Details

The general relationship between the post-detection signal-to noise ratio as a function of the pre-detection signal-to-noise ratio and the modulation index is given by [1]:

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References

[1] L. E. Couch, Digital and Analog Communications Systems, 7th ed., Upper Saddle River, NJ: Pearson/Prentice Hall, 2007.

[2] S. O. Rice, "Statistical Properties of a Sine Wave plus Random Noise," in Bell System Technical Journal, 27(1), 1948 pp. 109–157. doi:10.1002/j.1538-7305.1948.tb01334.x.

[3] F. L. Stumpers, "Theory of Frequency-Modulation Noise," Proceedings of the IRE, 36(9), 1948 pp. 1081–1092. doi:10.1109/JRPROC.1948.232308.

[4] H. Taub and D. L. Schilling, Principles of Communication Systems, 2nd ed. New York: McGraw-Hill Book Company, 1986.

[5] V. S. Frost. "Introduction to Communication Systems: An Interactive Approach Using the Wolfram Language." University of Kansas Libraries. (Jun 8, 2023) kuscholarworks.ku.edu/bitstream/handle/1808/31779/Introduction-to-Communication-Systems-Deployed-V3.cdf?sequence=5&isAllowed=y.