Multiple-input Multiple-output Intersymbol Interference Channels Research Articles

Iterative Equalizer Based on Kalman Filtering and Smoothing for MIMO-ISI Channels

This paper proposes an iterative equalizer based on Kalman filtering and smoothing (IEKFS) for multiple-input multiple-output inter-symbol interference (MIMO-ISI) channels. A state-space model with a priori information and the corresponding Kalman filtering (KF) and Kalman smoothing (KS) operations are developed. The KF operations perform a linear minimum mean-square error (MMSE) equalization procedure with soft interference cancellation. In addition, the KF and KS operations produce and exchange the updated extrinsic information. During this IEKFS process, the soft estimate of a desired symbol does not participate in the equalization procedures for the desired symbol; only the feedback information of the other transmit symbols is used. Therefore, the proposed IEKFS performs iterative linear MMSE equalization based on the Kalman framework and turbo principle. The complexity of the IEKFS is linear with respect to the number of transmit signal vectors in a transmission block, and simulation results show that the IEKFS can achieve near-optimum bit error rate performances approaching the matched filter bound (MFB) of the channel in various environments.

Low-Complexity Detection in Large-Dimension MIMO-ISI Channels Using Graphical Models

In this paper, we deal with low-complexity near-optimal detection/equalization in large-dimension multiple-input multiple-output inter-symbol interference (MIMO-ISI) channels using message passing on graphical models. A key contribution in the paper is the demonstration that near-optimal performance in MIMO-ISI channels with large dimensions can be achieved at low complexities through simple yet effective simplifications/approximations, although the graphical models that represent MIMO-ISI channels are fully/densely connected (loopy graphs). These include 1) use of Markov random field (MRF)-based graphical model with pairwise interaction, in conjunction with message damping, and 2) use of factor graph (FG)-based graphical model with Gaussian approximation of interference (GAI). The per-symbol complexities are O(K <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ) and O(Kn <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</sub> ) for the MRF and the FG with GAI approaches, respectively, where K and n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</sub> denote the number of channel uses per frame, and number of transmit antennas, respectively. These low-complexities are quite attractive for large dimensions, i.e., for large Kn <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</sub> . From a performance perspective, these algorithms are even more interesting in large-dimensions since they achieve increasingly closer to optimum detection performance for increasing Kn <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</sub> . Also, we show that these message passing algorithms can be used in an iterative manner with local neighborhood search algorithms to improve the reliability/performance of M-QAM symbol detection.

Precoder Design for Multiuser MIMO ISI Channels Based on Iterative LMMSE Detection

Precoding has been widely investigated for multiple-input multiple-output (MIMO) and inter-symbol interference (ISI) channels. Most related work so far has been on uncoded systems and the impact of forward-error-correction (FEC) codes has not been well studied. In this paper, we present an optimized precoding technique that takes into account iterative joint LMMSE detection and FEC decoding. The proposed scheme has some interesting features. First, the design problem is convex. Second, the proposed scheme achieves water-filling gain when channel state information at the transmitter (CSIT) is available and diversity gain when CSIT is not available, as well as multi-user gain in multi-user environments. Third, the water-filling gain is achieved using a single code (instead of multiple codes as in conventional approaches), which greatly simplifies the design and implementation problems. Both simulation and evolution analyses are provided to show that significant performance improvement can be achieved with the proposed scheme.

Decision-Feedback Detection for MIMO-ISI Channels: Design Using Fixed and Adaptive Constraints

In this correspondence, we investigate the decision-feedback detection for multiple-input multiple-output intersymbol-interference (MIMO-ISI) channels. First, a novel constrained symbol-by-symbol decision-feedback detector (DFD) is proposed, in which a constraint on the feedback filter provides robustness against error propagation and outperforms the conventional DFD. However, we find that an error floor is observed at high signal-to-noise ratios (SNRs) if a fixed constraint is used. To resolve this problem, we then propose an iterative symbol-by-symbol DFD in which an adaptive constraint is implicitly used to update the DFD's coefficients. Simulation results show that the error-floor problem is overcome and that the performance becomes satisfactory at high SNRs through iterations.

