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New solutions to the signal design problem for coherent channels | IEEE Journals & Magazine | IEEE Xplore

New solutions to the signal design problem for coherent channels


Abstract:

A fundamental problem of statistical communication theory is that of selecting the optimal set ofMequipowered finite duration waveforms to minimize the error rate for a c...Show More

Abstract:

A fundamental problem of statistical communication theory is that of selecting the optimal set ofMequipowered finite duration waveforms to minimize the error rate for a coherent channel perturbed by white Gaussian noise, the signals being restricted toDdegrees of freedom, whereD < M. It is demonstrated that the concept of placing lower-dimensional regular simplicities mutually orthogonal to one another (the technique of known solutions) can be extended. In fact, such signal structures are solutions to the signal design problem for the cases where the dimensionality is restricted to be at mostM-K, whereKis any fixed integer between2andM/2. Of the several solutions for eachK, the most preferred of these is determined at large signal-to-noise ratio, and in certain cases numerical computation has shown this preference to agree with that at small signal-to-noise ratio. Finally, the effect on probability of error due to successive reductions in the allowed dimensionality of the signal set is analyzed for the optimal solutions known to date.
Published in: IEEE Transactions on Information Theory ( Volume: 12, Issue: 2, April 1966)
Page(s): 161 - 167
Date of Publication: 06 January 2003

ISSN Information:


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