Linear Precoders for Parallel Gaussian Channels with Low Decoding Complexity

Consider the transmission of complex-valued symbols over N parallel channels in additive white Gaussian noise. It is well known that linear precoding of the complex-valued data improves system performance (e.g. symbol error rate, information rate, MMSE, etc.) at a cost of increased decoding complexity at the receiver. This work constructs precoders that are constrained to have a decoding complexity which equals that of no precoding, while still improving the system performance significantly compared with the no precoding case. This is achieved by designing the precoder so that it precodes the complex data streams separately, by utilizing the latest result from optimal real-valued precoding, and transmitting the real and complex parts of one symbol over different antennas.