)−1 (

1−GHR−1XX RXDa∗

)The obtained beamformer is a linear combination of

• Temporal reference: wTE = R−1XX RXDa∗

• The second term in (52) is a linear combination of the columns ofR−1

XX G(GHR−1

XX G)−1

, each column being a MVB pointing to thedirection given by one column of G.

• They show a different behavior against multipath: while wTE triesto combine constructively the desired signal with other replicas inorder to increase the SINR, wMVB combines destructively suchsignals to minimize the output signal power.

Result: wMHB has an inherent capability in multipath and interferencemitigation.



Example of radiation pattern

South

Azi

mut

h

North

−1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

• 12–element circular array

• GPS–like BPSK signal

• LOSS: φd = 45o, θd = 80o,CN0 = 30 dB-Hz

• Echo: φm = 0o, θm = 55o,3 dB below LOSS,Tc4 delayed



Equivalence between hybrid beamforming and MLestimation

For a generic pointing vector p, the problem can be reformulated as:

w, f, τ |hybrid = arg minw,f,τ

J2(w, f,τ ) = arg minw,f,τ

wHWw (52)

subject to wHG = p (53)

Then:whybrid = W−1G

(GHW−1G

)−1pT (54)

When this last expression is inserted in (52) results in

J3(f,τ ) = p(GHW−1G

)−1pT (55)




Matrix inversion lemma lets an insightful inversion of W:

W−1 = R−1XX + R−1

XX RXD

(RDD − RH

XDR−1XX RXD

)−1RH

XDR−1XX (56)

Expression (56) shows that the minimization of (55) takes place whenRDD − RH

XDR−1XX RXD is the null matrix. Therefore:

RDD − RHXDR−1

XX RXD =1K

DDH − 1K

DXH (XXH)−1XDH = 0 ⇒

⇒ DDH = DXH (XXH)−1XDH ⇒

⇒ I = DPXH DH (DDH)−1 ⇒⇒ D = DPXH PDH ⇒

⇒ I = PXH PDH

This is the same condition than in equation (38) for the minimizationof the ML cost function




Such equivalence is particularly interesting because

• The beamforming approach consists of a minimization of a costfunction that has a clear interpretation, and there is no need ofassumptions about the data statistics. However, no a priori claimsabout the optimality of the obtained estimates can be done.

• In contrast, the ML approach provides a procedure to obtainoptimum estimates based on a probabilistic statement, but itsinterpretation in terms of how the signals are processed is notintuitive at all.

• The equivalence is accomplished regardless the chosen pointingvector.



Robust hybrid beamforming

• There are many potential causes of pointing errors.

• Recently, convex optimization theory has been applied to robustbeamforming in order to cope with such mismatches.

• Assuming that pointing errors are bounded ‖E‖F ≤ ε, ε > 0,the problem can be reformulated as

minw

wHWw (57)

subject to |wHS| ≥ 11×M ∀S ∈ S(ε) (58)

where |·| stands for the absolute value and

S(ε) = S | S = G(φ,θ)+E,‖E‖F ≤ ε (59)



Casting in a Second-Order Cone Program• After some manipulations, the problem can be rewritten as a

(convex) second-order cone program:

minχ,w

χ

subject to ‖Uw‖ ≤ χ,

ε1‖w‖ ≤ wT g1−1,...

εM‖w‖ ≤ wT gM −1,wT g1 = 0,

...wT gM = 0.

where:

w =

[ℜwℑw

],

gi =

[ℜgiℑgi

],

gi =

[ℑgi−ℜgi

],

W =

[ℜW −ℑWℑw ℜW

],

W = UHU.

• It can be solved efficiently in polynomial time via interior pointalgorithms.



Hybrid beamforming and its robust version

• 8–element uniform linear array

• GPS–like BPSK signal 1 kHzDoppler–shifted

• CN0 = 30 dB-Hz

• rb = 1.023 Kbps

• 4 samples per bit

• LOSS: 45o from the broadside.

