Recursive Construction of Minimum Euclidean Distance-Based Precoder for Arbitrary-Dimensional MIMO Systems

The objective of maximizing the minimum Euclidean distance between two received data vectors via real-valued linear precoding is considered for multiple-input multiple-output (MIMO) systems with arbitrary dimensions. Assuming that perfect channel state information (CSI) is available at both the transmitter side and the receiver side, a novel low-complexity precoding algorithm is proposed to recursively construct the full-rank, the rank-deficient and the rank-one precoders with respect to particular channel realization. From the lattice theoretical perspective, the full-rank precoder is generated by using well-known dense packing lattices, which can also be recursively involved into the construction of higher-dimensional rank-deficient precoders. Moreover, the optimal solution is clearly figured out for the specific case of rank-one precoder. The closed-form expression of the achievable minimum distance is obtained and the analytical results reveal the performance bounds for different rank-constraint precoders. Simulation results validate the efficiency of the proposed precoder as compared with the state of the art.