Exact Expression and a Simple Tight Upper Bound for the SER of Odd CAP/QAM Constellation

In this paper, we derive the exact closed-form expression for the symbol-error rate (SER) of carrierless amplitude and phase/quadrature amplitude modulation (CAP/QAM) where the number of symbols is an odd power of two. The presented formula is simply in the form of the well known Gaussian Q-function and its second power. In the low signal-to-noise ratio range where the bounding techniques fail, our expression accurately predicts the SER. Furthermore, based on this expression, we introduce a simple upper bound for the SER which is tighter and more accurate than the existing bounds.