adaptive trellis-coded modulation with imperfect csi at ...[1] x. cai and g. b. giannakis,...

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Adaptive Trellis-Coded Modulationwith Imperfect CSI at Receiver andTransmitter, and Receive AntennaDiversity

Duc V. Duong∗, Geir E. Øien∗ and Kjell J. Hole†

∗NTNU, Dept. of Electronics and Telecommunications†University of Bergen, Coding Theory Group

This presentation and the paper can also be found at http://www.tele.ntnu.no/projects/beats/

Duc V. Duong @ BEATS/Wireless IP workshop, Gotland 25.08.2004

http://www.tele.ntnu.no/projects/beats/

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Outline

1. Motivation.

2. System model description.

3. BER analysis for both estimation and prediction cases.

4. ASE analysis and the optimization process.

5. Results and concluding remarks.


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Motivation

• Adaptive coded modulation (ACM) is a promising technique to enhance

average spectral efficiency (ASE) of wireless transmission over fading

channels.

• Diversity mitigates fading and makes the channel look Gaussian-like.

• Constellation size, transmit power are adjusted according to the channel

quality, which increases the ASE without wasting or sacrificing error

probability performance.

• Non-zero estimation error.

• Goal: Maximize ASE while keeping instantaneous BER ≤ BER0 when

both estimation and prediction error are considered.


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System Overview

Constellationselection

BufferFadingchannel

Pilotinsertion

Adaptive encoderand modulator

Fadingchannel .............

Buffer MRC combiner,adaptive decoderand demodulator

Powercontrol

Powerselection

Channelpredictor Estimator

EstimatorZero−errorFeedbackchannel

......... .........

PD D D D P D D D P D..... .....L

ypl,b(k) =√Eplhb(k; l)s(k; l) + ηb(k; l) l = 0 (1)

yd,b(k; l) =√Edhb(k; l)s(k; l) + ηb(k; l) l ∈ [1, L− 1] (2)


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Assumptions

• E[|s(k; l)|2] = |s(k; 0)|2 = 1.

• hb(k; l) is stationary complex Gaussian RP with zero mean, and variance

σ2h = 1.

• Subchannels are mutually uncorrelated.

• ηb(k; l) is complex AWGN with zero mean and variance N0/2 per com-

ponent, with the components being uncorrelated.

• The channel statistics are known.


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Channel Estimation

• The linear channel estimate of the bth branch:

he,b(k; l) = wHe y(k), (3)

• MSE of the estimation error:

σ2εe,b

= 1−√Eplr

He D∗(s)we (4)

= 1−Ke∑k=1

∣∣∣uHk re

∣∣∣2 (1− α)Lγb

(1− α)Lγbλk + 1(5)


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Channel Estimation cont’d

• Given he,b(k; l), we do symbol-by-symbol ML detection. The CSNR of

a single branch [1] and after MRC are respectively given by

γb(k; l) =Ed

∣∣he,b(k; l)∣∣2

N0 + gEdσ2εe,b

(l), (6)

γ(k; l) =

B∑b=1

γb(k; l) =Ed

N0 + gEdσ2εe

(l)

B∑b=1

∣∣he,b(k; l)∣∣2 (7)


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BER Accounts for Estimation Error• Approximated BER performance for TCM on AWGN channels

BER(en|γ) =

I∑i=1

an(i) exp

(−bn(i)

Mnγ

)(8)

0 5 10 15 20 25 30 3510

−6

10−5

10−4

10−3

10−2

10−1

100

M=4

M=8

M=16

M=32

M=64

M=128

M=256

M=512

CSNR [dB]

BE

R


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BER Accounts for Estimation Error cont’d

• Replacing (7) into (8) we have

BER(en|{he,b

}) =

I∑i=1

an(i)

B∏b=1

exp(−AnEd

∣∣he,b(k; l)∣∣2) (9)

where An = bn(i)/(Mn(N0 + gEdσ2εe

(l))).


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Channel Prediction

• The linear predicted channel of a single branch:

hp,b(k; l) = wHp y(k), (10)

• MMSE of the prediction error

σ2εp,b

= 1−Kp∑k=1

∣∣∣uHk rp

∣∣∣2 (1− α)Lγb

(1− α)Lγbλk + 1(11)


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BER Accounts for both Prediction andEstimation Errors• Consider the relationship

he,b(k; l) = hb(k; l)− εe,b(k; l)

= hp,b(k; l) + εp,b(k; l)− εe(k; l). (12)

• For single antenna sysems, given hp,b(k; l) =⇒ p(∣∣he,b

∣∣ ∣∣∣hp,b) ∼ Rice

distribution with

K =|(1− ρ)hp,b(k; l)|2

σ2he,b

,

where ρ = correlation between estimation error εe,b(k; l) and the pre-

dicted channel hp,b(k; l) (very small ⇒ set equal to 0).

σ2he,b

≈ σ2εe,b

+ σ2εp,b

(ρ = 0, εe,b(k; l) and εp,b(k; l) uncorrelated).


