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Multi-Dimensional Signal Analysis

Multi-Dimensional Signal Analysis. Rebekah Moore Advisor: Dr. John Komo SURE 2005. Outline. Background Results 2-Dimensions 3-Dimensions 4-Dimensions Summary of Results Conclusions. Background. MFSK (M-ary Frequency Shift Keying) Signal space has N mutually orthogonal axes

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Multi-Dimensional Signal Analysis

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  1. Multi-Dimensional Signal Analysis Rebekah Moore Advisor: Dr. John Komo SURE 2005

  2. Outline • Background • Results • 2-Dimensions • 3-Dimensions • 4-Dimensions • Summary of Results • Conclusions

  3. Background • MFSK (M-ary Frequency Shift Keying) • Signal space has N mutually orthogonal axes • M signals, N dimensions

  4. Background, cont’d • AWGN • Eb/N0 – ratio of bit energy to noise power spectral density • Normalized SNR • Eb = S • Tb • N0 = N / W • R/W - data rate / bandwidth (bandwidth efficiency)

  5. Background, cont’d • Coherent vs. Noncoherent Detection • Coherent – phase reference • Noncoherent – no phase reference • Different measures of R/W

  6. Power is scarce, bandwidth is available • Savings in Eb/No desired • Decreased R/W (increased bandwidth) • Bandwidth is scarce, power is available • Large R/W desired • Increased Eb/N0 Power-Bandwidth Trade-Off Power-limitedBandwidth-limited

  7. R = C boundary Bandwidth-limited region Power-limited region Bandwidth-efficiency plane

  8. Two-dimensional example d Bit Errors: S1: 2 S3: 2 S2: 2 S4: 2

  9. Two-dimensional example

  10. 3-Dimensional Example

  11. Correlation Receiver Select largest signal

  12. 4-Dimensional Example Signal set for a 4-dimensional cube (hypercube).

  13. 4-Dimensional Example Signal set for a 4-dimensional skewed cube.

  14. 4-Dimensional Example

  15. Summary of Results

  16. 4-D Skewed Cube MPSK, M=4 MPSK, M=2 4-ary Biorthogonal 3-D Pyramid Bandwidth-Efficiency Plane

  17. Conclusions • 4-dimensional signal sets decrease Eb/N0 for a fixed R/W • Bandwidth efficiency improves with coherent detection • Coherent – W = (N+1)/(2log2M) • Noncoherent – W = N/(log2M) • Use of sin and cos increases R/W

  18. Acknowledgements • Dr. Komo • Dr. Noneaker and Dr. Xu • Javier Schlömann

  19. Questions?

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