Statistical Precoding With Decision Feedback Equalization Over a Correlated MIMO Channel

We report a very efficient semianalytical approach for the performance evaluation of differential detection schemes for GMSK signals of the DECT standard. Precisely, for a given channel, the performance is determined by means of an analytical procedure which includes the saddlepoint approximation. We consider both static channels (with impulse response generated by the simulation program SIRCIM) and two-ray Rayleigh and log-normal fading channels. As a departure from previous works, our receiver includes an all-digital part after the analog differential detection scheme. The digital part includes: (1) a block for the estimation of both the optimum sampling phase and the nonlinear channel coefficients (by making use of the DECT training sequence), (2) a one-tap decision feedback (DF) equalizer, and (3) a block for the evaluation of the approximate optimum bias level (/spl gamma//sub e/) in the threshold detector. Both the DF equalizer coefficient and /spl gamma//sub e/ are based on the nonlinear channel coefficients estimate. For channels with a normalized delay spread up to 0.2, the use of the optimum threshold together with the DF equalizer permits a gain of about 2 dB at BER=10/sup -6/ with respect to a receiver without equalization and a zero-level decision threshold. In addition, we discover that, in indoor environments, the 2-bit GMSK detector performs roughly the same as the 1-bit detector. The threshold optimization is also effective in the presence of channels affected by fading. To support this statement, we report the performance of the 1-bit differential detection scheme combined with antenna selection diversity in the presence of a two-ray log-normal and Rayleigh fading channel.

We consider the design of the precoder for a multi-input multi-output (MIMO) communication system equipped with a decision feedback equalizer (DFE) receiver. For such design problems, perfect knowledge of the channel state information (CSI) at both the transmitter and the receiver is usually required. However, in the wireless communications environment, it is often difficult to provide sufficiently timely and accurate feedback of CSI from the receiver to the transmitter for such designs to be practically viable. In this paper, we consider the optimum design of a precoder for a wireless communication link having M transmitter antennas and N receiver antennas (M ≪ N), in which the channels are assumed to be flat fading and may be correlated. We assume that full knowledge of CSI is available at the receiver. At the transmitter however, only the second order statistics of the channels are available. Our goal here is to come up with an efficient design of the optimal precoder for such a MIMO system by minimizing the average arithmetic mean-squared error (MSE) of zero-forcing (ZF) decision feedback detection subject to a constraint on the total transmitting power. Applying some of the properties of the matrix parameters, this non-convex optimization problem can be transformed into a convex geometrical programming problem which can then be efficiently solved using an interior point method. The superior performance of our MIMO system equipped with the optimum precoder is verified by computer simulations.

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 this paper, the theoretical as well as experimental results of BER characteristics of three different modulation schemes, ASK, FSK and BPSK, in a multi-path Rician channel are addressed. These BER characteristics are analyzed as a function of E b / N o and the power ratio of the line of sight (LOS) component to the Rayleigh scattered component The theoretical as well as computer simulation results shows the ASK is the most suitable modulation scheme for the dedicated short range communication (DSRC) in terms of implemental cost and system complexity. The decision feedback equalizer is proved to be very effective in canceling the multi-path interference in the DSRC channel environment. The simulation result of the equalized ASK, reveals the performance enhancement achievable with decision feedback (DFE) equalizer for the first generation DSRC system. The multi-ray DSRC channel model is also provided to predict the received carrier power and fluctuation, which are quite dependent on the surroundings of a cell.

SUMMARYThis paper proposes a novel adaptive decision feedback equalizer (DFE) based on compact self‐constructing recurrent fuzzy neural network (CSRFNN) for quadrature amplitude modulation systems. Without the prior knowledge of channel characteristics, a novel training scheme containing both compact self‐constructing learning (CSL) and real‐time recurrent learning algorithms is derived for the CSRFNN. The proposed CSL algorithm adopts two evaluation criteria to intelligently decide the number of fuzzy rules that are necessary. The real‐time recurrent learning is performed simultaneously with the CSL at each time instant to adjust DFE parameters. The proposed DFE is compared with several neural network‐based DFEs on a nonlinear complex‐valued channel. The results show that the CSRFNN DFE is superior to classical neural network DFEs in terms of symbol‐error rate, convergence speed, and time cost. Copyright © 2011 John Wiley & Sons, Ltd.