• Echo:−45o, CN0 = 20 dB-Hz andwith a time delay of a half a bit(coherent multipath) with respectto the LOSS

• DOA mismatch: 5o



Application to satellite-basedSearch & Rescue systems



System overview

1. A beacon emitsa distress signal

PLBELTEPIRB

2. A constellation of satellitesrelays the signal

3.A Local User Terminalreceives the replicas andcomputes the beaconposition.

4. A Mission Control Centervalidates the alert and informthe corresponding RCC

5. A Rescue Coordination Centercoordinates the rescue responseto the distress.



Problem definition

• Currently, the system works with 4 Low Earth Orbit and 3Geostationary Earth Orbit (GEO) satellites ⇒ no globalcoverage, high false alarm probability.

• Taking advantage of Medium Earth Orbit satellites (GPS &Galileo) is under consideration ⇒ Tight power budget restrictions.

• Problem: Estimate time delay and Doppler shift of all the replicasreceived at MEOLUT with enough accuracy to perform precisepositioning.



2G COSPAS/SARSAT 406 MHz distress beacon

6 6 6 6Tone Preamble Data

160 ms 15 bits 9 bits88 bits – short message

120 bits – long message

• Tone: the initial 160 ms ±1 percent of the transmitted signalconsists of an unmodulated carrier at the transmitter frequency.

sT1(t) = A∏

(t − t1

2

t1

)t1 = 160 ms (60)

• Preamble: which is formed of two known sequences of 15 and 9bits

sP1(t) = A

(cos(1.1)+ j sin(1.1)

24

∑k=1

ak pman(t − t1 − kTb)

)∏

(t − t1 − t2

2

t1

)(61)

t2 = 60 ms.



2G COSPAS/SARSAT 406 MHz distress beacon• Data: this field is where the information of the specific distress

beacon is transported and is 87 and 120 bits long for the shortand long message respectively.

sD1(t) = A

(cos(1.1)+ j sin(1.1)

L

∑k=1

dk pman(t − t1 − t2 − kTb)

)∏

(t − t1 − t2 − t3

2

t3

)(62)

L = 88/120, t3 = 220/300 ms, (short / long message)

Resulting on the following model:s2G(t) = sT1

(t)+ sP1(t)+ sD1

(t) (63)

1.1 rad

1

2

0.89 Eb

0.45 Eb

0.89 Eb

Ψ1 = 1√Tb

∏

(t− Tb

2Tb

)Ψ2 = 1√

Tbpman(t)



2G spurious emission markThe complete message, when generated, is filtered by a signal maskwhose lowpass equivalent is

(a) Specifications (b) Implementation



3G COSPAS/SARSAT 406 MHz distress beacon

• The pure tone sT2(t)

sT2(t) = A∏

(t − t1

2

t1

)t1 = 82 ms (64)

• The preamble sP2(t), where ak=±1 and bk=±1 are thesequences described above:

sP2(t) = A

15

∑k=1

(ak p(t − t1 − kTs)+ jbk pman(t − t1 − kTs))∏

(t − t1 − t2

2

t2

)(65)

t2 = 37.5 ms



3G COSPAS/SARSAT 406 MHz distress beacon• The data sD2(t), where ck=±1 and dk=±1 are the

convolutionally encoded and scrambled in-phase and quadratureuser data

sD2(t)= A

L

∑k=1

(ck p(t − t1 − t2 − kTs)+ jdk pman(t − t1 − t2 − kTs))∏

(t − t1 − t2 − t3

2

t3

)(66)

L = 96/129, t3 = 240/322.5 ms (short / long message.

Resulting on the following signal:s3G(t) = sT2

(t)+ sP2(t)+ sD2

(t) (67)

(1,1)(-1,1)

(-1,-1) (1,-1)

1

2

~

~

bE

bE

bE

bE

Ψ1 = 1√Tb

∏

(t− Tb

2Tb

)Ψ2 = 1√

Tbpman(t)



Single antenna approach

• The measurements are considered to be a superposition of planewaves corrupted by noise and, possibly, interferences andmultipath.

