Preprocessing for Iterative ML-Detection in Frequency-Selective MIMO Channels

We consider realizable linear and decision feedback equalization (DFE) of frequency selective multiple-input multiple-output (MIMO) channels in the presence of cochannel interference (CCI). Equalizers that are optimal in the minimum mean square error (MMSE) sense are derived with and without zero forcing (ZF) constraint. It is shown that all problems can be reduced to H 2 optimal deconvolution, for which a novel algorithm is presented.

Finite impulse response (FIR) precoders are efficient precoding framework for frequency-selective multiple-input multiple-output (MIMO) channels. In this paper, the optimal linear FIR precoder is investigated to maximize the capacity of frequency-selective MIMO channel under average transmit power constraint. We use Kronecker product to regenerate the nonconvex optimization problem and propose a semidefinite programming (SDP) relaxation scheme with Gaussian randomization to provide approximate solutions. Numerical results indicate that the proposed algorithm outperforms the existing algorithms in the high signal to noise ratio (SNR) regime, especially when the FIR precoder has large filter taps.

In a companion paper, we have studied the zero-forcing (ZF) transceiver with decision feedback equalizer (DFE) over slowly time-varying narrowband multiinput multioutput (MIMO) channels. The space-time generalized triangular decomposition (ST-GTD) was used for the design of ZF-DFE transceivers. The space-time geometric mean decomposition (ST-GMD) ZF transceiver minimizes both the arithmetic mean square error (MSE) at the feedback detector and the average uncoded bit error rate (BER) in moderate high signal-to-noise ratio (SNR). This paper addresses the design problem of DFE transceiver without zero-forcing constraint. In the first part, a channel independent temporal precoder is superimposed on the conventional block-wise GMD-based minimum mean square error (MMSE) DFE transceiver to take advantage of the temporal diversity. In the second part, ST-GTD is applied for the design of MMSE DFE transceivers. With accurate channel prediction and space-time powerloading, the proposed ST-GMD MMSE transceiver minimizes the arithmetic MSE at the feedack detector, and maximizes Gaussian mutual information. For practical applications, the ST-GTD MMSE transceiver which does not require channel prediction but shares the same asymptotic BER performance with the ST-GMD MMSE system is also developed. In the convex region, our analysis shows that the proposed MMSE transceivers has better BER performance than the conventional GMD-based MMSE transceiver; the average BERs of the proposed systems are nonincreasing functions of the ST-block size. The superior performance of ST-GMD MMSE transceiver over the ST-GMD ZF transceiver is also verified analytically.

The performance of linear filters degrade drastically when applied to mitigate intersymbol interference caused by channels with frequent nulls in their spectral characteristics like, e.g., time-dispersive radio channels. In such cases, the well-known decision feedback equalizer (DFE) is one possible nonlinear approach to improve the quality of the receiver. However, adapting the DFE filter coefficients to equalize time-varying channels is computationally intense, especially if the dimension of the observation vector is very high. In this paper, we apply the conjugate gradient (CG) algorithm to a conventional minimum mean square error (MMSE) DFE in order to reduce its computational complexity. Moreover, we compare its performance to the one of MMSE DFE versions which are based on the computationally efficient least-mean-square (LMS) or recursive least-squares (RLS) algorithm, respectively. The analysis additionally includes a detailed investigation of computational complexity with respect to the required number of floating point operations (FLOPs). Simulation results when applied to a digital communications system show the ability of the CG based MMSE DFE to outperform either the LMS and the RLS based MMSE DFE although its computational complexity is even smaller in most of the cases.

This letter proposes channel training designs for two-hop multi-relay networks, where a source, a destination and multiple amplify-and-forward (AF) relays are all equipped with multi-antenna, based on mean square error (MSE) and signal-to-noise ratio (SNR) criteria with taking into account spatial fading correlation between multiple-input multiple-output (MIMO) channel elements. The minimum MSE and maximum SNR channel estimators are initially derived and, then, optimal structures on source training signal and relay matrices are determined. An iterative and a closed-form power allocation solutions are proposed for both channel estimators. Simulation results show that the proposed schemes outperform the conventional schemes.

Precoding is a technique which exploits transmission diversity by weighting the information stream, i.e. the transmitter sends the coded information to the receiver to achieve pre-knowledge of the channel. Visible light communication (VLC) channels inherently exhibit frequency-selective and multi-path fading effects that result in intersymbol interference (ISI) and thus reduces the data rate. To this end, optical multiple input multiple output (MIMO) can provide spatial diversity and thus achieve a high data rate. Inspired by these facts, we investigate different precoding and equalization schemes for $2 \times 2$ MIMO for the vehicle to vehicle (V2V-VLC) system. In this work, we consider three detection schemes, Zero Forcing (ZF), Maximum likelihood (ML), and Minimum Mean Squared Error (MMSE). Also, we consider flickering/dimming control and the nature of outdoor VLC channel as a frequency selective channel. Moreover, we investigate a transceiver considering perfect CSI based on different detection algorithms. Simulation results of the investigated transceiver demonstrate improvements in Bit Error Rate (BER) and Mean Squared Error (MSE) for the MMSE scheme.

