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8/19/2019 Impulse Radio Ultra-Wideband Antenna Array Correlation BeamformingImpulse Radio Ultra-Wideband Antenna Array Correlation Beamforming

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Impulse Radio Ultra-Wideband Antenna ArrayCorrelation Beamforming

Igor Dotlić, Kamya Yekeh Yazdandoost, Huan-Bang Li and Ryu Miura

National Institute for Information and Communications Technology, Japan

2016 International Conference on Electronics, Information andCommunication

Dotlić, Yazdandoost, Li & Miura (NICT) IR-UWB Correlation Beamforming ICEIC 2016 1 / 27

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Outline1 Introduction

2 PreliminariesWideband antenna array time-domain modelCorrelation beamformer

Received signal down-conversionSignal correlationBeamformer output

Beamformer gainBeamformer gain denitionMaximum attainable beamformer gain

3 Gain pattern synthesisGeneral principlesProposed method

Overall optimization problemGain reduction constraint

4 Numerical examplesSimulation setup

Pulse p (t )Antenna array element

Dotlić, Yazdan doost, Li & Miura (NICT) IR-UWB Correlation Beamforming ICEIC 2016 2 / 27

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Introduction

1 IntroductionWideband antenna array time-domain modelCorrelation beamformerBeamformer gainGeneral principlesProposed methodSimulation setupBeamformer pattern shaping examples


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Introduction

Introduction of Impulse Radio Ultra-Wideband (IR-UWB)

UWB RegulationsIn 2002 US FCC published its sub-part F of Part 15 regulations

Receiver architecturesEnergy Detection (ED) receivers

Low complexityFirst to appearHigh sensitivity to multiple access interference.

Commercially available coherent IR-UWB

Appeared considerably laterHigh accuracy two-way indoor positioning and radar




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Introduction

Rationale for beamforming in IR-UWB

Low regulated EIRP spectral density of only -41.3dBm/ MHz.The most limiting factor for range and data rate in the IR-UWBsystems.

Range and/or data rate may be increased by employing antennaarrays.Phase shifters can be used for beamforming in small UWB arrays.For larger arrays more complex signal processing techniques arenecessary

UWB beamforming in the digital domain ⇒ high sampling rates.Analog delay lines ⇒ large space required




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Introduction

Correlation beamforming paradigm

Radar ⇒ single range bin is of interest (range gating).Radio receiver

⇒ known TOA and DOA.

Array pattern shaping in correlation beamformers is little investigated.

Topic of this work.Arbitrary array geometry.Arbitrary elements’ patterns.


l

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Preliminaries

2 PreliminariesWideband antenna array time-domain modelCorrelation beamformerBeamformer gainGeneral principlesProposed methodSimulation setupBeamformer pattern shaping examples


P li i i Wid b d i d i d l

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Preliminaries Wideband antenna array time-domain model

Wideband antenna array time-domain model

Antenna array comprising M elements with indexesk ∈ {0, 1, . . . , M −1}.Position vector of the k -th element r k .

Time-domain radiation pattern is denoted g k ( u , t ).Wideband pulse p (t ) incident on the array from direction u .

Signal produced at the output of the k -th array element:

s k ( u , t ) = p (t )⊗g k ( u , t ). (1)

⊗ denotes convolution.


Preliminaries Correlation beamformer

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Received signal down-conversion

× LPF

π / 2

cos(2π f 0t ) s̃ k ( u , t ) × (· ) d t z k ( u )

× LPF ζ ∗k (t )

s k ( u , t )

s̃ Q k ( u , t )

s̃ I k ( u , t )

To other array elements.

Figure: A single element of correlation beamformer.

s̃ k ( u , t ) = p̃ (t ) ⊗̃g k ( u , t ), (2)



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Signal correlation

The correlation template has the form:

ζ k (t ) = p̃ (t −τ maxk ). (3)The correlator output z k ( u ) is calculated as

z k ( u ) =+ ∞

−∞

s̃ k ( u , t )ζ ∗

k (t ) dt . (4)

τ maxk = argmaxτ

+ ∞

−∞

s̃ k ( u max , t )p̃ ∗ (t −τ ) dt (5)



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Beamformer output

Calculated as a weighted sum of correlators’ outputs:

v ( u ) = w H z ( u ). (6)

z ( u ) = [ z k ( u )]M − 1

k =0 – the column vector of the correlator outputs.Superscript “H ” denotes Hermitian transposition.

w – column vector of complex weights.


Preliminaries Beamformer gain

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Beamformer gain denition

Dened as signal-to-noise ration (SNR) gain relative to the SNR at theoutput of the reference isotropic receiver.

G ( u ) =w H z ( u ) 2E 2p w 2

, (7)

where E p =+ ∞

−∞

|p̃ (t )

|2 d t is the energy of the pulse p̃ (t ).



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Maximum attainable beamformer gain

The weighting distribution that maximizes the gain for some direction u

w opt ( u ) = C w z ( u ), (8)

where C w is an arbitrary complex constant. Inserting (8) in (7) yields

G max ( u ) = z ( u ) 2E 2p

. (9)

w opt ( u max ) and G max ( u max ) are of particular importance.