• Given the measurements, the objective is to estimate a set ofparameters associated with the wavefronts.

• Frequency Difference Of Arrival (FDOA)• Time Difference Of Arrival (TDOA)

• An antenna receives M scaled, time–delayed andDoppler–shifted replicas of the distress signal relayed by theMEO satellites:

x(t) =M

∑i=1

ais(t − τi)expj2πfdi t+n(t) (68)



Frequency Of Arrival estimation: 2G results

0 5 10 15 20 25 30 35 4010−12

10−10

10−8

10−6

10−4

10−2

100

102

C/NO

[dB−Hz]

FDO

A E

stim

atio

n M

SE

[KH

z2 ]FFTBarlettMinimum VarianceMUSICCRB

MSE for FDOA estimation: single antenna techniques applied to the2G SARSAT distress beacon



Frequency Of Arrival estimation: 3G results

0 5 10 15 20 25 30 35 4010−12

10−10

10−8

10−6

10−4

10−2

100

102

C/NO

[dB−Hz]

FDO

A E

stim

atio

n M

SE

[KH

z2 ]FFTBarlettMinimum VarianceMUSICCRB

MSE for FDOA estimation: single antenna techniques applied to the3G SARSAT distress beacon



Time Of Arrival estimation: 2G results

0 5 10 15 20 25 30 35 4010

−10

10−8

10−6

10−4

10−2

100

102

104

C/NO

[dB−Hz]

TD

OA

Est

imat

ion

MS

E [m

s2 ]TPTPDCRB

MSE for TDOA estimation: single antenna techniques applied to the2G SARSAT distress beacon



Time Of Arrival estimation: 3G results

0 5 10 15 20 25 30 35 4010

−10

10−5

100

105

C/NO

[dB−Hz]

TD

OA

Est

imat

ion

MS

E [m

s2 ]TPTPDCRB

MSE for TDOA estimation: single antenna techniques applied to the3G SARSAT distress beacon



Antenna array approach

• There is a need of steerable antennas in order to decrease therequired C/N0. Two approaches:

• Mechanically moved dishes: high mechanical complexity, largearea (“dish farm”), any capability in space processing, highmaintenance cost.

• Electronically steerable antenna arrays: remain physicallyimmobile, signal processing capabilities.

• In this dissertation, we propose the use of antenna arrays in theMEOLUT.



Multiple beamforming architecture• We propose a digital structure implementing one beamforming

per tracked satellite, each one selecting a particular satellite andnulling the contribution of others (Selection Of Satellites)

whSOS,i = R−1XX RXDa∗+ R−1

XX G(GH R−1

XX G)−1 (

ei −GH R−1XX RXDa∗

)(69)

• Digital beamforming architecture



Proposed algorithm for hSOS

@@N

- LNA -N - ADC -

@@1

- LNA -N - ADC -

... l∼fLO

6

?

X -Beamforming Modules

G

-

a

-

wi

fd1 , τ1-

fdM , τM-

@@R

...

D

-



FDOA estimation: single antenna vs arrays

0 5 10 15 20 25 30 35 4010−14

10−12

10−10

10−8

10−6

10−4

10−2

100

102

C/NO

[dB−Hz]

FDO

A F

FT E

stim

atio

n M

SE

[KH

z2 ]

Single antennaCRB − single antennaTRBMVBhSOSCRB − antenna array

(a) 2G beacon

0 5 10 15 20 25 30 35 4010−12

10−10

10−8

10−6

10−4

10−2

100

102

C/NO

[dB−Hz]FD

OA

FFT

Est

imat

ion

MS

E [K

Hz2 ]


(b) 3G beacon

Comparison between FFT-based frequency estimation error for asingle antenna receiver and for an 8-element antenna array receiver



TDOA estimation: single antenna vs arrays

0 5 10 15 20 25 30 35 4010−10

10−8

10−6

10−4

10−2

100

102

104

C/NO

[dB−Hz]

TDO

A T

P E

stim

atio

n M

SE

[ms2 ]


(a) 2G beacon

0 5 10 15 20 25 30 35 4010−12

10−10

10−8

10−6

10−4

10−2

100

102

104

C/NO

[dB−Hz]TD

OA

TP

Est

imat

ion

MS

E [m

s2 ]


(b) 3G beacon

MSE of TDOA for a single antenna receiver and for an 8-elementantenna array using only the tone and the preamble to generate theadapted–filter bank.



