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EE359 – Lecture 14 Outline. Announcements Graded MTs and solns ready by tomorrow, will go over in class Monday Regrades: turn in exam and written explanation Adaptive MQAM: optimal power and rate Finite Constellation Sets Update rate Estimation error Estimation delay.
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EE359 – Lecture 14 Outline • Announcements • Graded MTs and solns ready by tomorrow, will go over in class Monday • Regrades: turn in exam and written explanation • Adaptive MQAM: optimal power and rate • Finite Constellation Sets • Update rate • Estimation error • Estimation delay
Review of 11/2 Lecture • MGF Approach to MRC Diversity Analysis • EGC and transmit diversity • Introduction to adaptive modulation: • Adapt modulation parameters relative to instantaneous channel SNR • Can adapt constellation size, transmit power, instantaneous BER, symbol time, coding rate/scheme, or combinations of these. • Optimization criterion can be throughput, minimum BER, or minimum transmit power.
One of the M(g) Points log2 M(g) Bits To Channel M(g)-QAM Modulator Power: P(g) Point Selector Uncoded Data Bits Delay g(t) g(t) 16-QAM 4-QAM BSPK Variable-Rate Variable-Power MQAM Goal: Optimize P(g) and M(g) to maximize R=Elog[M(g)]
Optimization Formulation • Adaptive MQAM: Rate for fixed BER • Rate and Power Optimization Same maximization as for capacity, except for K=-1.5/ln(5BER).
gk g Optimal Adaptive Scheme • Power Adaptation • Spectral Efficiency g Equals capacity with effective power loss K=-1.5/ln(5BER).
K2 K1 K=-1.5/ln(5BER) Spectral Efficiency Can reduce gap by superimposing a trellis code
Constellation Restriction • Restrict MD(g) to {M0=0,…,MN}. • Let M(g)=g/gK*, where gK* is later optimized. • Set MD(g) to maxj Mj: Mj M(g). • Region boundaries are gj=MjgK*, j=0,…,N • Power control maintains target BER M3 M(g)=g/gK* MD(g) M3 M2 M2 M1 M1 Outage 0 g0 g1=M1gK* g2 g3 g
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(g) • Average Rate
Efficiency in Rayleigh Fading Spectral Efficiency (bps/Hz) Average SNR (dB)
Practical Constraints • Constellation updates: fade region duration • Error floor from estimation error • Estimation error at RX can cause error in absence of noise (e.g. for MQAM) • Estimation error at TX causes mismatch of adaptive power and rate to actual channel • Error floor from delay: let r(t,t)=g(t-t)/g(t). • Feedback delay causes mismatch of adaptive power and rate to actual channel
Estimation Error and Delay ^ • Error floor from estimation error () • Joint distribution p(,) depends on estimation: hard to obtain. For PSAM the envelope is bi-variate Rayleigh • Error floor from delay: let =g[i]/g[i-id]. • p(|) known for Nakagami fading ^
Main Points • Adaptive MQAM uses capacity-achieving power and rate adaptation, with power penalty K. • Adaptive MQAM 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.
