MIMO Decision Feedback Equalization from an<tex>$H^infty$</tex>Perspective

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 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.

In this contribution, we present a multiple-input multiple-output (MIMO) transceiver scheme for high-speed chip-to-chip communication over low-cost electrical interconnects. Linear MIMO pre-equalization at the transmitter is combined with decision feedback equalization (DFE) at the receiver to counteract the adverse effect of inter symbol interference (ISI) and crosstalk (XT). Considering an energy constraint at the transmit side, we derive elegant closed-form expressions for the equalization filters under a minimum mean square error (MMSE) criterion. Numerical analysis shows that the combination of linear MIMO pre-equalization and MIMO DFE allows to significantly improve the reliability of future high-speed off-chip communication.

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.

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.

Multiple-input multiple-output (MIMO) systems can achieve high data-rate and high capacity transmission. In MIMO systems, the scheme that weight substreams based on minimum mean square error (MMSE) criterion at the transmitter using feedback channel state information (CSI) achieves good performance (denoted hereafter as MMSE precoder). However, if the optimum number of substreams is not selected based on CSI and methods for reducing the performance degradation due to feedback delay is not used, MMSE precoder cannot achieve the full performance possible. In this paper, we propose an MMSE precoder with mode selection for MIMO systems, which selects both the number of substreams and the modulation scheme for each substream to minimize the average BER at a fixed rate. We evaluate the BER of the proposed MMSE precoder with two methods for reducing performance degradation due to feedback delay, channel prediction and receive weight robust to feedback delay. We also evaluate the BER of the proposed MMSE precoder with the method that combines channel prediction with receive weight robust to feedback delay. Simulation results show that the BER of the proposed MMSE precoder is improved compared to that of the conventional MMSE precoder using the fixed number of substreams. We also show that the method that combines channel prediction with receive weight robust to feedback delay can achieve good BER even when the large feedback delay exists.

The paper proposes a receiver scheme for multicarrier-CDMA (MC-CDMA) that while not making use of the well known technique of guard interval is able to combat the effects of intersymbol as well as intercarrier interference (ISI, ICI). This is achieved by means of an adaptive multiple input multiple output (MIMO) fractionally spaced (FS) decision feedback equaliser (DFE) receiver scheme performing joint detection (JD). The forward section of the equaliser is designed to operate at a fractional rate, while the feedback section is symbol spaced. The analysis and design of the MIMO FS/DFE scheme is made for the minimum mean square error (MMSE) criterion. In this context, the steady state behaviour is analysed and the receivers performance are computed by means of the residual mean square error (MSE). Using Gaussian approximation an expression of the bit error rate (BER) for binary phase shift keying (BPSK) modulation is derived for both the down link (DL) and up link (UL) communication scenarios.

3GPP (3rd Generation Partnership Project) LTE (Long Term Evolution) Advanced standards are currently under way, where 4×4 MIMO (Multiple Input Multiple Output) scheme is the minimum structure. One of the best solutions to support the maximum data rate transmission is to adopt a MIMO scheme, especially spatial multiplexing mode, which means that each antenna port can transmit separate data. To realize this algorithm, the main issue is to cancel interferences added to each antenna port, and therefore, the algorithm at the receiver should have good performances. In the aspect of implementation, MMSE (Minimum Mean Square Error) detection algorithm is a reasonable method considering both complexity and performance. Furthermore, an iterative receiver (IR) algorithm can also be applied to this system. An IR algorithm has a tradeoff between complexity and performance. In this paper, we designed a reasonable and implementable MIMO receiver structure and showed performance for 3GPP LTE Advanced system, and verified that hard decoded bits, PIC-MMSE (Parallel Interference Cancellation - MMSE) and 1-iteration PIC are enough to meet the required SNR using the implemented test-bed system.

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

Compared to wired channels, time dispersive radio channels possess more frequent nulls in their spectral characteristics. Thus, the performance of linear filters to compensate intersymbol interference degrades dramatically. The well-known nonlinear decision feedback equalizer (DFE) is one approach to improve this behavior. However, in systems with observations of high dimensionality, the optimum DFE structure is computational intensive. In this paper, we apply the method of the multi-stage Wiener filter (MSWF) to a conventional minimum mean square error (MMSE) DFE in order to reduce computational complexity. The application of the new algorithm to an Enhanced Data rates for GSM Evolution (EDGE) system demonstrates the ability to outperform the even more computational intensive linear Wiener filter (WF).

In broadband wireless communication systems, single-carrier transmission with frequency domain equalization (SC-FDE) is regarded as an alternative modulation technique to the orthogonal frequency division multiplexing (OFDM). Compared with OFDM systems, SC-FDE has similar implementation complexity and performance. However, SC-FDE with linear equalizer will suffer from serious performance deterioration under deep frequency selective fading channels. An effective method to solve this problem is to introduce non-linear decision feedback equalization (DFE) to SC-FDE. In this paper, a low complexity iterative decision feedback equalizer in the frequency domain for single- carrier systems is proposed. Based on the minimum mean square error (MMSE) criterion, a simplified parameter estimation method is introduced to calculate the coefficients of the feed-forward and feedback filters, which reduces the implementation complexity of the equalizer. Simulations show that the performance of the proposed algorithm is similar to the traditional iterative block DFE (IBDFE) under various multipath fading channels but with lower complexity.

Block data transmission is an efficient scheme to mitigate the inter-symbol interference (ISI) caused by dispersive channels. Recent research work attempt to obtain optimal designs of precoders given various linear and non-linear receivers. In this paper we focus on the systems with optimal precoder designs based on the minimization of bit error rate (BER) which is the more meaningful criterion in data communications. The linear receivers employed in these systems include zero-forcing (ZF) and minimum mean square error (MMSE) equalizers. Recently, block decision feedback equalization (DFE) has also been suggested to be used in the design of such block data transmission systems. We also revisit the jointly optimum designs of the precoder coupled with the DFE receivers. First we derive the block-data error rate for all of these different systems with their corresponding optimal precoders. Then we rank their performance accordingly. Simulation results are also obtained to verify our analysis. Later, we evaluate the computational complexity on the various systems and draw some conclusions on their relative merits. Finally, we derive the lower and upper bounds of bit error rate (BER) considering error propagation for systems employing nonlinear equalizers.

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.

In the field of multiple input multiple output (MIMO) decoder, K-best has been well investigated because it guarantees an SNR-independent fixed-throughput with a performance close to the optimal maximum likelihood detection (MLD). However, the complexity of its expansion and sorting tasks is significantly affected by the constellation size W. In this paper, we propose an algorithm and hardware design of a 2D sorter-based K-best MIMO decoder whose complexity is negligibly affected by W. The main novelties of the algorithm are the following: (1) Direct expansion and parent node grouping ideas are proposed for reducing the expansion task’s complexity. (2) Two-dimensional (2D) sorter is proposed for simplifying the sorting task. The hardware design of the decoder supports up to 256-QAM modulation, which aims to apply into 4 × 4 MIMO 802.11n and 11ac systems. The paper shows that the proposed decoder outperforms the Bell Labs layered space-time (BLAST) minimum mean square error (MMSE) and lattice-reduction aided (LRA) MMSE, and is close to the full K-best in terms of bit error rate (BER) performance. The hardware design of the decoder is synthesized in application specific integrated circuit (ASIC) and compared with the previous works. As a result, it achieves the highest throughput (up to 2.7 Gbps), consumes the least power (56 mW), obtains the best hardware efficiency (15.2 Mbps/Kgate), and has the shortest latency (0.07 µs).