FDOA estimation: multipath mitigation (2G)

0 5 10 15 20 25 30 35 4010−12

10−10

10−8

10−6

10−4

10−2

100

102

C/NO

[dB−Hz]

FDO

A F

FT E

stim

atio

n M

SE

[kH

z2 ]

TRBMVBhSOSCRB − antenna array

8-element antenna array receiver. The scenario is composed of three desired signals

(2G) plus a secondary path replica.



FDOA estimation: multipath mitigation (3G)

0 5 10 15 20 25 30 35 4010−12

10−10

10−8

10−6

10−4

10−2

100

102

C/NO

[dB−Hz]

FDO

A F

FT E

stim

atio

n M

SE

[kH

z2 ]


8-element antenna array receiver. The scenario is composed of three desired signals

(3G) plus a secondary path replica.



TDOA estimation: multipath mitigation (2G)

0 5 10 15 20 25 30 35 4010−10

10−5

100

105

C/NO

[dB−Hz]

TDO

A T

P E

stim

atio

n M

SE

[ms2 ]


8-element antenna array receiver. The scenario is composed of threedesired signals (2G) plus a secondary path replica. Only tone andpreamble have been used.



TDOA estimation: multipath mitigation (3G)

0 5 10 15 20 25 30 35 4010−10

10−5

100

105

C/NO

[dB−Hz]

TDO

A T

P E

stim

atio

n M

SE

[ms2 ]


8-element antenna array receiver. The scenario is composed of threedesired signals (3G) plus a secondary path replica. Only tone andpreamble have been used.



Space resolution

0 50 100 150 200 250 3000

5

10

15

20

25

30

Minimum signal separation ensuring a gain of 10Â·log10

(N)

Sig

nal s

epar

atio

n [d

egre

es]

Number of antennas

FOA

TOA (TP)

TOA (TPD)

Two 2G distress signals with CN0 = 15 dB, same time delay and 3kHz of Doppler separation have been considered.



Implementation of a GPSantenna array receiver



Philosophy of the implementation

• There is a bridge between signal theory and hardwareimplementation.

• Development of an 8-channel antenna array receiver devoted toGPS L1 C/A signal.

• Software Defined Radio (SDR) flavored. Paradigm: to sample asclose to the antenna as possible.

• SDR works with blocks of data rather than data streaming.• SDR avoids mismatch between hardware and signal model.• SDR allows the use of more sophisticated signal processing

algorithms.

• Architecture based on the commercial RF front-end GP2015 ofZarlink.



Block diagram of the antenna array receiver

LNA

Sign MagSampleCLK

AnalogIF Output

40 MhzOut

10 MHzGP2015SAWFilter

LNA

Sign MagSampleCLK

AnalogIF Output

40 MhzOut


LNA

Sign MagSampleCLK

AnalogIF Output

40 MhzOut


CalibrationSignal

Splitter

10 MhzRef

Splitter

Front-end 1 Front-end 2 Front-end 8



Antennas and Low Noise Amplifiers

LNA Specification ValueCenter Frequency 1575.42 MHz

Bandwidth 2 MHzGain 30 dB

Noise Factor < 4.5 dBInput impedance 50 Ω

Output impedance 50 Ω

Calibration signal coupling > 6 dB



RF front-end block diagram

LNA - Front EndMixer

- 175.42 MHzFilter

- 2nd StageMixer

- 35.42 MHzFilter

AGC3rd StageMixer

4.309 MHzFilter

AmplifierIF Output4.309 MHz

61.4 GHz

6140 MHz

631.11 MHz



Rack containing the eight RF down-shifting stages



IF sampling: exploiting intentional aliasing

f (MHz)

f (MHz)

2 MHz

4.309 5.714

4.309 MHz

5.7144.3091.405

−4.309

−4.309 −1.405

FrequencySampling



Testing the digital output

(a) Collecting digital data (b) GPS Development Board

(c) Accessing correlator inputs (d) More hacking details



Description of storage subsystem

• Each GPS front–end is sampled with 2 bits of resolution.

