Decision-feedback equalization for CDMA downlink

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 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.

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.

Several researches investigate the performance of the conventional adaptive equalizers for the medium data rates HF waveforms (up to 8 PSK) and show that they are suitable for mitigating the HF channel. However, the performance of these types of equalizers is very bad for the high data rates HF waveforms (up to 64QAM). Most of the later researches in the high data rates HF waveforms are based on the soft turbo equalizers which are very complicated. In this paper, we try to design the lowest complex equalizer can mitigate the HF channel for the high data rates waveforms. We investigate the performance of the minimum mean square error decision feedback equalizer (MMSE-DFE) indirectly adaptive through channel estimation based on least square estimation (LS). We show that the basic performance of the MMSE-DFE cannot satisfy the standard requirements, and then we introduce two additional enhancements. First, an effective channel estimation technique (double estimation) is proposed. The new estimator shows a clear performance enhancement over simple least square estimation with linear interpolation (about 3 dB gain at 1e-5 BER for the 64QAM). The second enhancement is to use the iterative structure through decoder using the same conventional equalizer and decoder and this gives another 3 dB gain at 1e-5 BER for the 64QAM. Iterative structure is less complicated than turbo equalizers for sure, as turbo equalizers require a lot of changes in the equalizer, decoder and demapper blocks to be SISO modules. Final equalizer model satisfies all the strict requirements of both (STANAG 4539 annex B) and (MIL-STD-188-110B app. C) standards under the ITU-R Poor channel conditions. In addition, we compare our performance with two different vendors of HF modems and other different research and show that our performance is very competitive.

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).

The two major obstacles toward high-capacity indoor wireless networks are distortion due to the indoor channel and the limited availability of bandwidth which necessitates a high spectral efficiency. A combined orthogonal-frequency division multiplexing/spatial-diversity multiple access (OFDM/SDMA) approach can effectively tackle both obstacles. The channel distortion due to multipath propagation is easily mitigated with OFDM while the bandwidth efficiency can be increased with the use of SDMA. In order to keep the network's cost acceptable, simplified SDMA processors are preferred over the exponentially complex optimal maximum-likelihood processors. However, these simplified processors perform significantly worse than the optimal ones in terms of average bit error rate (BER). In this paper, we show that by adapting the constellation sizes applied on the individual subcarriers to the channel conditions, the performance of OFDM/SDMA processors can be significantly enhanced. In the uplink, we derive simple closed-form equations for the optimal constellation sizes for both a simple linear minimum mean-square error (MMSE) detector and for a nonlinear MMSE decision feedback equalizer (DFE) detector. Furthermore, for each detector, we introduce a simplified loading algorithm which lowers the computational and signaling complexity substantially at a small performance penalty. In the downlink, we study the dual precoders of the uplink detectors, respectively, the linear MMSE precoder and the nonlinear Tomlinson-Harashima (TH) MMSE-based precoder. For both precoders, we derive expressions for the optimal and the simplified constellation sizes. Additionally, we show that in time-division duplexing systems, the constellation distribution of a set of dual detectors/precoders is identical for up- and downlink, which effectively halves the computational complexity of adaptive loading. In the fully loaded uplink, the proposed adaptive loading algorithm results in a gain of 9 dB for a BER=10/sup -3/ for the linear MMSE detector and a gain of 4.5 dB for the nonlinear MMSE-DFE detector. In the fully loaded downlink, a gain of 6.3 dB is achieved for the MMSE precoder and 5.5 dB for the TH-MMSE precoder.

Multiple-input/multiple-output (MIMO) frequency selective fading channels introduce both the intersymbol interference (ISI) and the inter-(sub)channel interference (ICI) that are the major performance limiting factors for MIMO wireless data communications. This paper focuses on joint suppression of such two interferences in receiver design under the criterion of the minimum mean-squared error (MMSE). The well-known Kalman filtering arises as a natural design tool to achieve the optimum joint suppression of the ISI and ICI in the sense of MMSE that results in a two-stage design method that suppresses the ISI and ICI in series. Specifically, a state-space solution is derived for the optimum decision-feedback equalizer (DFE) based on temporal Kalman filtering, and is shown to be equivalent to a conventional finite length DFE for ISI suppression. A novel spatial Kalman filtering scheme is proposed as the second stage to successively cancel the ICI. It is shown that the proposed two-stage method yields the realizable and optimum joint ISI and ICI suppression, while it admits lower computational complexity than the conventional finite length DFE for ISI suppression and the MMSE V-BLAST receiver for ICI suppression. The results are applicable to any linear channels that admit state-space realizations, including MIMO frequency selective time-varying channels, and are thus the most general. Simulation results show the effectiveness of the proposed two-stage method and its robustness to channel estimation uncertainties that may arise in practical systems.

