Information-Energy Capacity Region for SWIPT Systems with Power - - PowerPoint PPT Presentation

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Information-Energy Capacity Region for SWIPT Systems with Power - - PowerPoint PPT Presentation

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Information-Energy Capacity Region for SWIPT Systems with Power Amplifier Nonlinearity Ioannis Krikidis Dpt. of Electrical and Computer Engineering IRIDA Research Centre for Communication Technologies University of Cyprus E-mail:

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SLIDE 1

Information-Energy Capacity Region for SWIPT Systems with Power Amplifier Nonlinearity

Ioannis Krikidis

  • Dpt. of Electrical and Computer Engineering

IRIDA Research Centre for Communication Technologies University of Cyprus E-mail: krikidis@ucy.ac.cy

IEEE ISIT’20, Los Angeles, USA

  • I. Krikidis (ECE/UCY)

IEEE ISIT’20, Los Angeles, USA 21-26 June, 2020 1 / 21

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SLIDE 2

Outline

1

Background/Problem formulation

2

Information-energy capacity region

3

Numerical results

4

Conclusion/Future work

  • I. Krikidis (ECE/UCY)

IEEE ISIT’20, Los Angeles, USA 21-26 June, 2020 2 / 21

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SLIDE 3

SWIPT/Motivation (1)

Massive Connectivity:

  • 2017: 5 Billions phones
  • 2035: Trillions IoT devices

Low-power devices:

  • e.g., state-of-the-art sensors

10µWatt

Koomey's law electrical efficiency

  • f computing

doubled every 1.5 years

Low-power

Computations per Microjoules Year

  • I. Krikidis (ECE/UCY)

IEEE ISIT’20, Los Angeles, USA 21-26 June, 2020 3 / 21

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SLIDE 4

SWIPT/Motivation (2)

Simultaneous Wireless Information and Power Transfer (SWIPT).

  • Downlink: Simultaneous (same waveform) information and power

transfer.

Information Flow Energy Flow Co-located Information & Energy Receivers Separate Information & Energy Receivers

Fundamental information-energy trade-off

  • Input distribution, waveform design, beamforming design etc (Tx).
  • Receiver structure/signal processing techniques (Wireless devices).

Information-energy region: all the achievable information and energy tuples (R, E) under a given transmit power constraint P.

  • I. Krikidis (ECE/UCY)

IEEE ISIT’20, Los Angeles, USA 21-26 June, 2020 4 / 21

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SLIDE 5

Problem Formulation

Signals with high PAPR boost the wireless energy harvesting e.g., multisine signals, chaotic signals etc.

  • High-power amplifier (HPA)

nonlinearities. Information-energy capacity region

  • Linear information transfer channel.
  • Non-linear power transfer channel.
  • Average power (AP) and Peak power

(PP) constraints.

  • HPA nonlinearities.

Information-Energy Capacity Region

  • I. Krikidis (ECE/UCY)

IEEE ISIT’20, Los Angeles, USA 21-26 June, 2020 5 / 21

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SLIDE 6

Outline

1

Background/Problem formulation

2

Information-energy capacity region

3

Numerical results

4

Conclusion/Future work

  • I. Krikidis (ECE/UCY)

IEEE ISIT’20, Los Angeles, USA 21-26 June, 2020 6 / 21

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SLIDE 7

System model (1)

HPA

x[k]

IR ER Transmitter

hI

hE

Time-slotted real-valued transmission. Channel fading gains hI and hE are flat and fixed over all time slots and perfectly known at TX; AWGN channel. PAM signal x(t) = ∞

k=−∞ x[k]p(t − kT), with rectangular p(t).

x[k] i.i.d real random variable X with CDF FX(x). AP: E[X 2] ≤ σ2

x,

PP: |X| ≤ A, where A is the peak amplitude.

  • I. Krikidis (ECE/UCY)

IEEE ISIT’20, Los Angeles, USA 21-26 June, 2020 7 / 21

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SLIDE 8

System model (2)

HPA

x[k]

IR ER Transmitter

hI

hE

y(t) = hIˆ x(t) + n(t) (information channel) p(y|x) =

1 √ 2π exp

  • − (y−hId(x))2

2

  • (transition probability)

Energy harvesting ∝ E

  • I0(BhE|ˆ

X|)

  • (power channel).

Solid state power amplifier (SSPA) model i.e., ˆ X = d(X). d(r) = r

  • 1 +
  • r

As

2β 1

2β ,

  • 5
  • 4
  • 3
  • 2
  • 1

1 2 3 4 5 Input Voltage [Volts]

  • 1
  • 0.5

0.5 1 Output Voltage [Volts] =1 =2 =5 =80

  • 5

5

  • 1
  • 0.5

0.5 1

As A0 Non-linear regime

  • I. Krikidis (ECE/UCY)

IEEE ISIT’20, Los Angeles, USA 21-26 June, 2020 8 / 21

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SLIDE 9

Maximize energy transfer

We consider firstly the case where the IR is not present/active. (P1) max

FX

E

  • I0(BhE|ˆ

X|)

  • s.t.

