Adaptive MLSE equalizers with parametric tracking for multipathfast-fading channels

We use the parametric channel identification algorithm proposed by Chen and Paulraj (see Proc. IEEE Vehicular Technology Conf., p.710-14, 1997) and by Chen, Kim and Liang (see IEEE Trans. Veh. Technol., p.1923-35, 1999) to adaptively track the fast-fading channels for the multichannel maximum likelihood sequence estimation (MLSE) equalizer using multiple antennas. Several commonly-used channel tracking schemes, decision-directed recursive least square (DD/RLS), per-survivor processing recursive least square (PSP/RLS) and other reduced-complexity MLSE algorithms are considered. An analytic lower bound for the multichannel MLSE equalizer with no channel mismatch in the time-varying specular multipath Rayleigh-fading channels is derived. Simulation results that illustrate the performance of the proposed algorithms working with various channel tracking schemes are presented, and then these results are compared with the analytic bit error rate (BER) lower bound and with the conventional MLSE equalizers directly tracking the finite impulse response (FIR) channel tap coefficients. We found that the proposed algorithm always performs better than the conventional adaptive MLSE algorithm, no matter what channel tracking scheme is used. However, which is the best tracking scheme to use depends on the scenario of the system     

An efficient low complexity cluster-based MLSE equalizer for frequency-selective fading channels

Recently, a novel MLSE equalizer was reported, that does not require the explicit estimation of the channel impulse response. Instead, it utilizes, in an efficient manner, the estimates of the centers of the clusters formed by the received observations. In this paper, a novel cluster tracking scheme is presented, which extends the application of this equalizer in time-varying transmission environments. The proposed algorithm is shown to be equivalent in tracking performance with the classic LMS-based MLSE equalizer, yet much simpler computationally. This is a consequence of the fact that the new method allows for an efficient exploitation of the symmetries underlying the signaling scheme.     

Designing low-complexity equalizers for wireless systems

The demand on wireless communications to provide high data rates, high mobility, and high quality of service poses more challenges for designers. To contend with deleterious channel fading effects, both the transmitter and the receiver must be designed appropriately to exploit the diversity embedded in the channels. From the perspective of receiver design, the ultimate goal is to achieve both low complexity and high performance. In this article, we first summarize the complexity and performance of low-complexity receivers, including linear equalizers and decision feedback equalizers, and then we reveal the fundamental condition when LEs and DFEs collect the same diversity as the maximum-likelihood equalizer. Recently, lattice reduction techniques were introduced to enhance the performance of low-complexity equalizers without increasing the complexity significantly. Thus, we also provide a comprehensive review of LR-aided low-complexity equalizers and analyze their performance. Furthermore, we describe the architecture and initial results of a very-large-scale-integration implementation of an LR algorithm.     

An efficient nonlinear circuit simulation technique

This paper proposes a novel method for the analysis and simulation of integrated circuits (ICs) with the potential to greatly shorten the IC design cycle. The circuits are assumed to be subjected to input signals that have widely separated rates of variation, e.g., in communication systems, an RF carrier modulated by a low-frequency information signal. The proposed technique involves two stages. Initially, a particular order result for the circuit response is obtained using a multiresolution collocation scheme involving cubic spline wavelet decomposition. A more accurate solution is then obtained by adding another layer to the wavelet series approximation. However, the novel technique presented here enables the reuse of results acquired in the first stage to obtain the second-stage result. Therefore, vast gains in efficiency are obtained. Furthermore, a nonlinear model-order reduction technique can readily be used in both stages making the calculations even more efficient. Results will highlight the efficacy of the proposed approach     

A low-complexity eigenfilter design method for channel shortening equalizers for DMT systems

We present a new low-complexity method for the design of channel shortening equalizers for discrete multitone (DMT) modulation systems using the eigenfilter approach. In contrast to other such methods which require a Cholesky decomposition for each delay parameter value used, ours requires only one such decomposition. Simulation results show that our method performs nearly optimally in terms of observed bit rate.     

MLSE equalization and decoding for multipath-fading channels

The performance of a receiver using a combined MLSE (maximum likelihood sequence estimation) equalizer/decoder and D-diversity reception is analyzed for multipath Rayleigh fading channels. An upper bound on the (decoded) bit error probability is derived. Comparisons to simulation results show that this upper bound is quite tight when the system has a high signal-to-noise ratio or when diversity reception is used. The upper bound involves an infinite series that must be truncated at a point where the remainder can be safely assumed to be small. An algorithm based on a one-directional stack algorithm is proposed for this calculation because it makes efficient use of computer memory     