In diffusion-based communication, as for molecular systems, the achievable data rate is low due to the stochastic nature of diffusion which exhibits a severe inter-symbol-interference (ISI). Multiple-Input Multiple-Output (MIMO) multiplexing improves the data rate at the expense of an inter-link interference (ILI). This paper investigates training-based channel estimation schemes for diffusive MIMO (D-MIMO) systems and corresponding equalization methods. Maximum likelihood and least-squares estimators of mean channel are derived, and the training sequence is designed to minimize the mean square error (MSE). Numerical validations in terms of MSE are compared with Cramer-Rao bound derived herein. Equalization is based on decision feedback equalizer (DFE) structure as this is effective in mitigating diffusive ISI/ILI. Zero-forcing, minimum MSE and least-squares criteria have been paired to DFE, and their performances are evaluated in terms of bit error probability. Since D-MIMO systems are severely affected by the ILI because of short transmitters inter-distance, D-MIMO time interleaving is exploited as countermeasure to mitigate the ILI with remarkable performance improvements. The feasibility of a block-type communication including training and data equalization is explored for D-MIMO, and system-level performances are numerically derived.

For the code division multiple access (CDMA) downlink channel, the chip-level equalization has been considered in this paper. There is no interference after despreading if all spreading codes are orthogonal, as in IS-95. However, it cannot be true for a frequency-selective fading channel. In this case, the chip-level equalization can be applied to restore the orthogonality. We investigate the chip-level equalization using finite impulse response (FIR) equalizers for the mobile station with multiple receive antennas. A blind approach and the minimum mean square error (MMSE) approach with code-multiplexed pilot are considered. A generalized MMSE equalization, which combines the MMSE and blind approaches together, is also investigated. It is shown that the generalized MMSE equalizer can effectively increase the number of samples to track the variation of channel and thereby performs better when the coherence time is small. In addition, we derive closed-form solutions of the blind, MMSE, and generalized MMSE equalizers for given channels.

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.

We present a novel iterative (turbo) receiver with tunable complexity for reliable detection of (uncoded) payload data transmitted over long intersymbol interference (ISI) channels affected by crosstalk, as those typically encountered in emerging HDSL2 services standardized by ANSI T1.418 recommendation. The proposed receiver combines in an original way "minimum mean square error (MMSE) estimation principle," "turbo-processing principle" and "crosstalk-prediction principle" for achieving both suboptimal maximum a posteriori probability channel equalization and reliable soft-mitigation of ISI tail plus crosstalk. More in detail, according to the turbo-processing principle, at each iteration suitable extrinsic information is extracted from the equalizing and interference-canceling modules and used as "a priori information" for the next iteration. Several simulation results on typical HDSL-like test-loops confirm the superiority of the proposed turbo-detector (TD) over current solutions based on conventional MMSE decision-feedback equalizers and precoders (such as the Tomlinson-Harashima precoder). The numerical tests also point out that performance of the presented TD on typical high bit-rate digital subscriber lines (HDSL) is not limited by error-floor phenomena, even at error-probabilities below 10/sup -7/.

This correspondence deals with time-varying (TV) single-input multiple-output (SIMO) channels, which are both frequency selective (due to high data rate) and time selective (due to mobility). A complex exponential basis expansion model (CE-BEM) is used to model the channel. We consider a block transmission system, where on the transmit side a precoder is employed to enable the maximum available diversity for a CE-BEM channel. After direct decoding on the receive side, the resulting channel resembles a finite-impulse-response (FIR) filter on both block and symbol level. We therefore propose an equalizer that bears a structure analogous to the effective channel. In comparison with a standard block minimum mean-square error decision-feedback equalizer (BMMSE-DFE) that involves the inversion of a large-size matrix, the proposed parametric equalizer renders a similar performance but at a lower computational cost if there are multiple outputs present. Another contribution of this correspondence is a semiblind algorithm to estimate this equalizer when the channel state information is not available: the equalizer taps and the information symbol estimates are refined recursively by means of normalized least-mean-squares (NLMS) adaptation.

Pilot symbol assisted modulation and a minimum mean-square error (MMSE) channel predictor are used to employ feedback MMSE power control over a frequency nonselective slow Rayleigh fading channel. Feedback is assumed to be noiseless and delayless. First, the performance of the pilot symbol system using MMSE power control is derived in the case of the frame size of two. Lag error is noticed to cause severe performance degradation, even when the channel is very slowly fading. In order to decrease the lag error and to get a good system performance, the number of estimator coefficients is found to become quite large. The operating strategy of MMSE power control is studied by Monte Carlo simulations and compared to various strategies presented in the literature. Spectral efficiency of the pilot symbol system is increased by transmitting more than one data symbol in a given frame. Finally, the performance of the pilot symbol system using MMSE power control is derived in the case of an optimal frame size.

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.