Wireless Networks (PHY): Design for Diversity

Wireless Networks (PHY): Design for Diversity Y. Richard Yang 9/18/2012

Admin • Assignment 1 questions • am_usrp_710.dat was sampled at 256K • Rational Resampler not Rational Resampler Base • Assignment 1 office hours • Wed 11-12 @ AKW 307A • Others to be announced later today

Recap: Demodulation of Digital Modulation • Setting • Sender uses M signaling functions g1(t), g2(t), …, gM(t), each has a duration of symbol time T • Each value of a symbol has a corresponding signaling function • The received x maybe corrupted by additive noise • Maximum likelihood demodulation • picks the m with the highest P{x|gm} • For Gaussian noise,

Recap: Matched Filter Demodulation/Decoding • Project (by matching filter/correlation) each signaling function to bases • Project received signal x to bases • Compute Euclidean distance, and pick closest sin(2πfct) [a00,b00] [a01,b01] [ax,bx] cos(2πfct) [a10,b10] [a11,b11]

Recap: Wireless Channels • Non-additive effect of distance d on received signaling function • free space • Fluctuations at the same distance

Recap: Reasons • Shadowing • Same distance, but different levels of shadowing by large objects • It is a random, large-scale effect depending on the environment • Multipath • Signal of same symbol taking multiple paths may interfere constructively and destructively at the receiver • also called small-scale fading

Multipath Effect (A Simple Example) Assume transmitter sends out signal cos(2 fc t) d2 d1 phase difference:

Multipath Effect (A Simple Example) • Suppose at d1-d2the two waves totally destruct, i.e., if receiver moves to the right by /4: d1’ = d1 + /4; d2’ = d2 - /4; constructive Discussion: how far is /4? What are implications?

Multipath Effect (A Simple Example): Change Frequency • Suppose at fthe two waves totally destruct, i.e. • Smallest change to f for total construct: • (d1-d2)/c is called delay spread.

Multipath Delay Spread RMS: root-mean-square

Multipath Effect(moving receiver) example d d2 d1 Suppose d1=r0+vt d2=2d-r0-vt d1d2

Derivation See http://www.sosmath.com/trig/Trig5/trig5/trig5.html for cos(u)-cos(v)

deep fade Waveform v = 65 miles/h, fc = 1 GHz: fc v/c = 109 * 30 / 3x108 = 100 Hz 10 ms Q: how far does the car move between two deep fade?

Multipath with Mobility

Outline • Admin and recap • Wireless channels • Intro • Shadowing • Multipath • space, frequency, time deep fade • delay spread

Multipath Can Disperse Signal signal at sender LOS pulse Time dispersion: signal is dispersed over time multipath pulses signal at receiver LOS: Line Of Sight

JTC Model: Delay Spread Residential Buildings

Dispersed Signal -> ISI Dispersed signal can cause interference between “neighbor” symbols, Inter Symbol Interference (ISI) Assume 300 meters delay spread, the arrival time difference is 300/3x108 = 1 us • if symbol rate > 1 Ms/sec, we will have ISI In practice, fractional ISI can already substantially increase loss rate signal at sender LOS pulse multipath pulses signal at receiver LOS: Line Of Sight

Summary of Progress: Wireless Channels • Channel characteristics change over location, time, and frequency Received Signal Large-scale fading power Power (dB) path loss log (distance) LOS pulse time multipath pulses small-scale fading frequency signal at receiver

Representation of Wireless Channels • Received signal at time m is y[m], hl[m] is the strength of the l-th tap, w[m] is the background noise: • When inter-symbol interference is small: (also called flat fading channel)

Preview: Challenges and Techniques of Wireless Design received signal strength use fade margin—increase power or reduce distance today bit/packet error rate at deep fade diversity equalization; spread-spectrum; OFDM; directional antenna ISI

Outline • Recap • Wireless channels • Physical layer design • design for flat fading • how bad is flat fading?

Background For standard Gaussian white noise N(0, 1), Prob. density function:

Background

Baseline: Additive Gaussian Noise N(0, N0/2) =

Baseline: Additive Gaussian Noise

Baseline: Additive Gaussian Noise • Conditional probability density of y(T), given sender sends 1: • Conditional probability density of y(T), given sender sends 0:

Baseline: Additive Gaussian Noise • Demodulation error probability: assume equal 0 or 1

Baseline: Error Probability Error probability decays exponentially with signal-noise-ratio (SNR). See A.2.1: http://www.eecs.berkeley.edu/~dtse/Chapters_PDF/Fundamentals_Wireless_Communication_AppendixA.pdf

Flat Fading Channel Assume h is Gaussian random: BPSK: For fixed h, Averaged out over h, at high SNR.

Comparison flat fading channel static channel

Backup Slides

Wireless Networks (PHY): Design for Diversity