• Two samples of each front end are combined in a 16-bit word.

• These words are buffered in a RAM memory connected to a PCIbus.

• A computer software accedes this RAM memory via the PCI busand stores the data in the hard disk.

Some system details

Sampling frequency: fs = 407 = 5.714 MHz.

Bit rate: 11.428 Mbps x 8 front-ends = 91.428Mbps.Acquisition card: National Instruments PCI 6434.



Diagram of storage subsystem

Data storage is controlled by a specially developed LabView-based softwarewith friendly graphic user interface.Data are accessible to MATLAB via a specially developed interface tool.



Satellite acquisition

Acquisition results with real data integrating 10 ms. Only the mostsignificant bit (sign) of the collected samples has been used.



Results with real data

NordnavTM R–25 Output Coarse estimation Fine estimation3.2939 3.2000 3.28482.0928 2.0000 2.0976-1.2194 -1.2000 -1.2112-2.9506 -3.0000 -2.9408-4.2575 -4.2000 -4.28801.5666 1.6000 1.6080-2.7005 -2.6000 -2.6752-2.8449 -2.8000 -2.8304

Doppler coarse and fine estimation results (in kHz) of 8 in–viewsatellites compared to the NordnavTM R–25 output.



Conclusions and furtherresearch



Conclusions

• Multipath is the main source of performance degradation inGNSS from the receiver point of view.

• The traditional implementation of the ML estimator for time delaysynchronization (DLL), is biased when coherent multipathimpinges the antenna and jeopardizes the whole performance ofthe receiver.

• We have provided an overview of the state-of-the-art insynchronization technology devoted to GNSS receivers.



Conclusions

• Classical single-antenna receivers are inherently affected bysome insuperable drawbacks

• Discriminating the Line Of Sight Signal from the reflections islimited by the time resolution imposed by the signal bandwidth

• Any unbiased time delay estimator based in a single antenna havea variance that approach to infinity when the relative delaybetween the LOSS and its replica approach to zero

• Other approaches focused in communication applications sacrificedirect signal discrimination for better performance in datarecovering, but this is not the scope of a navigation receiver.

• To overcome these drawbacks, our proposal is to resort toantenna arrays.



Conclusions

• An array signal model which gathers noise, multipath and interferences in aGaussian term, assumed temporally white but spatially colored, captures thestatistical behavior of the signal while keeps the model simple.

• Applying the ML approach to such model leads to a function cost which is notdependent of the channel matrix. Its minimization gives the ML estimates oftime delays and Doppler shifts of a set of superposed waveforms.

• The computation of the CRB states that, asymptotically, the same accuracy canbe achieved in the structured and the unstructured array models. DOA andsynchronization parameters are uncoupled.

• We have proposed some suboptimal methods in order to palliate thecomputational burden required by the ML cost function.

• Simulation studies show the inherent robustness of such estimators againstmultipath, compared to the traditional white noise assumption.



Conclusions

• Provided that an a priori knowledge of DOA is a naturalassumption in GNSS, the problem has been attacked from abeamforming point of view.

• We have proposed a Hybrid Space-Time Multiple Beamforming,which combines the complementary behavior of the TemporalReference and Minimum Variance Beamforming.

• We have established a link between the ML estimator and theHybrid Beamforming, which comes from a completely differentapproach.

• Hybrid beamforming dramatically reduces the computational costcompared to the ML approach.



Conclusions

• Beamforming theory has been applied to a satellite–basedSearch & Rescue system, overcoming problems derived from atight power budget.

