In this paper, the achievable rates of the so called "multiple-input multiple-output interference channel", exploited by a couple of single antenna primary terminals and two antenna cognitive radios under specific interference constraints, are analyzed. In particular, by assuming perfect channel state information at the cognitive terminals, a closed form expression for a linear precoding and linear reception scheme, which guarantees to meet the achievable rates and no mutual interference between primary and cognitive terminals, is obtained. Numerical results regarding the effects of different fading channels and of an imperfect knowledge of the channel are provided to evaluate the performances of the proposed scheme in real environments.