Lecture6

# Lecture6 - E4703 Wireless Communications Slide Set 6...

This preview shows pages 1–7. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: E4703 Wireless Communications Slide Set 6 Outline • Summary of last lecture. • Coherent AWGN error probabilities revisited. ¾ BPSK and QPSK. ¾ M-PSK, M-PAM and M-QAM. ¾ General approximation. • Differential error probability. • Error probabilities in fading channels. ¾ Outage probability. ¾ Average error probability. ¾ Combined outage and average error probability. • Doppler Spread • Intersymbol Interference (ISI) Summary of Last Lecture • Modulation allows us to map bits onto a signal for transmission. • Two main classes of modulation: linear and nonlinear. Linear more spectrally efficient but requires linear amplifiers, which are less power efficient. Mixed use in 2G, but nowadays clear trend towards linear only. • No fading for now, only AWGN. Ideal synchronization. • Modulations defined (in lowpass equivalenr) by a constellation of possible points on the I-Q plane. • When points are equiprobable, optimum detection boils down to ML criterion. With Gaussian noise this is tantamount to minimum distance in the I-Q plane. • Exact computation of error probability requires numerical integration. The union bound provides a simpler expression via the Q function and, for high- SNR, a closed-form approximation. • Gray mapping minimizes the number of erroneous bits when a symbol is in error. • 3 linear modulations: PAM (amplitude only), PSK (phase only) and QAM (amplitude and phase). Simplest QAM are square, although better constellations can be obtained with careful shaping. • Best performance with coherent detection, which requires recovering the carrier phase. Noncoherent detection does away with this requirement at the expense of performance. • Pulse shapes must be chosen to minimize bandwidth usage without causing ISI (satisfying Nyquist criterion). Raised cosine pulses are a good solution. Digital Modulation over Wireless Channels • Thus far we have considered digital modulation over unfaded AWGN channels. We described the most common forms of modulation and studied the error probability in general. • We now proceed to: ¾ Specialize the error probability for each modulation. ¾ Study the impact on performance of flat fading, frequency- selective fading (delay spread and ISI) and Doppler spread. • We still assume perfect carrier (and phase in the case of coherent reception) recovery. Also perfect timing synchronization. AWGN Error Prob. Revisited • If the passband noise PSD is N /2, the signal-to-noise ratio is • The energy per symbol is E s = P r T s and thus • We will denote the ratio E s / N by γ s = SNR B T s . Since T s ≈ 1/ B , we have that γ s ≈ SNR . • The energy per bit is E b = E s / log 2 M and we denote the ratio E b / N by γ b = γ s / log 2 M ....
View Full Document

## This note was uploaded on 08/05/2008 for the course ELEN E4702 taught by Professor Lazano during the Summer '08 term at Columbia.

### Page1 / 36

Lecture6 - E4703 Wireless Communications Slide Set 6...

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online