A modified Schnorr-Euchner sphere decoding (SE-SD) algorithm to search for the receive minimum distance is presented. In the proposed algorithm, the visit to negative symmetric vectors of already spanned vectors is avoided by using a biased spanning, and the redundant processes to visit the all-zero vector are also eliminated. A numerical experiment shows that the modified SE-SD algorithm is much more efficient than the conventional algorithm in terms of average computational complexity.

A structured codebook with various codeword configurations is proposed to overcome the sum capacity limitation in a region with finite number of users. Specifically, based on multi-user MIMO platform with a codebook of multiple orthonormal sets, called as per user unitary rate control (PU2RC), we diversify the codeword configuration of each orthonormal set and expand the corresponding codeword configuration. Numerical experiments with respect to several system parameters, such as user density and received signal to noise ratio, show that the proposed codebook offers throughput gains over the conventional system in a small to moderate number of user region.

A new method to approximate the receive minimum distance is presented. In the proposed approximation, the geometric mean of the singular values of the channel matrix is used instead of the conventional minimum singular value. Numerical experiments show that the proposed approximation has less mean squared error than the minimum singular value bound and outperforms the minimum singular value bound in terms of bit error rate when they are applied to the antenna subgroup selection system.

For the closed loop multiple-input-multiple-output (MIMO) systems, Fisher's adaptive bit loading algorithm gives the best error performance by jointly optimizing the transmit powers, rates, and number of streams. However, its good performance comes at the cost of high and variable computational complexity for the joint optimization. In this letter, we propose an efficient multi-mode precoding algorithm using a simplified mode table. Numerical results show that the proposed algorithm provides almost the same performance as Fischer's with much less computational complexity.