We present a novel approach for low-complexity equalizer design well-suited for cellular massive MIMO systems. Our design allows to exploit the channel structure in terms of covariance matrices to improve the performance in the face of pilot-contamination, while basically keeping the complexity of a matched filter. This is achieved by restricting the equalizer to functions which are bilinear in the received data signals and the observations from a training phase. The proposed design generalizes several previous approaches to equalizer design for massive MIMO. We show by asymptotic analysis that with the proposed design the achievable rate grows without bound for growing numbers of antennas even in the presence of pilot-contamination. We demonstrate with numerical results that the proposed design is competitive with more complex approaches in a practical cellular setup.