• The Hybrid Beamforming with Selection Of Satellites pointingstrategy is the recommended method for MEOLUTimplementation.

• Simulation results show a better performance of this algorithm incase of the presence of multipath, compared to traditionalbeamforming methods.

• We have proposed a digital beamforming software-orientedarchitecture.



Conclusions

• An 8-element antenna array has been implemented and tested.

• We have provided a complete description of the receiver designand the specially-developed interfaces to a PC.

• The satellite signal acquisition has been discussed from aSoftware Defined Radio perspective.

• Results have been obtained using real data captured with thedeveloped array.



Further research (ongoing work)

• More simulation results of the ML estimator behavior are needed:robustness to frequency mismatches, impact of the number ofantennas, etc.

• The weight factor in the Steepest Descent and Newton-Raphsonmethod must be optimized.

• The Bayesian approach, taking advantage of the informationprovided by Inertial Measurement Units, should be investigated.

• The developed array must be calibrated in order to perform digitalbeamforming.

• More research have to be done in the position computation.



Further research (ongoing work)

• Maximum Likelihood Estimation of Position.• Pau Closas, C. Fernandez Prades, and Juan A. Fernandez-Rubio, “Maximum

Likelihood Estimation of Position in GNSS”, submitted to IEEE Signal ProcessingLetters.

• Application of Sequential Monte-Carlo methods (ParticleFiltering)

• Pau Closas, C. Fernandez Prades, and Juan A. Fernandez-Rubio, “SequentialMonte-Carlo Approximation to the ML Time-Delay Estimator in a MultipathChannel”, Proceedings of the IEEE Workshop on Signal Processing Advances inWireless Communications (SPAWC), Cannes, France, July 2006.

• Pau Closas, C. Fernandez Prades, and Juan A. Fernandez-Rubio, “SequentialMonte-Carlo Tracking Algorithm for Multipath Mitigation in Navigation Systems”,submitted to the IEEE Transactions on Aerospace and Electronic Systems.

• Development of Software Defined Radio techniques for GPS andGalileo software receivers.




Journal papers

• Gonzalo Seco, Juan A. Fernandez-Rubio, and C. Fernandez Prades, “MLestimator and Hybrid Beamformer for multipath and interference mitigation inGNSS receivers”, IEEE Transactions on Signal Processing, vol. 53, no. 3, pp.1194–1208, March 2005, ISSN: 1053-587X.

• C. Fernandez Prades, Pau Closas Gomez, Juan A. Fernandez-Rubio andGonzalo Seco, “Parameter estimation techniques in Local User Terminals forSearch & Rescue systems based on Galileo and GPS satellites”, submitted toIEEE Transactions on Aerospace and Electronic Systems, 2005.

• Pau Closas Gomez, C. Fernandez Prades, and Juan A. Fernandez-Rubio andGonzalo Seco, “Sequential Monte Carlo Tracking Algorithm for MultipathMitigation in Navigation Systems”, submitted to IEEE Transactions onAerospace and Electronic Systems, 2006.




Technical reports

• C. Fernandez Prades, Pau Closas Gomez, and Juan A.Fernandez Rubio, “Advanced Signal Processing techniques inLocal User Terminals for Search & Rescue systems Based onMEO satellites”, Tech. Rep. ESTEC/Contract no.17713/03/NL/LvH/jd, Dept. of Signal Theory andCommunications, Universitat Politecnica de Catalunya (UPC),Barcelona, February 2005.

• Juan A. Fernandez Rubio, Olga Munoz Medina, and C.Fernandez Prades, “Analysis of TDOA, Doppler frequency shiftand BER estimation at the MEOLUT”, Tech. Rep. INDRAEspacio, Dept. of Signal Theory and Communications, UniversitatPolitecnica de Catalunya (UPC), Barcelona, 2002.




International conferences• P. Closas Gomez, C. Fernandez Prades, and J.A. Fernandez-Rubio, “Sequential Monte-Carlo Approximation to the ML

Time-Delay Estimator in a Multipath Channel”, accepted in the Seventh IEEE International Workshop on SignalProcessing Advances for Wireless Communications SPAWC, Cannes, France, 2006.

