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Superposition Coding in the Downlink of CDMA Cellular Systems Surendra Boppana and John M. Shea Wireless Information Networking Group University of Florida Feb 13, 2006

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Superposition Coding in the Downlink of CDMA CellularSystems

Surendra Boppana and John M. Shea

Wireless Information Networking GroupUniversity of Florida

Feb 13, 2006

Wireless Information Networking Group

Outline of the talk

• Introduction and Motivation

• System Description

• User Capacity under Average Power Constraint

• Results and Discussion

• Conclusions

1

Wireless Information Networking Group

Introduction

• Fading induces great disparity in the channel gains of radios in a CDMAcellular network.

• Power control is employed at the base station to maintain a constantSNR at the mobile radios.

• Ideally, each mobile radio sees the same SNR on their spreading code.

• If a radio despreads another radio’s signal, it might receive the signal atmuch different SNR.

• Superposition coding offers significant advantages by transmitting tomultiple users on a single spreading code.

2

Wireless Information Networking Group

Motivating Example

Target SNR level

M1 M2 M3

Distance from the base station −>

Pow

er tr

ansm

itted

(dB

) −

>

A

B

C

• Base station at the origin and radios M1, M2, M3 arranged in decreasing order of

channel gains.

3

Wireless Information Networking Group

Motivating Example

Target SNR level

M1 M2 M3

Distance from the base station −>

Pow

er tr

ansm

itted

(dB

) −

>

A

B

C

• Base station at the origin and radios M1, M2, M3 arranged in decreasing order of

channel gains.

• Exponential path-loss channel with no fading. (Pr ∝ dr−α)

3

Wireless Information Networking Group

Motivating Example

Target SNR level

M1 M2 M3

Distance from the base station −>

Pow

er tr

ansm

itted

(dB

) −

>

A

B

C

• Base station at the origin and radios M1, M2, M3 arranged in decreasing order of

channel gains.

• Exponential path-loss channel with no fading. (Pr ∝ dr−α)

• Ordinate indicates the power transmitted by the base station to maintain the same

target SNR at the radios.

3

Wireless Information Networking Group

Motivating Example

Target SNR level

M1 M2 M3

Distance from the base station −>

Pow

er tr

ansm

itted

(dB

) −

>

A

B

C

• When base station transmits to M3, M2 sees an additional CdB of power above its

target SNR.

• Similarly, M1 sees AdB of additional power when it decodes the signal intended for

M2.

• Superposition coding can be employed to achieve higher throughout or equivalently

support more radios.

3

Wireless Information Networking Group

Motivating Example

Target SNR level

M1 M2 M3

Distance from the base station −>

Pow

er tr

ansm

itted

(dB

) −

>

A

B

C

• Superposition coding increases the total transmit power and hence the interference.

3

Wireless Information Networking Group

System Description

• Base station is at the center of a circular area of coverage.

• The radios are uniformly distributed in the area of coverage.

• The channel is modeled as an exponential path-loss channel with Rayleighflat fading.

Pr = Kpd−αr |hr|2Pt

• The bandwidth seen by each radio after despreading is W Hz.

• All the radios have a common target SNR of γ dB.

• The number of orthogonal channels available is N .

4

Wireless Information Networking Group

System Description

Basic Message: The message with lower SNR requirement for its accurate reception is

called Basic Message.

Additional Message:The message with higher SNR requirement for its accurate

reception is called Additional Message.

M2Z2Z1BS M1Ram = W log2

�1 +

aKpZ1P

N0W

�(1)

Rbm = W log2

�1 +

(1− a)KpZ2P

aKpZ2P + N0W

�(2)

4

Wireless Information Networking Group

User Capacity

User Capacity: Number of users supported by the base station under an average

transmit power constraint.

• The downlink user capacity under superposition coding depends on pairsof radios involved in superposition coding.

• Pairing Strategy: Let the radios be indexed in the decreasing order ofchannel gains. Pairing strategy f(i) is a one-to-one function which pairsradio Mi with radio Mf(i), f(i) > i, for 1 ≤ i ≤ N . This implies thatradios Mi and Mf(i) share the same spreading code and Mi pairs withMf(i) to recover an additional message superimposed on the message forMf(i).

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Wireless Information Networking Group

Pairing Strategies

f(i) = N + 1 − iM2 M3 M4 M5 M6M1

M2 M3 M4 M5 M6M1

M2 M3 M4 M5 M6M1

M1

M2

M4

M3 M5

M6

f(i) = i + 1

BS

6

Wireless Information Networking Group

Maximizing User Capacity

Proposition 1. Consider a cellular network with K radios and Northogonal channels such that N < K ≤ 2N . The total transmittedpower by the base station using N orthogonal channels and two-levelsuperposition coding is greater than that of direct transmission to the Kradios through K orthogonal channels.