Radial basis function (RBF) network based channel equalisers have a close relationship with Bayesian schemes. Decision feedback is introduced in the design of the RBF equaliser in order to reduce its computational complexity. The RBF decision feedback equaliser (DFE) was found to give similar performance to the conventional mean square error (MSE) DFE over Gaussian channels using various quadrature amplitude modulation (QAM) schemes, while requiring a lower feedforward and feedback order. Over Rayleigh-fading channels similar findings were valid for binary modulation, while for higher order modems the RBF based DFE requires increased feedforward and feedback orders in order to outperform the conventional MSE DFE scheme.

Assuming full channel state information (CSI) at both transmitter (CSIT) and receiver (CSIR), we consider optimizing a nonlinear MIMO transceiver with decision feedback equalizer (DFE) with respect to some global cost function f0. Setting the receiver to be a minimum mean-squared error (MMSE) DFE, the MIMO transceiver optimization problem reduces to optimizing a linear precoder. Based on the generalized triangular decomposition (GTD) and majorization theory, we prove that for any cost function f0 the optimum precoder is of the same special structure and hence the original complicated matrix optimization problem can be significantly simplified to an optimization problem with scalar-valued variables. Furthermore, if the cost function is specialized to the cases where the composite function f0 o exp is either Schur-convex or Schur-concave, then the nonlinear transceiver design becomes exceedingly simple. In particular, when f0 o oexp is Schur-convex, the optimum nonlinear transceiver design turns out to be the uniform channel decomposition (UCD) scheme; when f0 o exp is Schur-concave, the optimum nonlinear design degenerates to linear diagonal transmission.

Decision feedback equalizers (DFE) employing energy constraints have been successfully used to limit the feedback of wrong decisions that lead to the well known error propagation phenomenon. This paper extends the energy constraint formulation proposed for the scalar DFE, to the class of block memoryless DFE structures that employ zero-padding transmission redundancy. We further show how to make use of fast order recursive relations in order to obtain the filters efficiently. Computer simulations verify the improved BER performance of the proposed scheme over its unconstrained block DFE counterpart.

Severe intersymbol interference (ISI) is one of the main obstacles for reliable signal reception in ATSC DTV systems. Decision feedback equalizers (DFEs) are commonly used to suppress the ISI. However, DFEs may suffer from error propagation due to incorrect symbol decisions from the symbol slicer. This phenomenon deteriorates the performance even more when the post-cursor ISI is strong. In order to reduce error propagation, we present a novel hybrid equalization scheme for ATSC channels. The proposed scheme consists of an adaptive decision feedback sparsening filter (DFSF), and an iterative maximum a posteriori (MAP) equalizer based on the belief propagation (BP) algorithm. In the first stage, instead of removing all the ISI from post cursors, the DFSF employs a modified feedback filter which leaves the strongest post-cursor ISI taps uncorrected. As a result, a long ISI channel is equalized to a sparse channel having only a small number of nonzero taps. In the second stage, a belief propagation algorithm is applied to mitigate the residual ISI. Since the channel is typically time-varying and suffers from Doppler fading, the DFSF is adapted using the least mean square (LMS) algorithm, such that the amplitude and the locations of the nonzero taps of the equalized sparse channel appear to be fixed. As such, the channel appears to be static during the second stage of equalization which consists of the BP detector. Simulation results demonstrate that the proposed scheme outperforms the traditional DFE in symbol error rate, under both static channels and dynamic ATSC channels.

