Adaptive Trellis-Coded Modulation with Imperfect CSI at Receiver and ...

Department of Electronics and Telecommunications

Adaptive Trellis-Coded Modulation with Imperfect CSI at Receiver and Transmitter, and Receive Antenna Diversity 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

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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.

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


Outline

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• 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.


Motivation

• Non-zero estimation error. • Goal: Maximize ASE while keeping instantaneous BER ≤ BER0 when both estimation and prediction error are considered.


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Adaptive encoder and modulator

Power control

Pilot insertion

Zero−error Feedback channel

Fading channel Fading channel Power selection Constellation selection

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

Buffer Buffer

Channel predictor

.. .. .


System Overview MRC combiner, adaptive decoder and demodulator

Estimator . .. . Estimator

L

D P D D ..... D P D D ..... D P D ypl,b(k) =

q

Epl hb(k; l)s(k; l) + ηb(k; l)

l=0

(1)

yd,b(k; l) =

p

Edhb(k; l)s(k; l) + ηb(k; l)

l ∈ [1, L − 1]

(2)


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• E[|s(k; l)|2] = |s(k; 0)|2 = 1. • hb(k; l) is stationary complex Gaussian RP with zero mean, and variance σh2 = 1. • Subchannels are mutually uncorrelated. • ηb(k; l) is complex AWGN with zero mean and variance N0/2 per component, with the components being uncorrelated.


Assumptions

• The channel statistics are known.


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• The linear channel estimate of the bth branch: he,b(k; l) = weHy(k), • MSE of the estimation error: q ∗ 2 σe,b = 1 − Epl rH e D (s)we 2 Ke uH re (1 − α)L¯ γb X k =1− γbλk + 1 (1 − α)L¯

(3)

(4)


Channel Estimation

(5)

k=1


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• 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 2 Ed he,b(k; l) , (6) γb(k; l) = N0 + gEdσ2e,b (l) γ(k; l) =

B X b=1

B

X 2 Ed γb(k; l) = he,b(k; l) 2 N0 + gEdσe (l)


(7)


Channel Estimation cont’d

b=1

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• Approximated BER performance for TCM on AWGN channels I X bn(i) γ BER(en|γ) = an(i) exp − Mn i=1

0

10

−1

10

(8)


BER Accounts for Estimation Error

−2

BER

10

−3

10

M=4

−4

M=16

M=64

M=256

10

M=8

−5

10

M=128

M=32

M=512

−6

10

0

5

10

15

20

25

30

35

CSNR [dB]


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• Replacing (7) into (8) we have

BER(en| he,b ) =

I X

an(i)

i=1

B Y

2 exp −AnEd he,b(k; l)

b=1

where An = bn(i)/(Mn(N0 + gEdσ2e (l))).


(9)


BER Accounts for Estimation Error cont’d

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• The linear predicted channel of a single branch: hp,b(k; l) = wpHy(k),

(10)

• MMSE of the prediction error σ2p,b = 1 −

2 Kp uH r (1 − α)L¯ γb X k p k=1


(1 − α)L¯ γbλk + 1

(11)


Channel Prediction

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• Consider the relationship he,b(k; l) = hb(k; l) − e,b(k; l) = hp,b(k; l) + p,b(k; l) − e(k; l). (12) • For single antenna sysems, given hp,b(k; l) =⇒ p( he,b hp,b) ∼ Rice distribution with |(1 − ρ)hp,b(k; l)|2 , K= σ˜ h2


BER Accounts for both Prediction and Estimation Errors

e,b

where ρ = correlation between estimation error e,b(k; l) and the predicted channel hp,b(k; l) (very small ⇒ set equal to 0). σ˜ h2 ≈ σ2e,b + σ2p,b (ρ = 0, e,b(k; l) and p,b(k; l) uncorrelated). e,b Duc V. Duong @ BEATS/Wireless IP workshop, Gotland 25.08.2004

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• For multiple uncorrelated receive antenna systems p he,b hp,b = QB b=1 p he,b hp,b • BER given the set of predicted channel can be obtained as: Z ∞Z ∞ BER en he,b BER en| hp,b = · · · 0 0 ×p he,b hp,b d he,1 · · · d he,B (13)