E[X 2] ≤ σ2

x

|X| ≤ A.

Proposition 1

The maximum average harvested energy and the associated mass point distribution are given by Emax = pI0

  • BhEd(λ)
  • + (1 − p), where

If A2 ≤ σ2

x, we have p = 1, λ = A, and mass point distribution ΠA = 1 2 (δ−A + δA).

If σ2

x ≤ A2 and g(x) ց (σx, A), we have p = 1, λ = σx, and ΠA = 1 2 (δ−σx + δσx ).

If σ2

x ≤ A2 and g(x) ր (σx, A), we have p = σ2 x A2 , λ = A, and ΠA = σ2 x 2A2 (δ−A + δA) +

  • 1 −

σ2 x A2

  • δ0.

If σ2

x ≤ A2 and the function g(x) ր (σx, A′) and g(x) ց (A′, A), we have p = σ2 x A′2 , λ = A′, and mass

point distribution ΠA =

σ2 x 2A′2 (δ−A′ + δA′) +

  • 1 −

σ2 x A′2

  • δ0, with A′ ≈ As for β ≫ 1,

where δx is the Dirac measure (point mass) concentrated at x, and g(x) =

1 x2 [I0(BhEd(x)) − 1].

Imin = ∞

−∞

  • j p(y|xj)pj log2

p(y|xj)

  • j p(y|xj)pj dy where pj = P[X = xj]; ΠA =

j pjδxj

is a binary/ternary distribution (low computation complexity).

  • I. Krikidis (ECE/UCY)

IEEE ISIT’20, Los Angeles, USA 21-26 June, 2020 9 / 21

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SLIDE 10

Maximize information capacity

We consider the case where the target of the system is to maximize the Shannon information capacity under both AP and PP constraints. (P2) max

FX

I(X; Y) s.t. E[X 2] ≤ σ2

x

|X| ≤ A,

  • Channel output Y = hI ˆ

X + N with ˆ X = d(X).

  • I(X; Y) =

A

−A

∞

−∞ p(y|x) log2

  • p(y|x)

p(y;FX )

  • dydFX.
  • Solution: The optimal input probability function FX is unique, finite and

discrete [Smith, 1971].

  • I. Krikidis (ECE/UCY)

IEEE ISIT’20, Los Angeles, USA 21-26 June, 2020 10 / 21

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SLIDE 11

Information-energy capacity region (3)

(P2) can be reformulated by the following convex opt. problem: (P3) max

p p p

I m

i=1

n

j=1 pijpj log2 pij n

k=1 pikpk

s.t. E[X 2] ≤ σ2

x

|X| ≤ A p p p 0, 1 1 1⊤p p p = 1, where 1 1 1 denotes a vector with ones, pij = P(Y = yi|X = xj), and p p p = [p1, p2, . . . , pn]⊤.

  • If p

p p∗ is the solution to (P3), the maximum mutual information becomes equal to Imax = m

i=1

n

j=1 pijp∗ j log2 pij n

k=1 pikp∗ k .

  • In case that ER is active, the average energy harvested is written as

Emin = n

j=1 p∗ j I0(BhEd(xj)).

Remark 1

If d(A) ≤ A ≈ 1.665 (peak output amplitude) and A2 ≤ σ2

x, there is not a

trade-off between information/energy and the same input distribution (i.e., equiprobable binary with mass points at ±A) maximizes both information and energy transfer simultaneously.

  • I. Krikidis (ECE/UCY)

IEEE ISIT’20, Los Angeles, USA 21-26 June, 2020 11 / 21

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SLIDE 12

Information-energy capacity region (4)

Then, we consider the case where both ER and IR are active/present. The IE-CR is defined as C(σ2

x, A) =

  • (I, E) : I ≤ Imax, E ≤ Emax, E[x2] ≤ σ2

x, |X| ≤ A

  • .
  • If I ≤ Imin, the maximum average harvested energy is given by the input

distribution that achieves the rate tuple (Imin, Emax); see (P1).

  • If E ≤ Emin, the maximum information rate is given by the input distribution

that achieves the rate tuple (Imax, Emin); see (P3).

  • The other points of the boundary Imin ≤ I ≤ Imax and Emin ≤ E ≤ Emax; see

(P3) with the extra constraint Emin ≤ E[I0(BhE|ˆ X|)] ≤ Emax (convex problem).

  • I. Krikidis (ECE/UCY)

IEEE ISIT’20, Los Angeles, USA 21-26 June, 2020 12 / 21

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SLIDE 13

Digital predistortion

  • Compansate the non-linear HPA effects and linearize the non-saturation

regime of HPA.

  • If d(r) is deterministic and known at the transmitter, an ideal PD

corresponds to the function q(r) i.e., q(r) =      As, If r ≥ As, d−1(r) =

r

  • 1−( r

As ) 2β 1 2β , If − As < r < As,

−As, If r ≤ −As.

  • the information energy capacity region is given by (P1), (P2), (P3).

1

the AP constraint is replaced by E[q(x)2] ≤ σ2

x.

2

HPA’s output is equal to ˆ X = d(q(X)).

