Precoder design for Fractional Interference Alignment

In this work, we consider a K user Interference Channel (IC), where all the transmitters employ Finite Alphabet (FA) signals. With M antennas at both transmitter and receiver nodes, the Interference Alignment (IA) scheme [1] was shown to provide 1/2 SpAC (Symbols transmitted per transmit Antenna per Channel use) per user, whereas, the Fractional Interference Alignment (FIA) scheme [2] provides a value of SpAC in the range [0,1]. When FA signals are used, the IA technique which uses a fixed value of SpAC = 1/2 is sub-optimal, and therefore will not provide the best possible rate and/or bit error rate (BER). Instead, the FIA scheme explicitly computes the maximum SpAC that can be supported for the interference channel model (assuming that accurate knowledge of the channel state information is available for the desired and the interfering signals). Hence, based on two different optimization criteria, namely (a) Coding Gain (CG) maximization, and (b) Goodput (GP) maximization, we use a simple conjugate gradient search approach to compute the sub-optimal SpAC value and the corresponding precoders for the FIA scheme. Numerical results show that for a 3 user IC, even at finite signal-to-interference ratio (SIR), (M1)/_M SpAC (upper bound in FIA scheme) is achieved, as signal-to-noise ratio (SNR) tends to infinity. The BER performance is also compared between CG and GP maximization problems. Finally, the BER performance of these two optimization schemes are compared with the IA scheme, where it is shown that the proposed FIA with CG criterion outperforms the IA scheme, and will provide 0.7 dB SNR gain for the same rate.