Performance analysis and multidimensional gray coding scheme for a real-number M-ary QAM

The number of signal points of a QAM constellation in LTE is an even power of 2, with the sizes of adjacent constellations differing by a factor of 4, resulting in very coarse granularity in constellation size selection. This paper presents real-number M-ary QAM constellations over multiple dimensions that fill the gap in the existing constellation sizes and result in lower PAPR. In addition, we propose a Gray coding scheme with a simple generating equation for easy implementation, and analyze various error rates for the AWGN channel.