• P. Closas Gomez, C. Fernandez Prades, and J.A. Fernandez-Rubio, “Bayesian DLL for multipath mitigation in navigationsystems using Particle Filters”, accepted in the IEEE International Conference on Acoustics, Speech and SignalProcessing ICASSP, Toulouse, France, 2006.

• C. Fernandez Prades, P. Closas Gomez, and J.A. Fernandez-Rubio, “Advanced signal processing techniques in LocalUser Terminals for Search & Rescue systems based on MEO satellites”, Proceedings of the ION GNSS, Institute OfNavigation, Long Beach, CA, September 2005. ION 2005.

• C. Fernandez Prades, P. Closas Gomez, and J.A. Fernandez-Rubio, “Time-frequency estimation in theCOSPAS/SARSAT system using antenna arrays: variance bounds and algorithms”, Proceedings of the 13th EuropeanSignal Processing Conference, EUSIPCO, Antalya, Turkey, September 2005.

• C. Fernandez Prades, P. Closas Gomez, and J.A. Fernandez-Rubio, “New trends in global navigation systems:implementation of a GPS antenna array receiver”, Proceedings of the Eight International Symposium on SignalProcessing and Its Applications, ISSPA, Sydney, Australia, August 2005.

• P. Closas Gomez, C. Fernandez Prades, J.A. Fernandez Rubio, Gonzalo Seco, and Igor Stojkovic, “Design of Local UserTerminals for Search and Rescue systems with MEO satellites”, Proceedings of the 2nd ESA Workshop on SatelliteNavigation User Equipment Technologies NAVITEC, ESA/ESTEC, Noordwijk, The Netherlands, December 2004.

• C. Fernandez Prades, and J. A. Fernandez Rubio, “Robust space-time beamforming in GNSS by means ofsecond-order cone programming”, Proceedings of the International Conference on Acoustics, Speech and SignalProcessing, ICASSP, vol. 2, pp. 181-184, Montreal, Quebec, Canada, May 2004.




International conferences• C. Fernandez Prades, and J.A. Fernandez-Rubio, “Multi-frequency GPS/Galileo receiver design using direct RF

sampling and antenna arrays.”, Third IEEE Sensor Array and Multichannel Signal Processing Workshop, SAM, Sitges,Barcelona, Spain, 18-21 July 2004.

• C. Fernandez Prades, A. Ramırez Gonzalez, Pau Closas Gomez, and Juan A. Fernandez Rubio, “Antenna arrayreceiver for GNSS”, Proceedings of the Eight European Symposium on Global Navigation Satellite System, GNSS,Rotterdam, The Netherlands, 2004.

• C. Fernandez Prades, J.A. Fernandez-Rubio, and Gonzalo Seco, “A Maximum Likelihood approach to GNSSsynchronization using antenna arrays”, Proceedings of the ION GPS/GNSS, Institute Of Navigation, Portland, OR,September 2003.

• A. Ramırez Gonzalez, C. Fernandez Prades, and Juan A. Fernandez Rubio, “Some experiments using EGNOS andGPS/INS in terrestrial navigation”, Proceedings of the Seventh European Symposium on Global Navigation SatelliteSystem, GNSS, Graz, Austria, 2003.

• C. Fernandez Prades, J.A. Fernandez-Rubio, and Gonzalo Seco, “On the equivalence of the joint Maximum Likelihoodapproach and the multiple Hybrid Beamforming in GNSS synchronization.”, Proceedings of the Sixth Baiona Workshopon Signal Processing in Communications, Baiona, Spain, September 2003.

• C. Fernandez Prades, J. A. Fernandez Rubio, and Gonzalo Seco, “Joint maximum likelihood of time delays and dopplershifts”, Proceedings of the Seventh International Symposium on Signal Processing and its Applications, ISSPA 2003,IEEE, Paris, France, July 14 2003, ISBN 0780379470.




