Exact Evaluation of Bit- and Symbol-Error Rates for Arbitrary Two-Dimensional Modulation and Nonuniform Signaling in AWGN Channel

Exact evaluation of the bit- and symbol-error rates in a 2-D constellation has closed solutions for particular modulations and/or bits-to-symbol mapping. To solve this fundamental problem of digital communications, we propose a general method which yields the exact results for arbitrary modulation symbols´ set, arbitrary bits-to-symbol mapping, and deals with the case of nonuniform signaling. These three conditions define any digital transmission using memoryless modulation, so the proposed method is a general tool solving all problems tackled in the literature, under constraints imposed on one or more of the parameters defining the modulation or signaling type. Such an evaluation tool is of practical importance during the design of the modulation. Our analysis and numerical simulations show the advantages offered by the new method when compared with the bounding techniques.