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Linear Modulation: Performance in AWGN & Fading Channels

Explore the performance of linear modulation techniques in AWGN and fading channels, including outage probability and average Ps calculation. Understand the tradeoffs and complexities involved in achieving high rates and spectral efficiency.

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Linear Modulation: Performance in AWGN & Fading Channels

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  1. EE359 – Lecture 9 Outline • Linear Modulation Review • Linear Modulation Performance in AWGN • Modulation Performance in Fading • Outage Probability • Average Ps (Pb)

  2. 1 g g0 g P Bc Review of Last Lecture • Capacity of Flat-Fading Channels • Fading Statistics Known • Fading Known at RX • Fading Known at TX and RX • Optimal Rate and Power Adaptation • Channel Inversion with Fixed Rate • Capacity of Freq.-Selective Fading Channels • Capacity is the sum of subband capacities Waterfilling 1/|H(f)|2 f

  3. Our focus Passband Modulation Tradeoffs • Want high rates, high spectral efficiency, high power efficiency, robust to channel, cheap. • Amplitude/Phase Modulation (MPSK,MQAM) • Information encoded in amplitude/phase • More spectrally efficient than frequency modulation • Issues: differential encoding, pulse shaping, bit mapping. • Frequency Modulation (FSK) • Information encoded in frequency • Continuous phase (CPFSK) special case of FM • Bandwidth determined by Carson’s rule (pulse shaping) • More robust to channel and amplifier nonlinearities

  4. Amplitude/Phase Modulation • Signal over ith symbol period: • Pulse shape g(t) typically Nyquist • Signal constellation defined by (si1,si2) pairs • Can be differentially encoded • M values for (si1,si2)log2 M bits per symbol • Ps depends on • Minimum distance dmin (depends on gs) • # of nearest neighbors aM • Approximate expression:

  5. Alternate Q Function Representation • Traditional Q function representation • Infinite integrand • Argument in integral limits • New representation (Craig’93) • Leads to closed form solution for Ps in PSK • Very useful in fading and diversity analysis

  6. Linear Modulation in Fading • In fading gsand therefore Psrandom • Performance metrics: • Outage probability: p(Ps>Ptarget)=p(g<gtarget) • Average Ps , Ps: • Combined outage and average Ps

  7. Ts Outage Ps Ps(target) t or d Outage Probability • Probability that Ps is above target • Equivalently, probability gs below target • Used when Tc>>Ts

  8. Average Ps • Expected value of random variable Ps • Used when Tc~Ts • Error probability much higher than in AWGN alone • Alternate Q function approach greatly simplifies calculations (switch integral order, becomes Laplace Xfm) Ts Ps Ps t or d

  9. Main Points • Linear modulation more spectrally efficient but less robust than nonlinear modulation • Psapproximation in AWGN: • Alternate Q function representation simplifies calculations • In fading Psis a random variable, characterized by average value, outage, or combined outage/average • Outage probability based on target SNR in AWGN. • Fading greatly increases average Ps . • Alternate Q function approach simplifies Pscalculation, especially its average value in fading (Laplace Xfm).

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