MIMO equalization for space-time coded signals using cyclostationarity

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.

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.

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.

We approach the multiple input multiple output (MIMO) decision feedback equalization (DFE) problem in digital communications from an H/sup /spl infin// estimation point of view. Using the standard (and simplifying) assumption that all previous decisions are correct, we obtain an explicit parameterization of all H/sup /spl infin// optimal DFEs. In particular, we show that, under the above assumption, minimum mean square error (MMSE) DFEs are H/sup /spl infin// optimal. The H/sup /spl infin// approach also suggests a method for dealing with errors in previous decisions.

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 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.

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.

Matrix decompositions play an important role in analyzing the capacity and designing the transceiver for multiple input multiple output (MIMO) channels. In the single user case, by relying on the decision feedback equalizer (DFE) at the receiver or Tomlinson-Harashima precoding (THP) at the transmitter, the geometric mean decomposition (GMD) can be used to create identical signal-to-noise ratios (SNR) for each decoupled subchannel. In this paper, we propose a new matrix decomposition, called the block-diagonal GMD (BD-GMD), for the multiuser MIMO broadcast channel. Applying THP at transmitter and linear equalization in each of the receivers, each user can achieve identical SNRs for its subchannels, thus equal-rate coding can be applied for each user. Furthermore, by using transmit power control and the BD-GMD, we design a scheme that achieves equal-rate coding for the subchannels of all users. Computer simulations have shown that the proposed schemes have better BER performances than zero-forcing THP (ZF-THP) and equal-rate ZF-THP schemes.

The paper derives a minimum bit error rate (BER) solution for the decision feedback equaliser (DFE) that employs a linear combination of the channel observations and the past decisions. We show that by using a geometric translation the DFE is reduced to a simpler linear equaliser. A BER expression for the linear equaliser is obtained under the assumption of linearly separable decision regions, and a method is proposed to optimally set the linear-combiner coefficients of the DFE. This minimum BER solution is superior to the usual minimum mean square error (MSE) solution.

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.

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).

A novel training-based channel estimation scheme is presented for an uncoded layered space-time system that operates in a wideband frequency selective fading environment of a time-varying multiple-input multiple-output (MIMO) channel. The method uses a pilot matrix consisting of pilot symbols derived from the Paley-Hadamard matrix to estimate the MIMO channel impulse response. The orthogonality of the pilot matrix resolves both the intersymbol interference and the cochannel interference of the wideband MIMO channel. The Toeplitz-like structure of the Paley-Hadamard matrix is exploited to minimise the length of the pilot sequence, reducing pilot symbol overhead. A decision feedback algorithm is used to track the time-varying MIMO channel. Results are presented which demonstrate the performance of the proposed MIMO channel estimator in a layered space-time system for different mobile velocities and system configurations.

We investigate the use of the minimum mean-squared- error decision-feedback-equalizer (MMSE-DFE) as a preprocessor to reduce the computational complexity of symbol detection in frequency-selective multiple- input multiple-output (MIMO) channels. The preprocessor delays and focuses the received signal energy which reduces the effects of inter-symbol- interference and multiple-access-interference. This property of the MMSE-DFE preprocessor is exploited to order and to reduce the number of symbol candidates considered by an iterative maximum- likelihood (ML) detector. Simulations show that the proposed detection scheme can achieve lower bit- error-rates than existing reduced-complexity algorithms in overdetermined and underdetermined receive scenarios. Near-optimum performance is achieved when the number of symbol candidates is increased.