Lecture5 - E4703 Wireless Communications Slide Set 5...

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E4703 Wireless Communications Slide Set 5
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Outline Summary of last lecture. Digital modulation & detection. Signal space analysis. ¾ Signal representation. ¾ Receiver structure. ¾ Decision regions & ML decision criterion. ¾ Error probability & union bound. Amplitude & Phase Modulation ¾ PAM ¾ PSK ¾ QAM ¾ Differential PSK ¾ Constellation shaping
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Pulse Shaping Summary
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Summary of Last Lecture Information theory allows determining the data rates that can be transmitted reliably over a channel given a certain power. Key notion: channel capacity. Below capacity, coding schemes are sure to exit that enable driving the error probability to 0 as the codewords get longer. Information theory does not show how we must encode to approach capacity. Coding engineers have been on that quest ever since Shannon’s seminal work. With Gaussian noise and no fading, C = B log(1+ γ ).
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In fading channels, several notions of capacity exist depending on how the fading coherence time (Doppler) relates to the codeword length. Analysis requires limiting idealizations: ¾ Shannon (ergodic) capacity. Many fading cycles within a codeword, revealing the fading distribution. ¾ Outage capacity. Slow fading, approximately constant over each codeword. With Rx CSI only, we must transmit and constant power and rate. Shannon capacity C = BE [log(1+ γ [ i ] )]. Outage capacity characterized by the distribution of C = B log(1+ γ min ) vs P out = p ( γ < γ min ) . Adding Tx CSI does not improve capacity unless power is adapted. Optimal adaptation in terms of Shannon capacity is waterfilling in time. Suboptimal schemes such as (truncated) channel inversion can greatly reduce encoding/decoding complexity.
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If channel fades in frequency but is fixed in time, we have the dual problem. Optimal power adaptation is waterfilling in frequency.
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Announcement Midterm results: ¾ Min 35 ¾ Max 95 ¾ Mean 57/100 ¾ Std 18
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Digital Modulation & Detection Modern systems are digital: information is transferred in the form of bits (binary digits). If the original source is not digital (e.g. voice) it is first sampled and quantized. To maximize efficiency, data is often compressed to before transmission squeezing out redundancies. Note that coding then re-introduces controlled redundancies. This separation approach was shown by Shannon to be asymptotically optimal in certain cases. Modulation: mapping of bits onto a transmit signal. Detection: estimation of the original bits from received signal.
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Two main classes of modulation: ¾ Linear. Embeds data into amplitude and/or phase of signal. Spectrally efficiency but more susceptible to noise and interference. Requires linear amplifiers, more expensive and power inefficient. ¾ Nonlinear. Embeds data into frequency of signal. Less spectrally efficiency but more robust to noise and interference. Can use nonlinear amplifiers, cheaper and more power efficient.
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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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Lecture5 - E4703 Wireless Communications Slide Set 5...

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