Remark 2

It is worth noting that r ≥ d(r) and therefore PD penalizes the AP constraint (increases transmit power), while it facilitates the objective functions in (P1)-(P3).

  • I. Krikidis (ECE/UCY)

IEEE ISIT’20, Los Angeles, USA 21-26 June, 2020 13 / 21

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SLIDE 14

Outline

1

Background/Problem formulation

2

Information-energy capacity region

3

Numerical results

4

Conclusion/Future work

  • I. Krikidis (ECE/UCY)

IEEE ISIT’20, Los Angeles, USA 21-26 June, 2020 14 / 21

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SLIDE 15

Numerical results (1)

5 10 15 0.5 1 1.5 2 2.5 3 x 10

−3

x g(x) −16 −10 −7 7 10 16 0.1 0.2 0.3 0.4 0.5 x p(x) −16 −10 10 16 0.2 0.4 0.6 0.8 x p(x) −16 −10 10 16 0.2 0.4 0.6 0.8 1 x p(x) As=10, β=1 As=10, β=10 As=10, β=80 As=100, β=10 (b) (a) (c) (d)

Figure: (a) The function g(x) for different parameters of the SSPA model; we also assume A = 16, B = 0.1, and σ2

x = 49, (b) Input distribution for g(x) ց (σx, A) , (c)

Input distribution for g(x) ր (σx, As) and g(x) ց (As, A), and (d) Input distribution for g(x) ր (σx, A).

  • I. Krikidis (ECE/UCY)

IEEE ISIT’20, Los Angeles, USA 21-26 June, 2020 15 / 21

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SLIDE 16

Numerical results (2)

  • 15
  • 10
  • 5

5 10 15 x 0.05 0.1 0.15 0.2 0.25 0.3 p(x) A=18 V

  • 2
  • 1

1 2

x

0.1 0.2 0.3 0.4 0.5 0.6 0.7

p(x) A=1.75 V (a) (b)

Figure: Input mass probability distribution for maximum information transfer; β = 1, B = 0.5, σ2

x = 30 dB, and (a) A = 18, and (b) A = 1.75.

  • For the case A = 1.75 (with d(1.75) = 1.6518 < A ≈ 1.665), the optimal

input distribution is binary with two mass points at ±A; (see Remark 1).

  • I. Krikidis (ECE/UCY)

IEEE ISIT’20, Los Angeles, USA 21-26 June, 2020 16 / 21

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SLIDE 17

Numerical results (3)

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Information Rate [bits/ch. use]

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Energy Rate [energy units/ch. use]

A=1,75 V (HPA) A=1,75 V (no- HPA) A=6 V (HPA) A=6 V (no- HPA) A=10 V (HPA)

Figure: Information-energy capacity region; As = 5, β = 1, B = 0.5, σ2

x = 30 dB.

  • I. Krikidis (ECE/UCY)

IEEE ISIT’20, Los Angeles, USA 21-26 June, 2020 17 / 21

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SLIDE 18

Numerical results (4)

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Information Rate [bits/ch. use] 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Energy Rate [energy units/ch. use] =1, HPA =1, PD =3, HPA =3, PD =10, HPA =10, PD no-HPA

Figure: Information-energy capacity region for the predistortion scheme; A = 6, As = 5, B = 0.5, σ2

x = 30 dB.

  • I. Krikidis (ECE/UCY)

IEEE ISIT’20, Los Angeles, USA 21-26 June, 2020 18 / 21

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SLIDE 19

Outline

1

Background/Problem formulation

2

Information-energy capacity region

3

Numerical results

4

Conclusion/Future work

  • I. Krikidis (ECE/UCY)

IEEE ISIT’20, Los Angeles, USA 21-26 June, 2020 19 / 21

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SLIDE 20

Conclusion/Future work

Conclusion: Information-energy capacity region with AP , PP and HPA. The optimal input probability function FX is unique, finite and discrete. For low peak output amplitudes, no tradeoff. Digital predistortion enlarges the information-energy capacity region. Future work: Scenarios with fading (e.g. Rayleigh fading). Two-dimension case (amplitude and phase). Time-varying amplitude constraints.

  • I. Krikidis (ECE/UCY)

IEEE ISIT’20, Los Angeles, USA 21-26 June, 2020 20 / 21

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SLIDE 21

Conclusion/Future work

Conclusion: Information-energy capacity region with AP , PP and HPA. The optimal input probability function FX is unique, finite and discrete. For low peak output amplitudes, no tradeoff. Digital predistortion enlarges the information-energy capacity region. Future work: Scenarios with fading (e.g. Rayleigh fading). Two-dimension case (amplitude and phase). Time-varying amplitude constraints.

  • I. Krikidis (ECE/UCY)

IEEE ISIT’20, Los Angeles, USA 21-26 June, 2020 20 / 21

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SLIDE 22

Information-Energy Capacity Region for SWIPT Systems with Power Amplifier Nonlinearity

  • I. Krikidis (ECE/UCY)

IEEE ISIT’20, Los Angeles, USA 21-26 June, 2020 21 / 21