Gain pattern synthesis

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p y


Correlation beamformerBeamformer gain

3 Gain pattern synthesisGeneral principlesProposed methodSimulation setupBeamformer pattern shaping examples


Gain pattern synthesis General principles

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y

General principles

z ( u ) is analogous to the so-called steering vector of the narrowband

antenna array.Analogous to the classic narrowband beamforming paradigm.Giving up the requirement for maximum possible gain

Optimize different parameters of the array pattern.


Gain pattern synthesis Proposed method

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Overall optimization problem

Second Order Cone Programming (SOCP) method.Mixed-norm minimization of the beamformer gain pattern sidelobes.Additional gain loss constraint.



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Overall optimization problem (math)

w o : Minimizew

βα + γ (1 −α),s.t.: z ( u max )H w = 1 ,

Z H sl w ≤β,|z ( u n )H w | ≤γ, for n = 0 , 1, . . . , N −1,

w ≤√ ηmax

z ( u max ).

(10)

u n for n = 0 , 1, . . . , N −1 is the set of directions uniformly distributedin the sidelobes area.N ≥10M 0 ≤α ≤1 is the factor of the α–norm of sidelobes



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Gain reduction constraint

Gain reduction:

η = G max ( u max )

G ( u max ) = w 2 z ( u max ) 2. (11)

Including in the problem the SOCP constraint

w ≤√ ηmax

z ( u max ), (12)

assurs that the loss in gain is no more than ηmax .


Numerical examples

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Correlation beamformerBeamformer gainGeneral principlesProposed method

4 Numerical examplesSimulation setupBeamformer pattern shaping examples


Numerical examples Simulation setup

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Pulse p (t )

The pulse used in the numerical examples:Linear chirp pulse.

The parameters specied in the mandatory mode of IR–UWB PHY inthe IEEE 802.15.6-2012 standard for Body Area Networks (BAN).Pulse duration: T p = 64 ns .Chirp frequency sweep: ∆f c = 520 MHz .



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Antenna array element

UWB L-Loop antenna was used.Designed for the frequency range of 3.1 GHz–5.1 GHz.The carrier frequency used for p (t ): f 0 = 4 GHz .



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Array geometry

Linear array with M = 15 elements.Elements are spaced at d 0 = 0 .4c / f 0, where c is the speed of light.

The k -th element position vector is r k = ( k −(M −1)/ 2) d 0 i z fork = 0 , 1, . . . , M −1. i z : unit vector along the z axis.

x and y : axes of the substrate on which the array elements are

printed.


Numerical examples Beamformer pattern shaping examples

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α parameter effect to the shape of sidelobes

− 90 − 60 − 30 0 30 60 90− 40

− 20

0

Angle ( ◦ )

G a

i n ( d B i )

w opt (0◦ )

w o (0◦ ) , α = 0 . 05

w o (0◦ ) , α = 0 . 5

w o (0◦ ) , α = 0 . 95

Figure: Effects of α parameter to level and

shape of the sidelobes, θmax = 0◦

and= 1 dB and BW = 14 ◦ .

Fig. illustrates the physicalmeaning of the α parameter.Low value of α ⇒ sidelobemaximum level reduction.High value of α ⇒sidelobes’ energy reduction.



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Effects of η max parameter

− 90 − 60 − 30 0 30 60 90− 40

− 20

0

Angle ( ◦ )

G a

i n ( d

B i )

w opt (0◦ )

w o (0◦ ) , η = 0 . 1 dB

w o (0◦ ) , η = 0 . 5 dB

w o (0◦ ) , η = 1 dB

w o (0◦ ) , η = 3 dB

Figure: Effects of η parameter, θmax = 0 ◦ ,

α = 0 .5 and BW = 14◦

.

Fig. illustrates the physicalmeaning of the ηmax

parameter as the maximumgain reduction.

η attained in theoptimization is practicallyalways equal to ηmax level.Cases with η < ηmax happenwith high levels of ηmax (notshown here).Increasing ηmax reduces thesidelobes level relative to themaximum.



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Effects of predened main-lobe beam-width to thesidelobes level

− 90 − 60 − 30 0 30 60 90− 40

− 20

0

Angle ( ◦ )

G a

i n ( d B i )

w opt (10◦ )

w o (10◦ ) , BW = 16 ◦ , η = 0 . 1 dB

wo (10

◦

), BW

= 18◦

, η = 1 dB

w o (10◦ ) , BW = 24 ◦ , η = 1 dB

Figure: Effects of predened main-lobebeam-width to the sidelobes level,

larger the main lobebeam-width, effective area inwhich the sidelobes need to

be reduced gets smaller ⇒The optimization has moredegrees of freedom to spendin suppressing sidelobes.With increasing the mainlobe beam width sidelobeslevel is reduced.


Conclusions

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Correlation beamformerBeamformer gainGeneral principlesProposed methodSimulation setup

Beamformer pattern shaping examples

5 Conclusions


Conclusions

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Conclusions

The paper presented the SOCP-based method for shaping the gainpatterns of the IR-UWB correlation beamformers.

A designer is able to tailor several parameters of the optimization.For example, if larger degree of gain reduction and main lobebeamwidth increase is allowed, then the method is able to reducemixed norm of sidelobes to lower levels.

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