Impulse Radio Ultra-Wideband Antenna Array Correlation BeamformingImpulse Radio Ultra-Wideband...
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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
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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.
Dotlić, Yazdandoost, Li & Miura (NICT) IR-UWB Correlation Beamforming ICEIC 2016 6 / 27
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Preliminaries
2 PreliminariesWideband antenna array time-domain modelCorrelation beamformerBeamformer gainGeneral principlesProposed methodSimulation setupBeamformer pattern shaping examples
Dotlić, Yazdandoost, Li & Miura (NICT) IR-UWB Correlation Beamforming ICEIC 2016 7 / 27
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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.
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Preliminaries Correlation beamformer
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Preliminaries Correlation beamformer
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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Preliminaries Correlation beamformer
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Preliminaries Correlation beamformer
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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Preliminaries Correlation beamformer
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Preliminaries Correlation beamformer
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.
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Preliminaries Beamformer gain
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Preliminaries Beamformer gain
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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Preliminaries Beamformer gain
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Preliminaries Beamformer gain
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.
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Gain pattern synthesis
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p y
Wideband antenna array time-domain model
Correlation beamformerBeamformer gain
3 Gain pattern synthesisGeneral principlesProposed methodSimulation setupBeamformer pattern shaping examples
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Gain pattern synthesis General principles
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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.
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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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Gain pattern synthesis Proposed method
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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 pattern synthesis Proposed method
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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 .
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Numerical examples
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Wideband antenna array time-domain model
Correlation beamformerBeamformer gainGeneral principlesProposed method
4 Numerical examplesSimulation setupBeamformer pattern shaping examples
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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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Numerical examples Simulation setup
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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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Numerical examples Simulation setup
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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.
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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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Numerical examples Beamformer pattern shaping examples
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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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Numerical examples Beamformer pattern shaping examples
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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.
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Conclusions
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Wideband antenna array time-domain model
Correlation beamformerBeamformer gainGeneral principlesProposed methodSimulation setup
Beamformer pattern shaping examples
5 Conclusions
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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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