On Precoding for Constant K-User MIMO Gaussian Interference Channel With Finite Constellation Inputs

This paper considers linear precoding for the constant channel-coefficient K-user MIMO Gaussian interference channel (MIMO GIC) where each transmitter-i (Tx-i) requires the sending of d(i) independent complex symbols per channel use that take values from fixed finite constellations with uniform distribution to receiver-i (Rx-i) for i = 1, 2, ..., K. We define the maximum rate achieved by Tx-i using any linear precoder as the signal-to-noise ratio (SNR) tends to infinity when the interference channel coefficients are zero to be the constellation constrained saturation capacity (CCSC) for Tx-i. We derive a high-SNR approximation for the rate achieved by Tx-i when interference is treated as noise and this rate is given by the mutual information between Tx-i and Rx-i, denoted as I(X) under bar (i); (Y) under bar (i)]. A set of necessary and sufficient conditions on the precoders under which I(X) under bar (i); (Y) under bar (i)] tends to CCSC for Tx-i is derived. Interestingly, the precoders designed for interference alignment (IA) satisfy these necessary and sufficient conditions. Furthermore, we propose gradient-ascentbased algorithms to optimize the sum rate achieved by precoding with finite constellation inputs and treating interference as noise. A simulation study using the proposed algorithms for a three-user MIMO GIC with two antennas at each node with d(i) = 1 for all i and with BPSK and QPSK inputs shows more than 0.1-b/s/Hz gain in the ergodic sum rate over that yielded by precoders obtained from some known IA algorithms at moderate SNRs.

Net-like Ferromagnetic Mnsb Film Deposited on Porous Silicon Substrates

MnSb films were deposited on porous silicon substrates by physical vapor deposition (PVD) technique. Modulation effects due to the substrate on microstructure and magnetic properties of the MnSb film's were studied by scanning electron microscope (SEM), X-ray diffraction (XRD) and measurements of hysteresis loops. SEM images of the MnSb films indicate that net-like structures were obtained because of the special morphology of the substrates. The net-like MnSb films exhibit some novel magnetic properties different from the unpatterned referenced samples. For example, in the case of net-like morphology, the coercive field is as low as 60 Oe.