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SYSC 4607 – Slide Set 11 Outline

SYSC 4607 – Slide Set 11 Outline. Review of Previous Lecture Error Probability and the Union Bound Bandpass Modulation Signal Constellation and Decision Regions of MPAM, MPSK, MQAM Pulse Shaping. Review of Previous Lecture. Vector space representation of signals

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SYSC 4607 – Slide Set 11 Outline

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  1. SYSC 4607 – Slide Set 11 Outline • Review of Previous Lecture • Error Probability and the Union Bound • Bandpass Modulation • Signal Constellation and Decision Regions of MPAM, MPSK, MQAM • Pulse Shaping

  2. Review of Previous Lecture • Vector space representation of signals • Receiver Structure and Sufficient Statistics • Optimal Detection

  3. Decision Regions Optimum coherent Detector (Correlation Receiver)

  4. Optimum Coherent DetectionMatched Filter Receiver

  5. Error Probability and the Union Bound • Union Bound • Nearest Neighbor Approximation • Gray mapping:

  6. Bandpass Modulation In-phase component Quadrature component Equivalent lowpass representation:

  7. Bandpass Modulation Tradeoffs • Desirable: high rates, high spectral efficiency, high power efficiency, robust to channel, low cost • Amplitude and Phase Modulation (MPAM,MPSK,MQAM) - Information in amplitude (MPAM), phase (MPSK) or both (MQAM) - More spectrally efficient than FSK - Issues: differential encoding, pulse shaping, … • 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

  8. Amplitude and Phase Modulations • Bits encoded in carrier amplitude or phase • Pulse shape g(t) typically Nyquist • Signal constellation defined by (an,bn) pairs • Can be differentially encoded • M values for (an,bn) → log2M bits per symbol • Ps depends on - Minimum distance dmin (depends on γs) - No. of nearest neighbors αM - Approximate Expression

  9. Signal Constellation and Decision Regions - MPAM Bit Mapping by Gray Encoding Decision Regions

  10. Coherent Demodulation - MPAM

  11. Signal Constellation and Decision Regions - MPSK Bit Mapping by Gray Encoding Decision Regions

  12. Signal Constellations and Decision Regions - MQAM Signal Constellation Decision Regions

  13. Pulse Shaping • Linear passband modulation with N=2: • Pulse shaping improves poor spectral characteristics of rectangular pulses

  14. Pulse Shaping • Pulse shaping function g(t) should improve spectral efficiency without compromising Zero-ISI requirement. Transmitted pulses pass through transmitter and receiver filters, and the channel. Received pulses p(t) should satisfy the Zero-ISI condition (Nyquist Criterion): Time-Domain Condition Frequency-Domain Condition • Example: Raised Cosine Pulses

  15. Main Points • Major Linear Modulation Schemes are MPAM, MPSK, MQAM • Linear modulations more spectrally efficient but less robust than nonlinear modulations • Decision regions are based on Maximum Likelihood Detection - Optimum coherent detection structure is based on Correlation Receivers and Matched Filter Receivers - Pe depends on constellation minimum distance and the number of nearest neighbors - Pe in AWGN approximated by: - Pulse-shaping improves spectral characteristics

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