his paper addresses the interference management in a MIMO interference channel (MIMO-IC) by proposing a decentralized transmit and receive beamformer optimization using improper (or circularly asymmetric complex) Gaussian signaling. For the ease of exposition, the downlink (DL) of a cellular network is considered. In order to generate improper Gaussian signals, widely linear precoding (WLP) is adopted at transmission, while at reception we consider that users might apply either widely linear estimation (WLE) or linear estimation. The coordination between transmitters for WLP design is attained by taking into account the received signal in the uplink (UL), provided that propagation channel reciprocity can be assumed and that transmit filters in the UL are appropriately designed. In this way the estimation of the interfering channels is avoided, while we can take advantage of both DL transmit coordination to adjust transmit power and beamformers and the use of improper Gaussian signaling to exploit the real and imaginary dimensions of the MIMO channel. Simulations show that the proposed decentralized technique allows reducing the mean square error (MSE) and increasing user throughput in highly interfered scenarios