Lecture6 - E4703 Wireless Communications Slide Set 6...

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

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Lecture6 - E4703 Wireless Communications Slide Set 6...

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