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Combined QPSK and MFSK Communication over an AWGN Channel

Combined QPSK and MFSK Communication over an AWGN Channel. Jennifer Christensen South Dakota School of Mines & Technology Advisor: Dr. Komo. Outline. Background Material and Terminology Bandwidth Efficiency Plane Reed Solomon Coding Results. Background.

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Combined QPSK and MFSK Communication over an AWGN Channel

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  1. Combined QPSK and MFSK Communication over an AWGN Channel Jennifer Christensen South Dakota School of Mines & Technology Advisor: Dr. Komo

  2. Outline • Background Material and Terminology • Bandwidth Efficiency Plane • Reed Solomon Coding • Results

  3. Background • Multiple Frequency Shift Keying (MFSK) • Multiple Phase Shift Keying (MPSK) • Combination of BFSK, QPSK: • 4 phases, 2 frequencies-16 signals

  4. Background (cont’d) • AWGN Channel –Gaussian distribution, μ=0, σ2 = No/2 • Eb/No-bit energy divided by spectral noise density • Probability of Bit Error for QPSK Q si2=Es I

  5. Decision Stage: z(T)=ai(T)+n0 . . . . . . r(t)=si(t)+n(t) si(t) M=4N Simulation Transmitted signal plus noise Correlator Receiver Output - Gaussian random variable Determine closest match

  6. At Pb=10-5 Eb/No = 9.52 dB for M=4, 16, 64 Error Probability Plane

  7. Bandwidth Efficiency • R/W=Data rate/Bandwidth • For coherently detected QPSK: • Minimum tone spacing = 1/(2Ts) • M=4N - Minimum tone spacing = 1/Ts

  8. Bandwidth-Efficiency Plane M=4N, Pb=10-5

  9. Reed-Solomon Coding • Error correction code adds redundancies to data • (n,k) notation • n = total number of code symbols • k = number of data symbols encoded • Corrects up to (n-k)/2 errors

  10. Probability of Bit Error Expand bit error calculations for M-ary signaling: where and • Rc is the code rate (k/n) • Coded Bandwidth: Wc=W/Rc

  11. Probability Curves

  12. n=256 Reed Solomon Codes Plot each point on Bandwidth Efficiency Plane

  13. Bandwidth-Efficiency Plane n=256, Pb=10-5 k=240 M=16, N=2 (no coding) k=224 k=192 k=160

  14. Qualitative Results • M=16 for N=2 with Reed Solomon Coding • (256, 192) Code: • R/W=2*(3/4 ) ≈1.5 bps/Hz • Coding gain = 9.52-5.71 = 3.81 dB • (256, 224) Code: • R/W=2*(7/8) ≈1.75 bps/Hz • Coding gain = 9.52-6.16 = 3.36 dB

  15. Bandwidth-Efficiency Plane (256, 224) M=16, N=2 (uncoded) (256, 192)

  16. Conclusions • MFSK and QPSK combination has same bandwidth efficiency as QPSK • Bandwidth efficiency decreases with Reed- Solomon coding • Bit error probability also decreases • Future work: • Soft-decision decoding • Evaluating across different channels

  17. Acknowledgements • Dr. Komo • Dr. Noneaker and Dr. Xu

  18. References • Sklar, Bernard. “Digital Communications: Fundamentals and Applications.” Prentice Hall, PTR, 2nd Edition. 2001. • Wicker, Stephen. “Error Control Systems for Digital Communication and Storage.” Prentice-Hall, 1995.

  19. Questions?

  20. Errors and Erasures • Add erasures for better performance

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