BER Accounts for both Prediction and Estimation Errors cont’d

2 ¯ • Let the predicted CSNR on each subchannel be γˆb = Ed hp,b(k; l) /N0 [2, 3] then the combined CSNR using MRC is B 2 E¯d X γˆ = hp,b(k; l) =⇒ γ¯ˆ = r¯ γbB where r = E¯d(1 − σ2p )/E N0 b=1


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• Assuming σ˜ h2e,b = σ˜ h2e ∀b, and letting dn = 1/(AnEdσ˜ h2e + 1), the BER given predicted CSNR is: I X γ ˆ d A EE n n d BER(en|ˆ γ) = an(i)dBn exp − (14) ¯ ¯ γ E b d i=1 • The overall BER (over all codes) R γˆn+1 PN R BER(en|ˆ γ )p(ˆ γ )dˆ γ n=1 n γˆn BER = PN n=1 Rn Pn



BER Accounts for both Prediction and Estimation Errors cont’d

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R1

outage γˆ1

R2 γˆ2

RN −1 γˆ3

γˆN −1

RN γˆN

• Set of codes {Mn}N n=1 and the corresponding spectral efficiencies (SE) {Rn}N n=1 . • If the predicted CSNR γˆ ∈ [ˆ γn, γˆn+1i, the nth code (thus SE Rn) will be used. γˆ0 = 0 and γˆN +1 = ∞.


ACM Concept

• BER(en|ˆ γ ) ≤ BER0 for all modes.


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• The average power per data symbol and pilot symbol: E¯d = αLE/(L − 1)

and

Epl = (1 − α)LE

• Since no transmission when γˆ < γˆ1 E¯d E¯d R = Ed = ∞ γ) Q(B, γˆ1/r¯ γ )dˆ γ p(ˆ γˆ1


ACM cont’d

where p(ˆ γ ) is the pdf of the predicted CSNR, which is Gamma distributed, and Q(·, ·) is normalized incomplete gamma function.


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ASE Performance • Average spectral efficiency is given by N

L−1X R n Pn ASE = L n=1 N L−1X 1 = log2(Mn) − L G n=1 n o × Q (B, γˆn/r¯ γb) − Q (B, γˆn+1/r¯ γb)

(15)

• For each value of L ∈ 2, b1/(2fdTs)c [4] we find max ASE(α) α

subject to 0 < α < 1


(16)

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• No data is transmitted when γˆ < γˆ1, the system suffers an outage of Z γˆ1 Pout = p(ˆ γ )dˆ γ = 1 − Q(B, γˆ1/r¯ γ) 0



Outage Probability

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• {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.


Simulation Parameters

• BER0 = 10−5. • B = {1, 2, 4}


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Results: Optimum α and L 180

1

160

0.95

B=1 B=2 B=4

140 0.9

120 0.85

L

α

100 0.8

Equal power

80 0.75

60

Equally allocated 0.7

0.6 5

40

Optimally allocated

0.65

20

B=1 B=2 B=4

10

15 20 25 Expected subchannel CSNR

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(a) Optimum power allocation


Optimal power

35

0 5

10


30

35

(b) Optimum pilot symbol spacing

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Results: ASE 9 B=1

Average Spectral Efficiency [bits/s/Hz]

8 7

B=2

6 5

B=4 Capacity

4 3 2 Optimal power, optimal L Optimal power, L = 10 Equal power, optimal L Capacity (constant power) [2 eq. (40)]

1 0 5

10



30

35

20


Results: BER −5

10

B=1 B=2 B=4

−6

Average BER

10

−7

10

−8

10

5

10



30

35

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Results: Outage probability 0

10

−1

10

Outage probability

B=1

B=2

−2

10

B=4 −3

10

Optimal power, optimal L Equal power, optimal L −4

10

5

10



30

35

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• Adaptive trellis-coded PSAM with receive antenna diversity is investigated. • 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 sacrificing BER performance.



Conclusion

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[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.


References

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

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