This paper investigates iterative frequency domain techniques for the reception of spatially multiplexed single carrier signals transmitted over frequency-selective multiple input multiple output (MIMO) channels. The investigated equalizers are based on the soft-cancellation (SC) and minimum mean square error (MMSE) altering technique for turbo-coded single carrier point-to-point MIMO systems. We consider two different transmit antenna separation techniques in the frequency domain: (1) antenna-by-antenna (AA) and (2) joint over antenna techniques (JA). (1) aims to separate signals in different layers by MMSE filtering antenna-by-antenna, whereas (2) aims to detect the composite signal comprised of the signals transmitted from the multiple antennas. In (2) the composite received signal is decomposed by using the spatial maximum a posteriori probability (MAP) algorithm. We evaluate performances in terms of frame error rate (FER) and throughput in point-to-point MIMO frequency-selective fading channels. Impacts of spatial correlation on performance of the two detectors are also investigated in this paper.

This paper proposes a low-complexity signal detection algorithm for spatially correlated multiple-input multiple-output (MIMO) channels. The proposed algorithm sets a minimum mean-square error (MMSE) detection result to a starting point, and searches for signal candidates in multi-dimensions of the noise enhancement from which the MMSE detection suffers. The multi-dimensional search is needed because the number of dominant directions of the noise enhancement is likely to be more than one over the correlated MIMO channels. To reduce computational complexity of the multi-dimensional search, the proposed algorithm limits the number of signal candidates to $O(N_T)$ where $N_T$ is the number of transmit antennas. Specifically, the signal candidates, which are unquantized, are obtained as the solution of a minimization problem under a constraint that a stream of the candidates should be equal to a constellation point. Finally, the detected signal is selected from hard decisions of both the MMSE detection result and unquantized signal candidates on the basis of the log likelihood function. For reducing the complexity of this process, the proposed algorithm decreases the number of calculations of the log likelihood functions for the quantized signal candidates. Computer simulations under a correlated MIMO channel condition demonstrate that the proposed scheme provides an excellent trade-off between BER performance and complexity, and that it is superior to conventional one-dimensional search algorithms in BER performance while requiring less complexity than that of the conventional algorithms.

Different multiple input - multiple output (MIMO) channel models are analyzed with regard to the indoor line-of-sight (LOS) MIMO channel. In the literature this channel is proven to achieve high capacities while being highly correlated. The modeling results from physical as well as analytical models are compared with measured channels, showing that none of the established models is exactly suitable for the considered indoor LOS MIMO channel. However, there is a promising approach that applies an extended Saleh model in conjunction with the physically correct spherical wave propagation. Although in its current state this basic approach cannot be regarded as a complete MIMO channel model, at least it provides an adequate origin for the correct prediction of MIMO capacities in different types of LOS channels. This is due to the fact, that the crucial prerequisites for an appropriate LOS MIMO channel model, which are by name the application of the physically correct spherical wave propagation, the correct modeling of the high correlation in LOS channels and the inclusion of the geometrical antenna setup, are regarded correctly. Contrarily, these prerequisites are included in none of the current models that are widely accepted in MIMO radio communications nowadays. The proof of this statement using measured data is a major objective of this paper.

This paper describes a broadband multiple input, multiple output (MIMO) channel characterization platform and capacity measurement results in indoor office environment. The MIMO testbed has been designed for broadband MIMO channel sounding, capacity measurements and for characterizing the directional-multipaths of the radio propagation channel. The MIMO channel data have been collected in 5 GHz band inside a modern office environment. Capacity results from these experiments are discussed for different propagation conditions, including non line-of-sight (NLOS) and LOS propagations with various spacings between array elements. Spatial correlations are analyzed from the measured data and a frequency selective MIMO channel model based on the correlation statistics is validated. Post-processing of the measured data with a sequential ESPRIT (Estimation of Signal Parameters via Rotational Invariance Techniques) algorithm is utilized to extract the directions of departures and arrivals of multipath components at the transmitting and receiving arrays, respectively. A method of obtaining broadband MIMO capacity, indirectly, from a single directional measurement of MIMO propagation channel is also proposed and verified from the measurement results.

