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.

Variable-Rate Variable-Power MQAM Uncoded Data Bits Delay Point Selector M(g)-QAM Modulator Power: P(g) To Channel g(t) log2 M(g) Bits One of the M(g) Points BSPK 4-QAM 16-QAM 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).

Optimal Adaptive Scheme gk g Power Adaptation Spectral Efficiency g Equals capacity with effective power loss K=-1.5/ln(5BER).

Spectral Efficiency Can reduce gap by superimposing a trellis code K2 K=-1.5/ln(5BER) 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 g0 g1=M1gK* g2 g3 g

Power Adaptation and Average Rate 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.