1. 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

2. 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.

3. 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)]

4. Optimization Formulation
Adaptive MQAM: Rate for fixed BER
Rate and Power Optimization
Same maximization as for capacity, except for K=-1.5/ln(5BER).

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

6. Spectral Efficiency Can reduce gap by superimposing a trellis code K2
K=-1.5/ln(5BER)
Can reduce gap by superimposing a trellis code

7. 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

8. 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

9. Efficiency in Rayleigh Fading
Spectral Efficiency (bps/Hz)
Average SNR (dB)

10. 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

11. 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 ^ ^

12. 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.