Low-Complexity Optimal Estimation of MIMO ISI Channels With Binary Training Sequences

In this letter, a novel low-complexity optimal channel estimator using uncorrelated periodic complementary sets of binary sequences is proposed for multiple-input multiple-output (MIMO) intersymbol interference (ISI) channels. The estimator is optimal since it attains the minimum possible Crameacuter-Rao lower bound (CRLB). Moreover, it can be implemented with very low complexity via ASIC/FPGA, which makes it suitable and ready for practical MIMO systems

Iterative joint optimization of minimal transmit redundancy FIR zero-forcing precoder-equalizer system for MIMO-ISI channel

An iterative joint finite-impulse response (FIR) zero-forcing (ZF) precoder-equalizer optimization algorithm for multiple-input multiple-output intersymbol interference (MIMO-ISI) channel is proposed. The existing joint precoder-equalizer design algorithms for MIMO-ISI channels require a guard period, which is longer than or equal to the channel order to avoid the interblock interference (IBI). This longer guard period is a kind of unnecessary redundancy consuming the valuable channel bandwidth. Based on space-time-modulated codes (STMC), this paper proposes the first algorithm for jointly optimizing the FIR precoder and equalizer without the guard-period constraint. Hence, the precoder-equalizer pairs obtained can achieve minimal transmit redundancy ISI-free communications for complex-valued signals. This greatly enhances the spectral efficiency for wide-band communications. The proposed algorithm is performed in an iterative basis. Sufficient conditions and convergence analysis of this algorithm are presented. The resultant precoder and equalizer are proved to be a least-square (LS) optimal solution for each other. The simulation results show that substantial performance gain is obtained with the proposed joint optimization algorithm.

Achievable Information Rates and Coding for MIMO Systems Over ISI Channels and Frequency-Selective Fading Channels

We propose a simulation-based method to compute the achievable information rates for general multiple-input multiple-output (MIMO) intersymbol interference (ISI) channels with inputs chosen from a finite alphabet. This method is applicable to both deterministic and stochastic channels. As an example of the stochastic MIMO ISI channels, we consider the multiantenna systems over frequency-selective fading channels, and quantify the improvement in the achievable information rates provided by the additional frequency diversity (for both ergodic and nonergodic cases). In addition, we consider the multiaccess multiantenna system and present some results on the achievable information-rate region. As for the deterministic MIMO ISI channels, we use the binary-input multitrack magnetic recording system as an example, which employs multiple write and read heads for data storage. Our results show that the multitrack recording channels have significant advantages over the single-track channels, in terms of the achievable information rates when the intertrack interference is considered. We further consider practical coding schemes over both stochastic and deterministic MIMO ISI channels, and compare their performance with the information-theoretical limits. Specifically, we demonstrate that the performance of the turbo coding/decoding scheme is only about 1.0 dB away from the information-theoretical limits at a bit-error rate of 10/sup -5/ for large interleaver lengths.

Signal Detection for MIMO-ISI Channels: An Iterative Greedy Improvement Approach

In this paper, we consider the signal detection for multiple input-multiple output intersymbol interference (MIMO-ISI) channels with diverse assumptions on the channel knowledge: perfect, blind, trained, etc. This general problem is cast into a unifying Bayesian statistics framework. With this formulation, the optimal detector is the one maximizing the posterior signal density [marginal maximum a posteriori (MAP)]. Since the marginal MAP is hard to deal with, a joint MAP formulation is proposed as a reasonable substitute that maximizes the posterior joint signal and channel density. It is also shown that for independent and identically distributed (i.i.d.) signals, the two formulations will lead to very close results. The joint MAP formulation leads to an iterative projection algorithm that alternates between the optimization over channel parameters and signaling matrices. The bottleneck of iterative projections is on the finite-alphabet constrained quadratic minimization. We show that the notion of error decomposition can be bridged with greedy optimizations to construct iterative greedy search algorithms and examine their performance. A particularization, called full greedy search, is shown to be able to reach the global optimum (maximum likelihood solutions) starting with any initialization. Since potential constraints in computational complexity may prohibit the application of this version of greedy search, we explore the performance (loss) for greedy search implementations with complexity constraints, arriving at deterministic performance bounds and a bit-error rate (BER) upper bound. The effect of model imprecision is also theoretically characterized. Based on the theoretical development, an iterative local optimization with interference cancellation (LOIC) algorithm is proposed to achieve low complexity and exploit the finite alphabet constraint. Motivated by the Sylvester structure, it approximates the full greedy search by focusing on local error sequences. It can also be regarded as a flexible interference cancellation strategy with noncausal information and iterative computations. An empirical comparison of detectors with perfect channel knowledge demonstrated that the proposed LOIC algorithms can offer very attractive BER/complexity tradeoffs.