Bandwidth Scaling in UWB Communications

Dana Porrat and David TseDana Porrat and David Tse

University of California, BerkeleyUniversity of California, Berkeley

Capacity of Fading Channels

• UWB over Multipath channel

• Combine Duty Cycle and spreading modulations?

• Theory– Kennedy, Gallager

1968

FSK + Duty Cycle

achieves

• Spreading Modulations– DSSS no Duty Cycle

zero capacity

Telatar & Tse,

Médard & Gallager, Subramanian & Hajek

The UWB Channel

Delay [nsec]

[Vol

t]

Measurement Bandwidth ~1 GHz

Multipath Channel Model

• Block constant: coherence time• Delay spread• L independent paths

How many paths in channel?

• Antennas separation up to 10 m, LOS and NLOS

• Strong paths counted: 60-90% of power

• Number of paths increases with Bandwidth

DSSS Capacity in Multipath Channel

• No Duty Cycle Telater & Tse:

• With Duty Cycle:

Capacity depends on scaling of number of paths with W

Direct Sequence Spread Spectrum

DSSS Capacity with Duty Cycle

• Theorem 1:

DSSS systems with duty cycle achieve

for

if

• Theorem 2:

DSSS systems with duty cycle, where the receiver knows the path delays achieve

for if

Parameters:W=10 GHzTc=0.1 msecTd=200 nsec

Why does duty cycle make a difference?

Because of the channel uncertainty penalty

Number of Paths

Dat

a R

ate

[bit

s/se

c]C(AWGN)

DSSS with Coherence Time Duty Cycle (LB)

DSSS with No Duty Cycle (UB)

Parameters:W=10 GHzTc=0.1 msecTd=200 nsecL=100

Duty Cycle for Spread Spectrum

Duty Cycle

Extremely Bursty:Infrequent Transmission

Not so Bursty: Transmit on 1 coherence time of 500

C(AWGN) D

ata

Rat

e [b

its/

sec]

DSSS Capacity (LB)

Duty Cycle for Spread Spectrum

Gain Uncertainty Penalty (UB)

C(AWGN)

Delay Uncertainty Penalty (UB)

Extremely Bursty:Infrequent Transmission

Not so Bursty: Transmit on 1 coherence time of 500

Duty Cycle

DSSS Capacity (LB)

Dat

a R

ate

[bit

s/se

c]Parameters:W=10 GHzTc=0.1 msecTd=200 nsecL=100

Duty Cycle for Spread Spectrum

DSSS with Perfect Channel Knowledge

Extremely Bursty:Infrequent Transmission

Not so Bursty: Transmit on 1 coherence time of 500

Gain Uncertainty Penalty (UB)

C(AWGN)

DSSS Capacity (LB)

Delay Uncertainty Penalty (UB)

Duty Cycle

Dat

a R

ate

[bit

s/se

c]Parameters:W=10 GHzTc=0.1 msecTd=200 nsecL=100

Pulse Position Modulation - PPM

DS Spread Spectrum vs. PPM

Parameters:W=10 GHzTc=0.1 msecTd=200 nsec

Number of Paths

Dat

a R

ate

[bit

s/se

c]

PPM with Coherence Time Duty Cycle (UB)

C(AWGN)

DSSS with Coherence Time Duty Cycle (LB)

Duty Cycle for Two Modulations

Duty Cycle

Dat

a R

ate

[bit

s/se

c]C(AWGN)

Extremely Bursty:Infrequent Transmission

Not so Bursty: Transmit on 1 coherence time of 100

PPM (UB)DSSS (LB)

DS Spread Spectrum allows a lower duty cycle because it is more efficient spectrally.

Parameters:W=10 GHzTc=0.1 msecTs=Td=200 nsecL=100

DS Spread Spectrum vs. PPM

PPM: Low data rate per Tc has to transmit often Large Penalty

DSSS: High data rate per Tc Infrequent transmission Small Penalty

PPM Capacity with Duty Cycle

• Theorem 3:

PPM systems with duty cycle, where the receiver knows the path delays achieve

for

if

• Theorem 4 (inverse):

PPM systems with duty cycle, where the receiver knows the path delays have

for if

DS Spread Spectrum vs. PPM

0

?

DS Spread Spectrum PPM

WW

LL

• Spectral efficiency determines max number of paths that can be handled by system

• Delays known, gains unknown

The Message

• Direct sequence spread spectrum and PPM achieve the channel capacity for if there are not too many channel paths, because duty cycle reduces the channel uncertainty penalty

• In situations that require low duty cycle spectral efficiency is key

Extra Slides

How Often to Transmit?

Duty Cycle

Extremely Bursty:Infrequent Transmission

Not so Bursty: Transmit on 1 coherence time of 500

CalculatedWith L=100 Paths

C(AWGN) D

ata

Rat

e [b

its/

sec]