Robust Frequency-Hopping System for Channels with ...community.wvu.edu/~mcvalenti/documents/51presentation.pdf · with Interference and Frequency-Selective Fading ... [h(x|y)] where

Robust Frequency-Hopping System for Channelswith Interference and Frequency-Selective Fading

Don Torrieri1, Shi Cheng2, and Matthew C. Valenti2

1US Army Research Lab

2Lane Department of Computer Science and Electrical EngineeringWest Virginia University

June 26, 2007

Torrieri et al. ( US Army Research Lab, Lane Department of Computer Science and Electrical Engineering West Virginia University )Robust Frequency-Hopping June 26, 2007 1 / 20

Outline

1 Why Use CPFSK for FH Systems?

2 Capacity of Noncoherent CPFSK

3 Applications

4 Conclusion


Why Use CPFSK for FH Systems? Motivation

A Tale of Two Philosophies

BW

B

W

Philosophy # 1

Large B.

Wideband hopping channels.

Better AWGN performance.

Fewer hopping channelsM = B/W .

Worse performance withinterference.

Philosophy # 2

Small B.

Narrowband hopping channels.

Worse AWGN performance.

More hopping channelsM = B/W .

Better performance withinterference.


Why Use CPFSK for FH Systems? CPFSK Modulation

Modulation Choices for Frequency Hopping

sd(t) =1√Ts

ej2πdt/Ts , d = 0, 1, · · · , q − 1

Philosophy #1: Orthogonal FSK

Suitable for noncoherent reception.Reasonable energy efficiency.Poor bandwidth efficiency because adjacent tones are 1/Ts apart.

Philosophy #2: Nonorthogonal CPFSK

Reduce bandwidth by using modulation index h < 1.Adjacent frequency tones are h/Ts apart.Continuous-phase constraint controls the spectrum.Transmitted x(t) = ejφsd(t) where phase φ is accumulated

φ = φ′ + 2πdh



Modulation Choices for Frequency Hopping

sd(t) =1√Ts

ej2πdht/Ts , d = 0, 1, · · · , q − 1

Philosophy #1: Orthogonal FSK

Suitable for noncoherent reception.Reasonable energy efficiency.Poor bandwidth efficiency because adjacent tones are 1/Ts apart.

Philosophy #2: Nonorthogonal CPFSK

Reduce bandwidth by using modulation index h < 1.Adjacent frequency tones are h/Ts apart.Continuous-phase constraint controls the spectrum.Transmitted x(t) = ejφsd(t) where phase φ is accumulated

φ = φ′ + 2πdh



Bandwidth of CPFSK

h (modulation index)

Ban

dwid

th B

(Hz/

bps)

0 0.2 0.4 0.6 0.8 10

0.5

1

1.5

2

2.5

3

3.5

4

q=2q=4

q=8

q=16q=32

q=64

99% Power Bandwidth


Capacity of Noncoherent CPFSK System Model

Discrete Time Model

The output of q complex filers matched to the tones is:

y = aejθ√Esx + n

where

Unlike orthogonal FSK, the x are not elementary vectors.Define K to be a correlation matrix with entry i, j

ki,j =∫ Ts

0

s∗i (t)sj(t)dt

x is chosen from columns of K = [k0,k1, · · · ,kq−1]n is colored noise, with E(nnH) = N0K.a is the fading amplitude, assumed to be constant for each hop.θ includes effects of continuous-phase constraint, fading, and oscillatorfrequency offset.



Demodulator Metric and Channel Estimation

∫ ⋅dt

cos(2πfdt)

sin(2πfdt)

∫ ⋅dt

log I0( )

∫ ⋅dt

cos(2πfq-1t)

sin(2πfq-1t)

∫ ⋅dt

log I0( )

The likelihood of symbol d ∈ {0, ..., q − 1} is

p(y|x = kd) ∝ I0

(2a

√Es

N0|yd|

)Channel estimation

a√Es/N0 is the channel state information (CSI).

EM algorithm used to estimate the CSI for each hop.Extrinsic information from decoder used to refine the CSI estimates.



Demodulator Metric and Channel Estimation

∫ ⋅dt

cos(2πfdt)

sin(2πfdt)

∫ ⋅dt

log I0( )

∫ ⋅dt

cos(2πfq-1t)

sin(2πfq-1t)

∫ ⋅dt

log I0( )

The likelihood of symbol d ∈ {0, ..., q − 1} is

p(y|x = kd) ∝ I0

(2a

√Es

N0|yd|

)Channel estimation

a√Es/N0 is the channel state information (CSI).

EM algorithm used to estimate the CSI for each hop.Extrinsic information from decoder used to refine the CSI estimates.


Capacity of Noncoherent CPFSK Computing Capacity

Capacity Calculation

Assuming equally-likely input symbols x, the capacity is the mutualinformation between x and y

I(x;y) = H(x)−H(x|y)= log q − Ex,y[h(x|y)]

where

h(x|y) = − log p(x|y)

= log∑

x′∈S p(y|x′)p(y|x)

Monte Carlo simulation can be used to evaluate the expectation.



