When Zero-Forcing (ZF) is adopted as a detector, decreasing the condition number of the channel matrix increases the BER performance. In this paper, we propose a new detection algorithm which reduces the condition number of channel matrix down to nearly 2 on average. Since the least singular value of the channel matrix is a major factor determining the condition number, we, first, project the received signal into a space spanned by singular vectors that are orthogonal to the one corresponding to the least singular value. Then, LR decomposition is performed to reduce further the condition number of the projected channel matrix. Computer simulations show that the performance of the proposed algorithm is comparable to that of the ML detector for both correlated and uncorrelated channels. And also the proposed algorithm provides an at least 2dB improvement compared to the conventional LR-based Ordered Successive Interference Cancellation (LR-OSIC) detector with a Bit Error Rate (BER) of 10-3 and a comparable computation load.

In a multi-user multiple-input multiple-output (MU-MIMO) system that adopts zero-forcing (ZF) as a precoder, the best selection is the combination of users who provide the smallest trace of the inverse of the channel auto-correlation matrix. Noting that the trace of the matrix is closely related to the determinant, we search for users that yield the largest determinant of their channel auto-correlation matrix. The proposed technique utilizes the determinant row-exchange criterion (DREC) for computing the determinant-changing ratio, which is generated whenever a user is replaced by one of a group of pre-selected users. Based on the ratio computed by the DREC, the combination of users providing the largest changing ratio is selected. In order to identify the optimal combination, the DREC procedure is repeated until user replacement provides no increase in the determinant. Through computer simulations of four transmit antennas, we show that the bit error rate (BER) per signal-to-noise ratio (SNR) as well as the sum-rate performance provided by the proposed method is comparable to that of the full search method. Furthermore, using the proposed method, a partial replacement of users can be performed easily with a new user who provides the largest determinant.

In this paper, we present an algorithm for reducing the transmit normalization factor by perturbing the transmit signal in a Multi-User Multiple Input Multiple Output (MU-MIMO) system which uses the channel inverse matrix as its precoding matrix. A base station must normalize unnormalized transmit signals due to the limitation of the constant transmit power. This paper defines the norm of the unnormalized transmit signal as the transmit normalization factor used to normalize the transmit signal. Recalling that the transmit normalization factor consists of a combination of the singular values from the channel inverse matrix, we provide a codebook that successively reduces the coefficients of these singular values. Through computer simulations, the proposed algorithm is compared to sphere encoding in terms of the Bit Error Rate (BER) and the outage probability in a MU-MIMO signal environment. Sphere encoding is known to be an optimal solution amongst the perturbation methods that reduce the transmit normalization factor [1]. This work demonstrates that the proposed algorithm is has very good performance, comparable to that of sphere encoding, while its computational load is nearly 200 times less. Since the codebook in our algorithm depends only on the given channel, the difference in the computational complexity becomes even greater when the channel state is not changed, because the codebook can be reused. Furthermore, the codebook exhibits the characteristic of robustness to the maximum Doppler shift.