Background:

1

• Background
• MFSK (M-ary Frequency Shift Keying)
• Signal space has N mutually orthogonal axes
• M signals, N dimensions
• 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)
• Coherent vs. Noncoherent Detection
• Coherent phase reference
• Noncoherent no phase reference
• Different measures of R/W

Multi-Dimensional Signal Analysis
Rebekah Moore Clemson University Advisor Dr.
John Komo SURE 2005

• Summary of Results

M Dims. Shape R/W R/W Eb/N0
4 3 Pyramid 1 8.64 dB
8 3 Multi-pyramid 3/2 9.645 dB
8 3 Cube 3/2 9.588 dB
8 3 Skewed cube 3/2 9.369 dB
8 4 Biorthogonal 6/5 3/2 8.301 dB
8 4 Sphere 6/5 3/2 9.008 dB
8 8 Orthogonal 2/3 3/4 8.418 dB
16 4 4-D Cube 8/5 2 9.588 dB
16 4 4-D Skewed cube 8/5 2 9.195 dB

• Correlation Receiver for Three-Dimensional
  Tetrahedron

Select largest signal

• Bandwidth-Efficiency Plane

• Four-Dimensional Example

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

• References
• Sklar, Bernard. Digital Communications
  Fundamentals and Applications. Prentice Hall,
  PTR, 2nd Edition. 2001.
• Acknowledgements
• Dr. John Komo
• Dr. Daniel Noneaker
• Dr. Xiao-Bang Xu
• NSF

• Conclusions
• 4-dimensional signal sets decrease Eb/N0 for a
  fixed R/W
• Bandwidth efficiency improves with coherent
  detection
• Coherent W (N1)/(2log2M)
• Noncoherent W N/(log2M)
• Use of sin and cos increases R/W

Signal set for a 4-dimensional skewed cube.