The Squaring-Loss Paradox

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 ha ve 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 � Funded by the Galileo receivers for mass market project (GREAT), co-funded by the European GNSS Supervisory Authority (GSA) with funding from the 6th Framework Programme of the European Community for research and technological development. and results in the paradox situation that the squaring opera tion can increase the SNR leading one to believe that the detection probability is improved by taking the signal into th e 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 MonteCarlo simulations. Examples of GPS C/A codes are given.