Channel equalization for very high-speed digital data communication

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.

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.

As the data rate has been increased over 10 Gb/s with copper interconnect, the intersymbol interference (ISI) caused from the channel loss should be compensated. While a decision feedback equalizer (DFE), which is widely used in the receiver can compensate the ISI, its ability to enhance the signal-to-noise ratio (SNR) is limited especially for high frequency data patterns (alternating data patterns). Even a DFE with a large number of taps, which has powerful compensation capacity for ISI, can improve only limited amount of SNR. To improve SNR, this brief presents a 1/4th baud-rate continuous-time linear equalizer (CTLE) and a two-tap DFE. The 1/4th baud-rate CTLE recovers data to be adequate for the DFE, and remaining ISI is removed by the DFE. To boost the high frequency gain of the DFE, exclusive or merged adders are introduced, so the proposed equalizer is more tolerant against channel noise. It compensates 21.7-dB channel loss and operates with 11.5-Gb/s data rate as it consumes 25.35 mW from 1.3 V supply in a 110-nm CMOS technology.

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 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.

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.

A decision-feedback equalizer (DFE) is the basis of a recent development of a quadruple diversity troposcatter modem which can operate up to a data rate of 12.6 Mbit/s in a 99% bandwidth of 15 MHz. In this paper a theoretical approach is developed for the calculation of average bit error rate (ABER), including the effects of intersymbol interference due to multipath and the finiteness of the transversal filters used to realize the DFE. By omitting the intersymbol interference effect, the calculation provides a lower bound which can be used to assess the intersymbol interference penalty for a particular DFE structure. The paper includes calculations of a DFE configuration which has a three tap forward filter with tap spacing equal to one-half a symbol interval. Measured performance results from fading channel simulator tests of a three tap forward filter DFE are presented for data rates from 1.5 to 12.6 Mbit/s and for a wide range of multipath statistical conditions. The results for this DFE configuration show (1) excellent agreement between calculated and measured ABER, (2) a small intersymbol interference penalty when the 2σ multipath spread is less than approximnately one-half the data symbol interval, and (3) successful operation at values of multipath spread up to twice the data symbol interval. In a sequel to this paper, the results of a field test of the DFE modem are presented. These live links test results are consistent with both the calculated and simulator measured data presented here.

A well-known receiver strategy for a linearly modulated signal transmitted over a frequency-selective channel is channel equalization. Recently it was proposed to employ a minimum mean-squared error (MMSE) channel equalizer for the downlink of CDMA. In this paper, we introduce a new receiver concept using MMSE channel equalization as a first stage and MMSE decision-feedback equalization (DFE) utilizing soft feedback from the decoding unit as a second stage. Both schemes are compared for the downlink of CDMA. It turns out, that after channel decoding we gain about 1 dB compared to conventional MMSE channel equalization.

The increasing demand for higher network data rates by new businesses and entertainment has never been fulfilled. Mixed-signal PAM - 4 transceivers prevail over their ADC - DSP counterparts in energy efficiency and chip area, but they have difficulties operating over high - loss links. Typically, a continuous-time linear equalizer (CTLE) and a multi-tap decision-feedback equalizer (DFE) are implemented in a mixed-signal receiver (RX). However, when the data rate reaches 112Gb/s, the implementation of the DFE suffers from stringent feedback timing. Direct DFE works only at 100Gb/s in an optical receiver [1], leaving no room for feedforward error correction (FEC). A speculative 1 - tap DFE is implemented in [2], but it requires an 8-tap feedforward equalizer (FFE) at the transmitter (TX) to generate a 1+0.5D response; this may be impractical without knowing the characteristics of the entire channel. Another drawback of a speculative DFE is the large 1 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">st</sup> -tap latency, which brings about challenges in realizing two or more taps. In addition, the DFE does not compensate for pre-cursor inter-symbol interference (ISI), which becomes significant for channels with higher loss. Without a DFE, the CTLE only covers a small loss of up to 10dB [3,4]. This paper presents a 112Gb/s mixed-signal transceiver using an RX analog FFE with adaptive pre- and post-cursor ISI equalization in 28nm CMOS, compensating for 20.8dB loss at a power efficiency of 2.29pJ/b.

Interpolated decision feedback equalization for long intersymbol interference channels

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 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 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.

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 considers equalization of the slow fading channel for a serial data transmission application. Linear and decision-feedback adaptive equalization techniques are contrasted. The error propagation effect in decision-feedback equalizers is analyzed by a Markov process model. The error probability magnification is computed for both fixed and fading channels and for both binary and quaternary phase-shift-keying (PSK) transmission. The results show that the error propagation effect is small and in regions of practical error probabilities the decision-feedback equalizer is superior to its linear counterpart. Parameters of a practical decisionfeedback equalizer are estimated and a performance evaluation is performed. The implicit diversity gain is shown to be significant and the intersymbol interference penalty is found to be less than 1 dB. Because the intersymbol interference penalty is small, more complex nonlinear processors such as the Viterbi algorithm cannot be recommended for this application. Time jitter effects for the equalizer are included in a calculation of average error probability.