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Understanding QPSK Modulation and BER Performance over AWGN Channels

This document explores QPSK (Quadrature Phase Shift Keying) modulation over Additive White Gaussian Noise (AWGN) channels, focusing on key parameters like energy per symbol (ES) and symbol error rates. It describes how noise affects the cosine and sine axes, and the implications for Bit Error Rate (BER) performance using concepts such as Gray coding and Union Bound analysis. The most likely symbol reception, signal distances between constellation points, and comparisons with other modulation methods like 8-PSK and 16-QAM are also discussed for a comprehensive understanding of modulation performance.

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Understanding QPSK Modulation and BER Performance over AWGN Channels

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  1. I. Previously on IET

  2. QPSK Modulation over AWGN Channels ES  Energy per Symbol Symbol Error given transmitted : Noise on Cosine axis < or Noise on Sine axis <

  3. BER of QPSK over AWGN Channels Notes: • Define N0 Total Noise Power • N0/2  Noise Power over Cosine axis, i.e., σ2=N0/2 • N0/2  Noise Power over Sine axis, i.e., σ2=N0/2 • Each symbol MOST LIKELY corresponds to a single bit (Gray Coding) • Eb = ES/2 • Pb ≈ Pe/2 01 11 10 00 Gray Coding: Neighbor constellations points vary in only one bit

  4. Union Bound for QPSK BER Performance Given transmitted : ES  Energy per Symbol 2 1 4 3

  5. Union Bound for QPSK BER Performance Given transmitted : ES  Energy per Symbol 2 1 d12 : Euclidian distance between constellation points 1 & 2 P12 : Probability received signal closer to constellation point 2 than constellation point 1 given constellation point 1 transmitted

  6. Union Bound for QPSK BER Performance Given transmitted : ES  Energy per Symbol 1 3 d13 : Euclidian distance between constellation points 1 & 3 P13 : Probability received signal closer to constellation point 3 than constellation point 1 given constellation point 1 transmitted

  7. Union Bound for QPSK BER Performance Given transmitted : ES  Energy per Symbol 1 4 d14 : Euclidian distance between constellation points 1 & 4 P14 : Probability received signal closer to constellation point 4 than constellation point 1 given constellation point 1 transmitted

  8. Union Bound for QPSK BER Performance Given transmitted : ES  Energy per Symbol 2 1 4 3

  9. Union Bound for BER Performance

  10. Union Bound for 8 PSK Modulation BER ES  Energy per Symbol M=8 001 011 000 dmin Θ 001 010 110 101 111

  11. Union Bound for 16 QAM Modulation BER ES  Energy per Symbol M=16 0010 0011 0001 0000 dmin 0110 0111 0101 0100 1110 1111 1101 1100 1010 1011 1001 1000

  12. Exact vs Union Bound BER Performance 12

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