Interference Alignment (IA) is a transmission scheme which achieves 1/2Degrees-of-Freedom (DoF) per transmit-antenna per user. The constraints imposedon the scheme are based on the linear receiver since conventional IA assumesGaussian signaling. However, when the transmitters employ Finite Alphabet (FA)signaling, neither the conventional IA precoders nor the linear receiver areoptimal structures. Therefore, a novel Fractional Interference Alignment (FIA)scheme is introduced when FA signals are used, where the alignment constraintsare now based on the non-linear, minimum distance (MD) detector. Since DoF isdefined only as signal-to-noise ratio tends to infinity, we introduce a newmetric called SpAC (number of Symbols transmitted-per-transmitAntenna-per-Channel use) for analyzing the FIA scheme. The maximum SpAC is one,and the FIA achieves any value of SpAC in the range [0,1]. The key motivationfor this work is that numerical simulations with FA signals and MD detector forfixed SpAC (=1/2, as in IA) over a set of optimization problems, likeminimizing bit error rate or maximizing the mutual information, achieves asignificantly better error rate performance when compared to the existingalgorithms that minimize mean square error or maximize signal-to-interferenceplus noise ratio.
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