In this paper we introduce a nonlinear equalizer using the radial basis function (RBF) network with decision feedback equalizer (DFE) for electronic dispersion compensation in optical communication systems with on-off-keying and a direct detection receiver. The RBF method introduces a non-linear equalization technique suitable for optical communication direct detection systems that include nonlinear transformation at the photodetector. A bit error rate performance comparison shows that the RBF with DFE out performs the RBF without DFE and achieves similar results provided by maximum likelihood sequence estimator.

We illustrate a new type of nonlinear obtained by placing a decision feedback and a decision feedforward in parallel. This type of called a parallel decision feedback and feedforward equalizer or, briefly, a equalizer, is characterized by substantially reduced error propagation if the eye diagram is open at the input of the decision device of the decision feedback and of the first decision device of the decision feedforward equalizer. The composite may be conveniently built up using a single decision device in the decision feedforward equalizer.

This paper investigates the performance of compromise Viterbi algorithm (VA) and standard equalization techniques by computation and simulation over band-limited channels using fourlevel vestigial sideband (VSB) modulation. Linear channel characteristics from the published telephone channel survey were used as examples of band-limited data transmission channels. One of the principal conclusions drawn from the study is that at data rates of 9600 bits/s and less, the linear characteristics of these channels do not limit performance even with linear equalization. It was found that at this data rate, receivers based on linear equalization are very sensitive to timing and carrier phase over some channels. Thus at 9600 bits/s the decision feedback equalizer was found to be a better choice because it is relatively insensitive to carrier phase and timing considerations. Moreover, at 9600 bits/s no problem with error propagation was encountered with the decision feedback equalizer. As the data rate was increased beyond 9600 bits/s the decision feedback tap gains became large enough to cause severe error propagation. The compromise VA receiver structure was effective at higher data rates and was almost unaffected by channel bandwidth up to 12 000 bits/s.

We present a novel turbo equalization structure for space-time coded systems. It is based on performing channel equalization via a decision feedback equalizer (DFE) designed using a novel maximum likelihood criterion. The resulting optimization problem is solved using the space-alternating generalized EM (SAGE) algorithm. This results in expressions for the forward and backward filters of the DFE that take large benefit from the more and more refined estimations of the transmitted symbols iteratively obtained by the outer decoder.

This paper considers a combined coding and equalization technique applied to the magnetic recording channel. The optimization of the coded-equalization scheme for this channel requires balancing the coding rate with its associated distance gain and equalization loss. A major concern in a coded-equalization scheme using decision feedback equalization (DFE) is error propagation. A new indicator to measure the effect of error propagation when using soft decision decoding is proposed. For medium to high normalized recording densities (S>1.5), it is shown that error propagation significantly degrades the theoretical performance of a detection scheme which combines a partial response DFE and simple trellis codes. In fact, this combined system performs worse than the uncoded one. The addition of delayed decision feedback sequence estimation (DDFSE) to limit the effect of error propagation is then investigated. With a moderate decoding complexity, positive coding gains have been achieved at such densities when choosing the partial response polynomial according to the derived indicator.

The structure of an optimum linear precoder for a rotation-invariant performance measure is obtained subject to the constraint of limited input power for a block transmission scheme. It is shown that several known performance measures of a communication system are rotation invariant. The rotation invariant property provides a unified framework for obtaining the structure of an optimum linear precoder for several criteria such as: 1) maximization of minimum distance; 2) maximization of channel capacity; and 3) optimization of different performance measures, such as bit-error rate (BER), mean square error, signal-to-noise ratio of optimum equalizers (linear minimum mean square error, zero-forcing, maximum likelihood (ML), zero forcing-block decision feedback, minimum mean square error-block decision feedback, etc.). This framework provides a method for obtaining the structure of an optimum linear precoder for BER performance measure of the ML equalizer. The structure turns out to be a channel diagonalizing structure after a prerotation of the input constellation. Using this structure, the properties of the optimum precoder that minimize the BER of the ML equalizer for two binary phase-shift keying symbols transmission under input-power constraint are studied.