An Efficient QR-based Selection Criterion for Selecting an Optimal Precoding Matrix Employed in a Simplistic MIMO Detection

In multiple-input multiple-output (MIMO) channel (H) communication, when channel status information (CSI) is known to the receiver but not to the transmitter, the precoding technique can achieve a highly reliable communication link, when the receiver informs an optimal precoding matrix index to the transmitter based on current CSI. To select an optimal precoding matrix (F), the maximum capacity selection criterion and the maximum minimum singular value selection criterion are developed. However, with QRdecomposition detection (HF = QR) in the precoding system, these two selection criteria may involve high complexity and poor detection performance due to the full matrix multiplication and inaccurate detection of the first layer, respectively. In this paper, to simplify the QR-decomposition processes, the real and imaginary parts of channel elements are rearranged to achieve a column-wise orthogonal structure to reduce the repeated computation. In precoding systems, to achieve 1) low-complexity and 2) performance enhancement, the efficient QR-based selection (QR-selection) criterion is proposed to select an optimal precoding matrix by maximizing the absolute value of the lowest layer of the upper triangular matrix R. For low-complexity, to reduce the multiplication complexity of computing R, we prove that the absolute value of R is equal to the absolute value of R ( R Q F R = & & ), where . Based on this equivalence, we can reduce the multiplication complexity because the number of multiplications for computing RF is less than the number of multiplications for computing HF. For performance enhancement, the proposed QR-selection criterion can effectively mitigate the impact of error-propagation because the probability of an early error in the sequence of decisions is lower. Simulation results show that the proposed scheme with a low-complexity level has a better performance than others, and that it can improve detection performance as the codebook size increases. R Q H & & = Key-Words: Multiple-input multiple-output, precoding, QR-decomposition, capacity selection, minimum singular value selection, QR selection, column-wise orthogonal structure, codebook.