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BER Accounts for both Prediction andEstimation Errors cont’d• For multiple uncorrelated receive antenna systems p

({∣∣he,b

∣∣} ∣∣∣ {hp,b

})=∏B

b=1 p(∣∣he,b

∣∣ ∣∣∣hp,b

)• BER given the set of predicted channel can be obtained as:

BER(en|

{hp,b

})=

∫ ∞

0· · ·

∫ ∞

0BER

(en

∣∣∣ {∣∣he,b

∣∣})×p

({∣∣he,b

∣∣} ∣∣∣ {hp,b

})d

∣∣he,1∣∣ · · · d ∣∣he,B

∣∣(13)

• Let the predicted CSNR on each subchannel be γb = Ed

∣∣hp,b(k; l)∣∣2 /N0

[2, 3] then the combined CSNR using MRC is

γ =Ed

N0

B∑b=1

∣∣hp,b(k; l)∣∣2 =⇒ ¯γ = rγbB where r = Ed(1− σ2

εp)/E


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BER Accounts for both Prediction andEstimation Errors cont’d• Assuming σ2

he,b= σ2

he∀b, and letting dn = 1/(AnEdσ

2he

+ 1), the BERgiven predicted CSNR is:

BER(en|γ) =

I∑i=1

an(i)dBn exp

(−γdnAnEEd

γbEd

)(14)

• The overall BER (over all codes)

BER =

∑Nn=1 Rn

∫ γn+1

γnBER(en|γ)p(γ)dγ∑N

n=1 RnPn


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ACM Concept

outage

γ1 γ2 γ3 γN−1 γN

R1 R2 RN−1 RN

• Set of codes {Mn}Nn=1 and the corresponding spectral efficiencies (SE)

{Rn}Nn=1.

• If the predicted CSNR γ ∈ [γn, γn+1〉, the nth code (thus SE Rn) will

be used. γ0 = 0 and γN+1 = ∞.

• BER(en|γ) ≤ BER0 for all modes.


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ACM cont’d

• The average power per data symbol and pilot symbol:

Ed = αLE/(L− 1) and Epl = (1− α)LE

• Since no transmission when γ < γ1

Ed =Ed∫∞

γ1p(γ)dγ

=Ed

Q(B, γ1/rγ)

where p(γ) is the pdf of the predicted CSNR, which is Gamma dis-

tributed, and Q(·, ·) is normalized incomplete gamma function.


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ASE Performance

• Average spectral efficiency is given by

ASE =L− 1

L

N∑n=1

RnPn

=L− 1

L

N∑n=1

(log2(Mn)− 1

G

)×

{Q (B, γn/rγb)−Q (B, γn+1/rγb)

}(15)

• For each value of L ∈[2, b1/(2fdTs)c

][4] we find

maxα

ASE(α)

subject to 0 < α < 1 (16)


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Outage Probability

• No data is transmitted when γ < γ1, the system suffers an outage of

Pout =

∫ γ1

0p(γ)dγ = 1−Q(B, γ1/rγ)


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Simulation Parameters

• {Mn} = {4, 8, 16, 32, 64, 128, 256, 512}.

• fc = 2 GHz.

• Symbol period Ts = 5 µs.

• Mobile velocity v = 30 m/s.

• System delay τ = DLTs = 1 ms (or τ = 0.2/fd).

• Estimator order Ke = 20, and predictor order Kp = 250.

• BER0 = 10−5.

• B = {1, 2, 4}


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Results: Optimum α and L

5 10 15 20 25 30 350.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

Expected subchannel CSNR

α

Equally allocated

Optimally allocated

B = 1B = 2B = 4

(a) Optimum power allocation

5 10 15 20 25 30 350

20

40

60

80

100

120

140

160

180

Expected subchannel CSNRL

Optimal power

Equal power

B = 1B = 2B = 4

(b) Optimum pilot symbol spacing


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Results: ASE

5 10 15 20 25 30 350

1

2

3

4

5

6

7

8

9

B=1

B=2

B=4

Capacity


Ave

rage

Spe

ctra

l Effi

cien

cy [b

its/s

/Hz]

Optimal power, optimal LOptimal power, L = 10Equal power, optimal LCapacity (constant power) [2 eq. (40)]


duong

Cross-Out

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Results: BER

5 10 15 20 25 30 3510

−8

10−7

10−6

10−5


Ave

rage

BE

RB = 1B = 2B = 4


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Results: Outage probability

5 10 15 20 25 30 3510

−4

10−3

10−2

10−1

100

B=1

B=2

B=4


Out

age

prob

abili

ty

Optimal power, optimal LEqual power, optimal L


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Conclusion

• Adaptive trellis-coded PSAM with receive antenna diversity is investi-

gated.

• The pilot symbol period and power allocation between pilot and data

symbols were optimized to maximize ASE.

• We achieved higher ASE and lower probability of outage without sacri-

ficing BER performance.


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References

[1] X. Cai and G. B. Giannakis, “Adaptive PSAM accounting for channel

estimation and prediction errors,” to appear in IEEE Transactions on

Wireless Communications, 2004.

[2] D. V. Duong and G. E. Øien, “Adaptive trellis-coded modulation with

imperfect channel state information at the receiver and transmitter,” in

Nordic Radio Symposium, Oulu, Finland, Aug. 2004.

[3] G. E. Øien, H. Holm, and K. J. Hole, “Impact of channel prediction

on adaptive coded modulation performance in Rayleigh fading,” IEEE

Transactions on Vehicular Technology, vol. 53, no. 3, pp. 758–769, May

2004.

[4] J. K. Cavers, “An analysis of pilot symbol assisted modulation for

Rayleigh fading channels,” IEEE Transactions on Vehicular Technology,

vol. 40, no. 4, pp. 686–693, Nov. 1991.


adaptive trellis-coded modulation with imperfect csi at ...[1] x. cai and g. b. giannakis,...

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