Lecture4_Adaptive_Modulation

γ(t)
Goal: Optimize P(γ) and M(γ) to maximize R=Elog[M(γ)]
BSPK
4-QAM
16-QAM
The rate and power of MQAM are varied to maximize spectral efficiency while meeting a given instantaneous Pb target.
Adaptive Technologies
Rate Control
Fixing symbol rate，using multiple modulation schemes or constellation sizes
• Fairly easy, used in current systems, such as GSM, IS-136 EDGE or 802.11a, et. al.
Fixing the modulation, changing the symbol rate
• Varying signal bandwidth is impractical and complicates bandwidth sharing.
Power Control
Adapting the transmit power alone is generally used to compensate for SNR variation due to fading. To maintain a fixed bit error probability, or a constant received SNR. The power adaptation thus inverts the channel fading so that the channel appears as an AWGN channel to the modulator and demodulator.
Variable-Rate Variable-Power MQAM
log2 M(γ) Bits
Uncoded Data Bits
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One of the M(γ) Points Point Selector M(γ)-QAM Modulator Power: P(γ)
γ(t)
To Channel
Delay
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K2 K1
K=-1.5/ln(5BER)
Can reduce gap by superimposing a trellis code
Constellation Restriction
Restrict MD(γ) to {M0=0,…,MN}. Let M(γ)=γ/γΚ*, where γΚ* is later optimized. Set MD(γ) to maxj Mj: Mj ≤ M(γ). Region boundaries are γj=MjγΚ*, j=0,…,N Power control maintains target BER
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Average Rate R N = ∑ log 2 M j p (γ j ≤ γ < γ j +1 ) B j =1
Байду номын сангаас
Efficiency in Rayleigh Fading
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Practical Constraints
Constellation updates: fade region duration
Optimization Formulation
Adaptive MQAM: Rate for fixed BER
1.5γ P(γ ) P (γ ) = 1 + Kγ M (γ ) = 1 + − ln(5 BER) P P
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Rate and Power Optimization
P (γ ) max E log 2 [ M (γ )] = max E log 2 1 + Kγ P (γ ) P (γ ) P
Same maximization as for capacity, except for K=-1.5/ln(5BER).
Optimal Adaptive Scheme
Power Adaptation
1 1 γK P(γ ) γ0 − γK γ ≥ = = P else 0
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Only 1-2 degrees of freedom needed for good performance
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Optimization criterion:
Maximize throughput Minimize average power Minimize average BER
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Pb = ∫ ∫ .2[5 BERtarget ]
0 γK
∞ ∞
γ / γˆ
)d γ d γ p (γ , γˆˆ
Joint distribution p(γ,^ γ) depends on estimation: hard to obtain. For PSAM the envelope is bi-variate Rayleigh
Error floor from delay: let ξ=γ[i]/γ[i-id].
Pb = ∫ ∫ .2[5 BERtarget ]ξ p (ξ | γ ) p (γ )dξdγ
0 0 ∞∞
p(ξ|γ) known for Nakagami fading
Main Points
Adaptive modulation leverages fast fading to improve performance (throughput, BER, etc.)
Error probability is typically adapted along with some other form of adaption such as constellation size or modulation type.
Hybrid techniques
Adapt multiple parameters of the transmission scheme, including rate, power, coding, and instantaneous error probability. Joint optimization of the different techniques is used to meet a given performance requirement. Rate adaption is often combined with power adaptation to maximize spectral efficiency.
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Adaptive Modulation
Outline
Adaptive MQAM: optimal power and rate Finite Constellation Sets Update rate Estimation error Estimation delay
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Practical Considerations in Adaptive Modulation
πj > T >> TM τj = N j +1 + N j
τ j = AFRD
TM = delay spread N j = level crossing rate at min fade in region N j +1 = level crossing rate at max fade in region
γ0 K
1
γ
0
Spectral Efficiency
R = ∫ log B γ
K
γk
1 γK
γ
∞
2
γ p(γ )dγ . γ
K
Equals capacity with effective power loss K=-1.5/ln(5BER).
Spectral Efficiency
M3 MD(γ) M2 M1 0
Outage M1 M2
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M(γ)=γ/γΚ*
M3
γ0
γ1=M1γK*
γ2
γ3
γ
Power Adaptation and Average Rate
Power adaptation:
Fixed BER within each region • Es/N0=(Mj-1)/K • Channel inversion within a region Requires power increase when increasing M(γ) Pj (γ ) ( M j − 1) /(γK ) γ j ≤ γ < γ j +1 , j > 0 = γ < γ1 0 P
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Adaptive MQAM uses capacity-achieving power and rate adaptation, with power penalty K.
Comes within 5-6 dB of capacity
Discretizing the constellation size results in negligible performance loss. Constellations cannot be updated faster than 10s to 100s of symbol times: OK for most dopplers. Estimation error and delay lead to irreducible error floors in adaptive MQAM