What is it about?
When mapping a Gaussian RV Y into a finite alphabet signal X, the cross correlation properties of both signals are of course different. Here, we developed a closed form relationship between the cross-correlation of both signals which is only function of the applied mapping function.
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Why is it important?
1) The beampattern design and waveform design problems are solved jointly 2) Once the transmit covariance matrix R is found, easily generated Gaussian RV are mapped into any modulation scheme to construct the waveforms. 3) No iterative methods are needed 4) The generated signals have finite alphabets and are drawn from known modulation schemes 5) QAM signals generated through our method outperform shifted 4-PAM signals in matching non symmetric beampatterns.
Perspectives
I find this article very interesting in the sens that it develops a general close form relationship between the correlation of Gaussian RV and their mapped finite alphabet signals. It also shows that this relationship depends solely on the applied mapping function. Deriving the relationship wasn't straightforward at the beginning, but now with the benefit of hindsight and better references, I found a shorter way to prove it.
Dr Seifallah Jardak
King Abdullah University of Science and Technology
Read the Original
This page is a summary of: Generation of Correlated Finite Alphabet Waveforms Using Gaussian Random Variables, IEEE Transactions on Signal Processing, September 2014, Institute of Electrical & Electronics Engineers (IEEE),
DOI: 10.1109/tsp.2014.2339800.
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