The Squaring-Loss Paradox

Cassian Strassle, Daniel Megnet, Heinz Mathis and Clemens Burgi

Abstract:	Much confusion has been created by the fact that negative squaring losses were reported in documents comparing SNR obtained from non-coherent and coherent integration methods. In the quest for a more consistent measure of the squaring loss, which approaches zero as the presquaring SNR increases, statistical detection probabilities have to be employed. This paper compares the traditional definitions of SNR before and after squaring with more statistical means of measuring detection success. The comparison of SNR values for different amplitude distributions is tricky and results in the paradox situation that the squaring operation can increase the SNR leading one to believe that the detection probability is improved by taking the signal into the square operation. Thus, we present a unifying measure to compare the coherent with non-coherent detection without a discrepancy for the high-SNR situation. Theoretical expressions evaluated numerically confirm well with Monte- Carlo simulations. Examples of GPS C/A codes are given.
Published in:	Proceedings of the 20th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2007) September 25 - 28, 2007 Fort Worth Convention Center Fort Worth, TX
Pages:	2715 - 2722
Cite this article:	Strassle, Cassian, Megnet, Daniel, Mathis, Heinz, Burgi, Clemens, "The Squaring-Loss Paradox," Proceedings of the 20th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2007), Fort Worth, TX, September 2007, pp. 2715-2722.
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