Single-carrier Multiple-input Multiple-output Systems Research Articles

LU-Based Beamforming Schemes for MIMO Systems

We present a time-domain broadband beamforming based on a unimodular-upper polynomial matrix decomposition. The unimodular factor is the product of elementary $J$ - orthogonal matrices and a lower-triangular matrix with 1's on the diagonal, as in the constant matrix lower upper (LU) decomposition. This leads to a $J$ - orthogonal LU polynomial matrix decomposition, as a combination of two classical matrix factorization methods: Smith canonical form and LU Gaussian elimination. The inversion of the unimodular factor, for use as a pre/postfilter in the beamforming scheme, is immediate and can be achieved with O(1) complexity. The resulting reduced multiple-input multiple-output (MIMO) channel is exactly diagonal, leading to separate single-input single-output (SISO) channels with no cochannel inteference. There is no need to model the MIMO channel as a Laurent polynomial as usual, thus introducing unnecessary delays just for technical reasons. In addition, it turns out that each of the resulting SISO channels, except to the last channel, reduces to a simple additive noise channel, with no intersymbol interference (ISI), except for unprobable original MIMO channels. However, these very interesting features are to be balanced with the possible noise enhancement in the postfiltering step. The performance in terms of bit error rate (BER) is studied and compared with the QR-based frequency-domain and time-domain broadband beamforming. In particular, the proposed beamforming scheme can be used both in orthogonal frequency-division multiplexing (OFDM) and in single-carrier MIMO systems, without a cyclic prefix (CP). Meanwhile, the QR-based scheme requires a CP extension.

On the optimality of training signals for MMSE channel estimation in MIMO-OFDM systems

In this paper, we investigate the optimality of training signals for linear minimum mean square error (LMMSE) channel estimation in multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) with frequency-selective fading channels. This is a very challenging problem due to its mathematical intractability and has not been analytically solved in the literature. Using the Lagrange multiplier method, we derive the optimality conditions for training signal design. Important findings revealed on optimal training signals are twofold: (i) the energies of the training signals on each subcarrier are equal, and (ii) on each subcarrier, the training signals transmitted from the different antennas are orthogonal and of equal energy. We verify that our results are in line with the design principles that have been derived in single-carrier MIMO systems. Two types of optimal training signal examples that satisfy the optimality conditions are presented for practical implementations in MIMO-OFDM systems. Simulation results show that the training signals based on the optimality conditions outperform other non-optimal training signals in terms of channel estimation performance.

A General Framework for Optimum Iterative Blockwise Equalization of Single Carrier MIMO Systems and Asymptotic Performance Analysis

The paper proposes a general framework for both time-domain (TD) and frequency-domain (FD) iterative blockwise equalization in single carrier (SC) wideband multiple-input multiple-output (MIMO) channels. First, a novel turbo blockwise operating equalizer structure is proposed by jointly optimizing the feed-forward and feedback filters at each iteration based on the minimum mean squared error (MMSE) criterion. Optimization of the filter coefficients, utilized for feed-forward equalization and decision feedback, is performed in both time and frequency domains, and the equivalence between them is established by unifying the iterative block equalization with the feed-forward and feedback filters in various domains. The corresponding filters are obtained analytically in a closed form as a solution of the constrained Wiener-Hopf equation with the use of average reliability information. Second, asymptotic performance and diversity analysis of the proposed single carrier frequency domain equalizer (SC-FDE) is carried out that leads to insights on the structures of the filters in the high SNR regime. Furthermore, we elaborate on the rate and diversity tradeoff of the space-time coded SC-FDE based on the proposed equalizer structure and the space-frequency coded OFDM systems. Performance comparison between the proposed SC-FDE scheme and OFDM is made. The proposed SC-FDE scheme performs very close to the genie-aided performance bounds and better than OFDM based transmission.

Cyclic-delay time-reversal space-time block codes for single-carrier transmission with frequency-domain decision-feedback equalization

Transmit diversity is an important multiple-input multiple-output (MIMO) approach to improve the transmission reliability; however, it is usually designed with maximum-likelihood detection. In this paper, we investigate a simple transceiver structure for single-carrier MIMO systems, in which the cyclic-delay time-reversal space-time block code (CDTR-STBC) is employed at the transmitter, and the frequency-domain decision-feedback equalization (FD-DFE) is used at the receiver. We separate the transmit antennas into two groups, and then, encode the groups by STBC and cyclically delay the data streams within each group. Such processing can mitigate the impact of error-propagation and reduce the signal-to-noise ratio (SNR) loss when FD-DFE is employed, in which SNR is defined as the ratio of the received signal power over the noise power at each receive antenna. To support our proposal, this paper also provides the performance analysis of FD-DFE. It is shown that the proposed scheme can achieve full diversity and full transmission rate for a MIMO system employing arbitrary antennas. Therefore, it has considerable performance improvement over the existing schemes.

Layered Space-Frequency Equalization in a Single-Carrier MIMO System for Frequency-Selective Channels

Frequency-domain equalization (FDE) has been shown to be an effective approach to combat frequency-selective wireless channels. In this letter, we propose a layered space-frequency equalization (LSFE) architecture for a single-carrier (SC) multiple-input multiple-output (MIMO) system, where MIMO FDE is employed at each stage or (layer) of detection. At a particular stage, a group of the best data streams in the minimum mean square error sense are detected and are canceled from the received signals. Simulation results show that our proposed LSFE structures can outperform layered space-time equalization (LSTE) structures and uncoded orthogonal frequency division multiplex (OFDM), especially at a higher delay spread. Performance is enhanced further, by incorporating the FDE with time-domain decision feedback at each stage of LSFE. We also provide performance analysis for LSFE, in comparison with OFDM.