Odd-Bit Quadrature Amplitude-Shift Keying

The selection of a particular signal set design for a bandwidth-constrained multiple amplitude-and-phase-amplitude-and-phase-shift-keyed (MAPSK) communication system with a linear additive Gaussian noise channel is influenced by a number of factors, such as average and/or peak signal-to-noise ratio for a given error probability, dynamic range of signal amplitudes, simplicity of generation and detection, and number of bit errors per adjacent symbol error (Gray code properties). This paper compares two possible quadrature amplitudes-shift-keyed (QASK) signal sets when the number of bits per symbol is odd (for the even-bit case, the square array is the only viable QASK choice). The "symmetric" QASK version outperforms the "rectangular" QASK set at a very modest implmentation penalty.