ISIT 2007 — 1 Throughput (bits/sec/Hz) of Capture- Based Random-Access Systems with SINR Channel Models ______________________________________________

ISIT 2007 — 1

Throughput (bits/sec/Hz) of Capture-Based Random-Access

Systems with SINR Channel Models

Throughput (bits/sec/Hz) of Capture-Based Random-Access

Systems with SINR Channel Models

______________________________________________This work was supported by the Office of Naval Research.

Jeffrey E. Wieselthier and Gam D. Nguyen

Information Technology DivisionNaval Research Laboratory

Anthony EphremidesElectrical and Computer Engineering Department

and Institute for Systems ResearchUniversity of Maryland

ISIT 2007 — June 2007

ISIT 2007 — 2

Random-Access System

Collision channel no capture

General Multiple-Access channel all users “succeed”

In-between: Reception in the presence of interferenceSINR-based model

One or more users can be successful

Receiver

ISIT 2007 — 3

SINR-based Capture Model

A packet from user j is successful if and only if

b = 0: Perfect capturesingle detector: largest always successfulmultiple detectors: all are successful

b = ∞: No capture (collision channel)when 2 or more transmit, none are successful

SINR( j) P( j)

N P(i)i1,ij

n

b

P(j) = Power at receiving node from user j

b = Threshold that depends on many system parameters (increasing function of rate)

Receiver

j

ISIT 2007 — 4

Measures of Throughput

Scenario: Single destination Random-access transmissions

“Packet throughput” (ISIT 2006)Expected number of successful packets in a slot:

Sn = E{number of successful packets | n simultaneous transmissions}

Performance depends on threshold b

“Bit throughput” (this paper)Spectral efficiency (bits/sec/Hz)

We address impact of: b Specified BER Modulation scheme

Destination

ISIT 2007 — 5

Packet Throughput: E{Successful packets | n}

All packets for which SINR > b are successful Sn = n Pr{SINR(1) > b} We addressed this problem at ISIT 2006

Model for b < 1 Performance evaluated via simulation

Shape of curves is dramatically different from previous results Because of our propagation model

0

1

2

3

4

5

1 10 100 1000number of transmitted packets (n)

b = 0

b = 0.1

b = 0.2

b = 0.5

b = 1b = 2b = 10

0

1

2

3


b = 0

b = 0.1

b = 0.2

b = 0.5

b = 1

b = 2b = 10

PR 1

1 r 2

PR 1

1 r 4

0

1

2

3

4

0 1 2 3 4 5r

= 2

ISIT 2007 — 6

What is the Significance of the Parameter b?

Small value of b high packet throughputBut we pay a price to achieve small values of b:

Fewer bits in each packetExpand BWRelax BER requirement

How does b relate to spectral efficiency (bits/sec/Hz)?

Impact of specified BERImpact of modulation scheme

ISIT 2007 — 7

Key Modeling Assumptions

Modulation scheme: M-ary PSK Minimum symbol duration: t = 1/W W = channel bandwidth

Ways to vary data rate Rb

Choice of k = log2M Increase symbol duration ts > t

This does NOT affect channel BW

No error-control coding

Other-user interference is uniform Gaussian in BW W = 1/t We neglect background noise

Equivalent noise spectral density: Pint P( j)

ji

N0

2Pint

W2Pintt

ISIT 2007 — 8

Es/N0 and its Relationship to b

Evaluate Es/N0 Noise spectral density (background noise = 0):

Bit energy:

Symbol-energy-to-interference ratio:

Relationship to b

For signal i to be successful, we require:

Specifying a value of b is equivalent to requiring:

N0

2Pint

W2Pintt

P(i)

P( j)ji

P(i)

Pint

b

Eb

Rec'd energy in packet

# bits in packet

P(i)T

RbT

P(i)

Rb

P(i)ts

k

Es

N0

kEb

N0

1

2

P(i)

Pint

ts

t

Es

N0

b

2

ts

t

ISIT 2007 — 9

Impact of BER Constraint on Achievable Data Rate

Define:

Esno(BER,k) = value of Es/N0 that is needed to achieve the specified BER when M-ary PSK is used

Spectral efficiency (bits/sec/Hz) is a function of BER, k and b:

Rb

WBER,k,b k min 1,

b

2Esno(BER,k)

ISIT 2007 — 10

Alternative Approximate Model: Shannon Capacity

Shannon capacity

C = W log2(1+b)

Simple, inaccurate modelDoes not address finite packet lengthAddresses operation at BER = 0

ISIT 2007 — 11

Spectral Efficiency of M-ary PSK vs b

Shannon capacity provides a decent approximation for spectral efficiency for BER = 0.1

0

1

2

3

4

0 5 10 15 20 25 30 35 40b

k = 1

k = 2

k = 3

BER = 0.01

0

1

2

3

4

0 2 4 6 8 10 12b

C

k = 1

k = 2

k = 3

BER = 0.1

C

Wlog2(1 b)

C

W

ISIT 2007 — 12

Spectral Efficiency of Binary PSK(in presence of other-user interference)

Relax BER constraint increase spectral efficiency Curves show value of n that provides highest spectral efficiency

0

0.05

0.1

0.15

0.2


b = 10

b = 2

b = 1

b = 0.5b = 0.2b = 0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7


b = 10

b = 2

b = 1

b = 0.5

b = 0.2

b = 0.1

BER = 0.01 BER = 0.1

Spectral Efficiency (Bit Throughput per Hz):

SnRb

W

PR 1

1 r 2

ISIT 2007 — 13

Spectral Efficiency of Binary PSK

(in presence of other-user interference)

0

0.05

0.1

0.15

0.2

0.25

0.3


b = 10

b = 2

b = 1

b = 0.5

b = 0.2b = 0.1

0

0.2

0.4

0.6

0.8

1


b = 10

b = 2

b = 1

b = 0.5

b = 0.2b = 0.1

BER = 0.01 BER = 0.1

Spectral Efficiency (Bit Throughput per Hz):

SnRb

W

PR 1

1 r 4

ISIT 2007 — 14

Summary and Conclusions

Addressed spectral efficiency of capture-based random-access systems

Relationships between “packet throughput” and “bit throughput”

Impact of threshold b Impact of BER

Developed basis of trade-offs in scheduled vs random-access systems

Model easily extended to multiple-destination networks with overlapping user populations

Using approach of our MILCOM 2006 paper

Provides link between information theory and networking

Documents

ISIT 2007 — 1 Throughput (bits/sec/Hz) of Capture- Based Random-Access Systems with SINR Channel Models ______________________________________________