Capacity Calculation

Assuming equally-likely input symbols x, the capacity is the mutualinformation between x and y

I(x;y) = H(x)−H(x|y)= log q − Ex,y[h(x|y)]

where

h(x|y) = − log p(x|y)

= log∑

x′∈S p(y|x′)p(y|x)

Monte Carlo simulation can be used to evaluate the expectation.



Binary Noncoherent CPFSK Capacity in AWGN

−10 −5 0 5 10 15 20 250

0.2

0.4

0.6

0.8

1

Es/No in dB

Mut

ual I

nfor

mat

ion

h=0.2

h=1

h=0.4

0.6

h=0.8dashed line

(a) channel capacity versus ES/N0

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 15

10

15

20

25

Min

imum

Eb/

No

in d

B

Code rate r

h=0.2

h=0.4

h=0.6

h=0.8

h=1

(b) minimum Eb/N0 versus coding rate



Binary Noncoherent CPFSK Capacity in AWGN underBandwidth Constraint

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 15

10

15

20

25

h

Min

imum

Eb/

No

in d

B

B = inf.

B= 3

B= 2

B = 1

B is normalized bandwidthin Hz/bps



Noncoherent CPFSK Capacity in AWGN

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

5

10

15

20

25

30

h

Min

imum

Eb/

No

in d

BB = 2 (solid lines)B = inf. (dashed)

q=2

4

8

16

32

64



Noncoherent CPFSK Capacity in Rayleigh Fading

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

5

10

15

20

25

30

h

Min

imum

Eb/

No

in d

B

B = 2 (solid lines)

B = 0 (dashed lines)q=2

4

8

16

32


Applications Multiple-access Interference

A Multi-user FH Network

d=1

Interference Nodes(d<4)

TransmissionsIndependent and asynchronous hopping.Equal transmit power.Interfering users randomly placed up to 4x away from desiredtransmitter.

ChannelPath loss coefficient of 4.Log-normal shadowing (σ = 8dB) of interfering users.Block Rayleigh fading.



Waveforms for FH Network

Total bandwidth W = 2000 Hz/bps.

All users use the same modulation and coding

h q Coding rate Number of channels

1 2 2048/6144 312

1 4 2048/6144 315

1 8 2048/6144 244

0.6 2 2048/3200 1000

0.46 4 2048/3456 1000

0.32 8 2048/3840 1000

UMTS turbo code

32 hops/codeword.

Channel estimation using EM algorithm.



Minimum Eb/N0 for BER = 10−4

0 10 20 30 40 506

8

10

12

14

16

18

20

22

24

Users

2CPFSK h = 14CPFSK h = 18CPFSK h = 12CPFSK h = 0.64CPFSK h = 0.468CPFSK h = 0.32

Eb/N

oin

dB


Applications Partial-band Jamming

Partial-band Jamming

Waveforms

Three systems:q h info bits code bits code rate

2 0.6 2048 3200 0.644 0.46 2048 3456 0.598 0.32 2048 3840 0.53

All three have BW efficiency η = 0.5 bps/Hz.Turbo code from UMTS standard used.16, 32, or 64 hops per codeword.

Interference

Interference covers fraction µ of the band.I0 is interference spectral density when µ = 1.Additional noise power of I0/µ if hop has interference.Eb/I0 = 13 dB.



Partial-band Jamming

Waveforms

Three systems:q h info bits code bits code rate

2 0.6 2048 3200 0.644 0.46 2048 3456 0.598 0.32 2048 3840 0.53

All three have BW efficiency η = 0.5 bps/Hz.Turbo code from UMTS standard used.16, 32, or 64 hops per codeword.

Interference

Interference covers fraction µ of the band.I0 is interference spectral density when µ = 1.Additional noise power of I0/µ if hop has interference.Eb/I0 = 13 dB.



Influence of Alphabet Size

0 0.2 0.4 0.6 0.8 1

4

6

8

10

12

14

16

18

20

22

24

μ

Eb/N

oin

dB

Perfect CSIEM estimator

q=8

q=4

q=8

q=4

q=2

q=2

AWGN

Rayleigh

Minimum Eb/N0

for BER = 10−3.

32hops/codeword.



Influence of the Number of Hops

0 0.2 0.4 0.6 0.8 18

10

12

14

16

18

20

22

24

26

μ

4-ary CPFSK, 16 hops4-ary CPFSK, 32 hops4-ary CPFSK, 64 hops8-ary CPFSK, 16 hops8-ary CPFSK, 32 hops8-ary CPFSK, 64 hops

Eb/N

oin

dB Minimum Eb/N0

for BER = 10−3.

Block Rayleighfading.


Conclusion

Conclusion

In FH systems, the bandwidth B per hopping channel must becarefully chosen.

Large B gives better performance in interference-free environment.Small B is beneficial in presence of interference.

Capacity analysis can be used to determine best h and r for aparticular bandwidth constraint.

Channel estimation can be performed using EM algorithm.

Nonbinary signaling (q > 2) with small h can provide additional gains.


Conclusion

Conclusion







Conclusion

Conclusion







Conclusion

Conclusion







Conclusion

Questions


Robust Frequency-Hopping System for Channels with ...community.wvu.edu/~mcvalenti/documents/51presentation.pdf · with Interference and Frequency-Selective Fading ... [h(x|y)] where

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