In recent times, there has been growing interests in integration of voice, data and video traffic in wireless communication networks. With these growing interests, WCDMA has immerged as an attractive access technique. The performance of WCDMA system is deteriorated in presence of multipath fading environment. The paper presents space-time coded minimum mean square error (MMSE) Decision Feedback Equalizer (DFE) for wideband code division multiple access (WCDMA) in a frequency selective channel. The filter coefficients in MMSE DFE are optimized to suppress noise, intersymbol interference (ISI), and multiple access interference (MAI) with reasonable system complexity. For the above structure, we have presented the estimation of BER for a MMSE DFE using computer simulation experiments. The simulation includes the effects of additive white Gaussian noise, multipath fading and multiple access interference (MAI). Furthermore, the performance is compared with standard linear equalizer (LE) and RAKE receiver. Numerical and simulation results show that the MMSE DFE exhibits significant performance improvement over the standard linear equalizer (LE) and RAKE receiver.

<p> Precoding is a technique which exploits transmission diversity by weighting the information stream, i.e. the transmitter sends the coded information to the receiver to achieve pre-knowledge of the channel. Visible light communication (VLC) channels inherently exhibit frequencyselective and multi-path fading effects that result in intersymbol interference (ISI) and thus reduces the data rate. To this end, optical multiple input multiple output (MIMO) can provide spatial diversity and thus achieve a high data rate. Inspired by these facts, we investigate different precoding and equalization schemes for 2 × 2 MIMO for the vehicle to vehicle (V2V-VLC) system. In this work, we consider three detection schemes, Zero Forcing (ZF), Maximum likelihood (ML), and Minimum Mean Squared Error (MMSE). Also, we consider flickering/dimming control and the nature of outdoor VLC channel as a frequency selective channel. Moreover, we investigate a transceiver considering perfect CSI based on different detection algorithms. Simulation results of the investigated transceiver demonstrate improvements in Bit Error Rate (BER) and Mean Squared Error (MSE) for the MMSE scheme </p>

We investigate the equalization and channel identification for space-time block coded signals over a frequency-selective multiple-input multiple output (MIMO) channels. The equalization is considered by taking into account the cyclostationarity of space-time block coded signals. The minimum mean square error (MMSE) solutions are derived for linear and decision feedback (DF) equalizers. Due to the redundancy induced by space-time block coding, a blind estimation for MIMO channels is investigated by using the subspace method. Together with pilot symbols, the semi-blind channel estimation can be used and it can result in less (bit error rate) performance degradation of the MMSE linear and DF equalizers.

In recent years, multiple-input multiple-output (MIMO) systems, which use several transmit and receive antennas, have attracted much attention for high performance radio systems. In MIMO systems, the channel estimation is important to distinguish transmit signals from multiple transmit antennas. While the space-alternating generalized expectation-maximization (SAGE) algorithm is known to offer good channel estimation and data detection. We proposed earlier the minimum mean square error (MMSE)-based SAGE algorithm for MIMO systems where the MMSE estimation is used for channel estimation. We showed that the proposed MMSE-based SAGE algorithm can achieve the better bit error rate (BER) than the maximum likelihood (ML) detection with training symbols. The MMSE channel estimation needs the knowledge of the maximum Doppler frequency F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</sub> for deriving the covariance matrix of the channel and the variance sigma <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> of additive white Gaussian noise (AWGN). Additionally, the computation of the MMSE channel estimation requires O(L <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> ) operations where L is the transmitted frame length. Thus, its computational complexity is high. In this paper, we propose a zero-forcing (ZF)-based SAGE algorithm for channel estimation and data detection in MIMO systems that does not need the knowledge of Fd and sigma <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> . Since the computation of the proposed ZF-based SAGE algorithm requires O(N <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> ) operations where N is the number of transmit antennas, its computational complexity is low. We show that the proposed ZF-based tracking SAGE algorithm with less computational complexity can achieve almost the same BER as that of the MMSE-based tracking SAGE algorithm

In this contribution we propose a tensor-based framework for the prediction of time-variant frequency-selective Multiple-Input Multiple-Output (MIMO) channels from noisy channel estimates. This method performs the prediction in a transformed domain obtained via the higher order singular value decomposition (HOSVD), namely on the transformed tensor elements. This is followed by the inverse transformation of the predicted transformed tensor elements onto a basis corresponding to the signal subspace. To verify our strategy, we compare the results in terms of the normalized mean square error using a known prediction method, e.g., a Wiener filter, applied to the transformed tensor elements with the identical method applied directly to the channel coefficients. The results of our investigation show that the tensor-based prediction method outperforms the direct prediction method. Although we concentrate in this contribution on the prediction in the time domain, this framework can also be used for the estimation in other domains.