ON GENERALIZED 2-DIMENSIONAL CROSS CONSTELLATIONS AND THE OPPORTUNISTIC SECONDARY CHANNEL

An optimum bits-to-symbol mapping for square constellations is introduced which allows a simple detection in narrow-sense quadrature amplitude modulation (QAM) systems. Then, a family of two-dimensional generalized cross constellations is presented as well as upper and lower bounds on the symbol error probability over an ideal band-limited channel which generalize those previously known for conventional QAM. The application of this scheme to the opportunistic secondary channel is analysed and it is shown how fractional rates (in bits per 2-dimensional signal) can be supported on 2D generalized QAM systems. These signaling schemes are compared with multidimensional generalized constellations recently proposed by Forney and Wei.