M1M1 M2 BSPbc > P1 + P2

Pbc Z1 Z2 M2P2P1 Z2Z1BS

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Wireless Information Networking Group

Maximizing User Capacity

Corollary 1. The minimum additional power required for broadcasting toa pair of radios having the same spreading sequence is γPi, where γ is thecommon target SNR and Pi is the power required by the base station tomaintain a constant SNR of γ at the radio Mi with better channel gain andwithout employing broadcasting.

M1M1 M2 BSPbc = P1 + P2 + P1

Pbc Z1 Z2 M2P2P1 Z2Z1BS

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Wireless Information Networking Group

Maximizing User Capacity

Corollary. A pairing strategy which minimizes the total transmitted powerfor a given number of pairs k ≤ N is

f(i) = i + N, 1 ≤ i ≤ k.

The choice of the optimum pairing strategy is not unique, but the minimumtotal transmitted power is unique.

7

Wireless Information Networking Group

User capacity under average power constraint

• Compare the user capacity of a system employing superposition codingand the optimum pairing strategy to that of a system employing GWBEsequences under an average power constraint.

• Generalized Welch Bound Equality (GWBE) sequences are employed tosupport more radios than the processing gain of the network.

• We derive the average power constraint from a CDMA system supportingN radios through N orthogonal channels.

• Path-loss exponent α = 2, for sake for analysis.

8

Wireless Information Networking Group

Cellular Network without superposition coding

• Cellular network with infinite population and N orthogonal channels.

• Radios are uniformly distributed in the circular area of coverage with unitradius.

• All the radios have target SNR requirement γ & outage probability of ρ.

• The distribution of the channel gain z of a radio is given by

FZ(z) = FZ(z = d−2|h|2)

= 1 +e−z − 1

z, z > 0

9

Wireless Information Networking Group

Cellular Network without superposition coding

• An outage event occurs if the instantaneous SNR of the radio falls belowγ, i.e.KpzPt

N0W < γ.

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Wireless Information Networking Group

Cellular Network without superposition coding

• An outage event occurs if the instantaneous SNR of the radio falls belowγ, i.e. KpzPt

N0W < γ.

• When an outage occurs, the base station doesn’t transmit to thatparticular radio.

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Wireless Information Networking Group

Cellular Network without superposition coding

• An outage event occurs if the instantaneous SNR of the radio falls belowγ, i.e. KpzPt

N0W < γ.

• When an outage occurs, the base station doesn’t transmit to thatparticular radio.

• Under infinite population assumption, it is always possible to find Nradios with channels gains z > Zρ, where Zρ is the maximum value ofchannel gain that results in an outage.

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Wireless Information Networking Group

Cellular Network without superposition coding

• An outage event occurs if the instantaneous SNR of the radio falls belowγ, i.e. KpzPt

N0W < γ.

• When an outage occurs, the base station doesn’t transmit to thatparticular radio.

• Under infinite population assumption, it is always possible to find Nradios with channels gains z > Zρ, where Zρ is the maximum value ofchannel gain that results in an outage.

• The average power transmitted by the base station to the N radios withz ≥ Zρ is

NEPT (Zρ) = NγN0W (Kp)−1

[1 + Z2

ρΓ(0, Zρ)− e−Zρ(1 + Zp)2Zρ(1− e−Zρ)

]

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Wireless Information Networking Group

Cellular Network with superposition coding

• The base station transmits to K radios in every transmission interval.

• All the radios have a common target SNR of γ′.

• Under infinite population, assumption we can find K radios with z ≥ Zρ.

• The total power transmitted to K radios through N orthogonal channelsusing superposition coding is

P bcT =

γ′N0W

Kp

(K∑

k=1

1zk

+ γ′K−N∑

k=1

1zk

), z1 > z2 > · · · > zK

= PnbcT + ∆P bc

T

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Wireless Information Networking Group

Cellular Network with superposition coding

• The total power transmitted to K radios through N orthogonal channelsusing superposition coding is

P bcT =

γ′N0W

Kp

(K∑

k=1

1zk

+ γ′K−N∑

k=1

1zk

), z1 > z2 > · · · > zK

= PnbcT + ∆P bc

T

• PnbcT can be interpreted as total power required to transmit to K users

using K orthogonal codes (and target SNR γ′).