National conferences• P. Closas Gomez, C. Fernandez Prades, and J.A. Fernandez-Rubio, “Optimizing the Likelihood with Sequential

Monte-Carlo Methods”, Submitted to the XXI Simposium Nacional de la Union Cientıfica Internacional de Radio (URSI),2006.

• P. Closas Gomez, C. Fernandez Prades, A. Ramırez Gonzalez, and J.A. Fernandez-Rubio, “Sincronizacion con arraysde antenas: aplicacin al sistema SARSAT”, XIX Simposium Nacional de la Union Cientıfica Internacional de Radio(URSI), Barcelona, Spain, September 2004, in Spanish.

• C. Fernandez Prades, A. Ramırez Gonzalez, and J.A. Fernandez-Rubio, “Rechazo de interferencias medianteconformacion de haz hıbrida multiple en GNSS”, XVIII Simposium Nacional de la Union Cientıfica Internacional deRadio (URSI), A Coruna, Spain, September 2003, in Spanish.

• P. Closas Gomez, C. Fernandez Prades, and J.A. Fernandez-Rubio, “Estimacion de parametros en sistemas searchand rescue basados en satelites”, XVIII Simposium Nacional de la Union Cientıfica Internacional de Radio (URSI), ACoruna, Spain, September 2003, in Spanish.

• C. Fernandez Prades, O. Munoz Medina, J.A. Fernandez-Rubio, and A. Ramırez Gonzalez, “Estimacion de MaximaVerosimilitud de Retardos y Desplazamientos Doppler”, XVII Simposium Nacional de la Union Cientıfica Internacionalde Radio (URSI), pp. 237-238, Alcala de Henares, Madrid, Spain, Sep. 2002, in Spanish.

• A. Ramırez Gonzalez, C. Fernandez Prades, and J.A. Fernandez-Rubio, “Integracion GPS/INS para NavegacionVehicular Terrestre en entornos de alta dinamica”, XVII Simposium Nacional de la Union Cientıfica Internacional deRadio (URSI), pp. 431-432, Alcala de Henares, Madrid, Spain, Sep. 2002, in Spanish.

• C. Fernandez Prades, A. Ramırez, and J.A. Fernandez-Rubio, “Implementacion de Correccion de Pseudodistancias ydel Algoritmo de Bancroft en MATLAB para el Posicionamiento Preliminar en GPS”, XVI Simposium Nacional de laUnion Cientıfica Internacional de Radio (URSI), pp. 287-288, Madrid, Spain, Sep. 2001, in Spanish.




Master Theses directed• F. J. Gonzalez Arranz, and V. Montoya Barrera, Implementacion Software en MATLAB y

Simulink de un correlador GPS de 12 canales, Master Thesis, Escola Tecnica Superiord’Enginyeria de Telecomunicacio de Barcelona (ETSETB), Universitat Politecnica deCatalunya (UPC), Barcelona, Spain, October 2003, in Spanish.

• P. Closas Gomez, Parameter Estimation in Search & Rescue Satellite-Based Systems,Master Thesis, Escola Tecnica Superior d’Enginyeria de Telecomunicacio de Barcelona(ETSETB), Universitat Politecnica de Catalunya (UPC), Barcelona, Spain, November2003.

• M. A. Jara Burgos, Plataforma basada en nuevas tecnologıas aplicadas a la docencia,Master Thesis, Escola Tecnica Superior d’Enginyeria de Telecomunicacio de Barcelona(ETSETB), Universitat Politecnica de Catalunya (UPC), Barcelona, Spain, 2004, inSpanish.

• A. Font Valverde, and J. Tena Lucia, Programacion de Applets en comunicaciones yprocesado de senyal dentro de una plataforma docente, Master Thesis, Escola TecnicaSuperior d’Enginyeria de Telecomunicacio de Barcelona (ETSETB), UniversitatPolitecnica de Catalunya (UPC), Barcelona, Spain, October 2004, in Spanish.

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