Shedding New Light on Merit Factor

Abstract

The merit factor (MF) introduced by Golay has long been accepted as the standard criterion to evaluate the binary sequence's anti-multipath property in sonar, radar, and communication systems for its simplicity and seemly infallibility. First we present two binary sequence pairs (of lengths 32 and 64) of identical MFs with great discrepancies between the respective binary sequence pairs' uncoded symbol-error rate (SER) performance and theoretical analysis (based on the MF) to shed new light on the hitherto unnoticed determining factor of the sequence's anti-multipath property. We then propose the weighted merit factor (WMF) based on a non-uniform weighting of the out-of-phase aperiodic autocorrelation function (ACF) which leads to better matches between the cited sequence pairs' analytical and experimental results. Ensuing theoretical analysis demonstrates that the WMF provides optimal measurement of self-generated interference for the constant amplitude complex-valued sequences and the nonconstant modulus ones. The MF is shown to be a biased metric for the binary sequences when the multipath delay spread exceeds one chip period. We conjecture that this conclusion continues to hold true for the constant amplitude complex-valued sequences.