• ∆P bcT can be interpreted as the increase in the transmitted power due to

employing superposition coding to support K radios through N codes.

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Wireless Information Networking Group

Cellular Network with superposition coding

• The total power transmitted to K radios through N orthogonal channelsusing superposition coding is

P bcT =

γ′N0W

Kp

(K∑

k=1

1zk

+ γ′K−N∑

k=1

1zk

), z1 > z2 > · · · > zK

= PnbcT + ∆P bc

T

• The average total power transmitted to K radios is

E{P bcT } = E{Pnbc

T }+ E{∆P bcT }

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Wireless Information Networking Group

Cellular Network employing GWBE sequences

• The base station transmits to Kg radios in every transmission interval.

• All the radios have a common target SNR of γ′and the processing gain

of the system is N .

• Under infinite population, assumption we can find Kg radios with z ≥ Zρ.

• The total power transmitted to Kg radios using GWBE sequences isgiven by

P gT =

Ng(γ′)N0W/Kp

N −Kg(γ′)

Kg∑

k=1

1zk

, g(γ′) =

γ′

1 + γ′

12

Wireless Information Networking Group

Cellular Network employing GWBE sequences

• The total power transmitted to Kg radios using GWBE sequences isgiven by

P gT =

Ng(γ′)N0W/Kp

N −Kgg(γ′)

Kg∑

k=1

1zk

, g(γ′) =

γ′

1 + γ′

• g(γ′) is called the effective bandwidth of the user.

• Kg is upper bounded by

Kg < N(1 +1γ′

)

12

Wireless Information Networking Group

Results and Discussion

• Compare the user capacities K and Kg of systems employing superposition coding and

GWBE sequences respectively, under the same average total power constraint.

0 0.5 1 1.5 2 2.5 310

10.5

11

11.5

12

12.5

13

13.5

14

14.5

15

Decrease in the target SNR (dB)

Use

r C

apac

ity

α=4, SPC

α=2, SPC

α=4,GWBE

α=2,GWBE

13

Wireless Information Networking Group

Results and Discussion• N = 10, γ = 10dB, N0 = 10−10W/Hz, W = 106Hz, ρ = 0.05.

• User capacities plotted as a function of the degradation in the target SNR, −10 log γ′

γ

0 0.5 1 1.5 2 2.5 310

10.5

11

11.5

12

12.5

13

13.5

14

14.5

15

Decrease in the target SNR (dB)

Use

r C

apac

ity

α=4, SPC

α=2, SPC

α=4,GWBE

α=2,GWBE

13

Wireless Information Networking Group

Results and Discussion

• Superposition coding supports 10% more users for α = 2 and 20% moreusers for α = 4 compared to a conventional CDMA system and for adegradation of 1dB.

• Increase in the path-loss exponent increases the user capacity undersuperposition coding.

• GWBE sequences do not offer any advantage in this particular scenario.

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Wireless Information Networking Group

Results and Discussion

0 0.5 1 1.5 2 2.5 340

42

44

46

48

50

52

54

56

Decrease in the target SNR

Num

ber

of u

sers

SPC, α=4

SPC, α=2

GWBE, α=2

GWBE, α=4

Similar trend is observed for N=40

15

Wireless Information Networking Group

User capacity under total power constraint

• Evaluate the average user capacity under finite radio assumption andtotal power constraint in a transmission interval.

• Comparison of the average user capacity of systems employingsuperposition coding and GWBE sequences under the same total powerconstraint.

• N = 10, N0 = 10−10, W = 106Hz, γ′= 10dB.

• The total power constraint is arbitrarily chosen to be equal to the averagepower constraint considered earlier.

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Wireless Information Networking Group

User capacity under total power constraint

10 15 20 25 30 35 40 45 508

10

12

14

16

18

20

Node population

Ave

rage

Use

r C

apac

ity

SPCGWBE

• Superposition coding achieves 2N user capacity when the radio population is about 5

times the number of orthogonal channels available.

• GWBE sequences do not provide any additional gain.

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Wireless Information Networking Group

Conclusions

• Evaluated the performance of superposition coding in increasing the usercapacity of the forward link of CDMA cellular systems.

• Results indicate that on average 20% increase in the user capacity ispossible for α = 4 under an average power constraint and a degradationof 1dB in the taget SNR.

• With a fixed power constraint and finite radio population, the increasein the user capacity due to superposition coding is far greater than thatof a system employing GWBE sequences.

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Wireless Information Networking Group

Thank You

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