FIR channel-shortening equalizers for MIMO ISI channels

Finite-length delay-optimized multi-input multi-output (MIMO) equalizers that optimally shorten the impulse response memory of frequency-selective MIMO channels are derived. The MIMO equalizers are designed to minimize the average energy of the error sequence between the equalized MIMO channel impulse response and an MIMO target impulse response (TIR) with shorter memory. Two criteria for optimizing the MIMO TIR are analyzed and compared. The presented analytical framework encompasses a multitude of previously-studied finite-length equalization techniques     

On low-complexity space-time coding for quasi-static channels

We propose a new space-time coding scheme for the quasi-static multiple-antenna channel with perfect channel state information at the receiver and no channel state information at the transmitter. In our scheme, codewords produced by a trellis encoder are formatted into space-time codeword arrays such that decoding can be implemented efficiently by minimum mean-square error (MMSE) decision-feedback interference mitigation coupled with Viterbi decoding, through the use of per-survivor processing. We discuss the code design for the new scheme, and show that finding codes with optimal diversity is much easier than for conventional trellis space-time codes (STCs). We provide an upper bound on the word-error rate (WER) of our scheme which is both accurate and easy to evaluate. Then, we find upper and lower bounds on the information outage probability with discrete independent and identically distributed (i.i.d). inputs (as opposed to Gaussian inputs, as in most previous works) and we show that the MMSE front-end yields a large advantage over the whitened matched filter (i.e., zero-forcing) front-end. Finally, we provide a comprehensive performance/complexity comparison of our scheme with coded vertical Bell Labs layered space-time (V-BLAST) architecture and with the recently proposed threaded space-time codes. We also discuss the concatenation of our scheme with block space-time precoders, such as the linear dispersion codes.     

On MLSE algorithms for unknown fast time-varying channels

We consider maximum-likelihood sequence estimation (MLSE) algorithms for unknown, time-varying intersymbol interference communication channels. We assume a statistical channel model, and marginalize over model parameters to derive expectation-maximization (EM) algorithms for both time-independent Gaussian and Gauss-Markov models, and we contrast these with direct MLSE and computationally efficient per-survivor processing implementations. We identify a general concern associated with the convergence of EM-based discrete parameter (e.g., symbol) estimators.     

Adaptive MLSE for DPSK in time- and frequency-selective channels

An adaptive equalizer structure based on a state space formulation and maximum likelihood sequence estimation (MLSE) is developed for a time-varying, frequency-selective channel. Differential phase shift keying (DPSK) is assumed at the transmitter and effective differential decoding is performed at the receiver. The standard models of a time-varying linear channel and the Karhunen-Lo`eve (KL) expansion underpin the receiver structure. Analytical and simulation results for the receiver are shown. The resulting receiver is a per-survivor structure.     

Performance analysis of linear MIMO equalizers for multitone DS/SS systems in multipath channels

In [11] the combination of multitone modulation with direct sequence spectrum spreading has been introduced. The performance of a correlation receiver has been evaluated for a multipath channel. In [12] the analysis has been extended to the presence of a multiple access interference. In the present paper we analyze the equalization problem of such a system for a single user scenario. In order to understand the potential of the system we first investigate the steady-state behavior of the MIMO equalizer for an MMSE design. The investigation is carried out for an equalizer following a receiver made of a bank of filters matched to both the symbol shape and the channel, which is a two-path channel. Assuming BPSK symbols an exact expression of the bit error probability before and after equalization is obtained in the form of an integral by means of the characteristic function method. Next adaptive LMS and RLS structures are proposed. The performance of the RLS algorithm is demonstrated.Part of this work has been presented at ICC '95, Seattle, June 1995.This author would like to thank the Belgian NSF for its financial support.This author is a Research assistant of FRIA.     

Performance of turbo equalizers for optical PMD channels

This paper investigates the performance of iterative (turbo) equalization to mitigate the effects of a polarization-mode dispersion (PMD) in nonreturn-to-zero (NRZ) intensity-modulated optical-fiber transmission systems. A PMD can lead to severe distortions in the received electrical signal and is a key limiter for the development of high-bit-rate transmission over currently used fibers. In order to reduce the distortions due to a PMD, the performance of symbol-by-symbol maximum a posteriori (sbs-MAP) soft-in/soft-out (SISO) decoders is studied. The SISO algorithms are adapted to the noise statistics of the optical channel where the photo detector leads to a non-Gaussian signal-dependent noise at the receiver side. The modified SISO algorithms are successfully employed for turbo equalization and results show that iterative (turbo) equalization and decoding for the compensation of a PMD can lead to a tremendous reduction in the bit error ratio (BER). Moreover, it is shown that, due to the robustness of mutual information, the extrinsic information transfer (EXIT) chart can be applied for the design of iterative receivers in optical transmission systems even with a non-Gaussian noise.     

Orthogonal-transformed variable-gain least mean squares (OVLMS)algorithm for fractional tap-spaced adaptive MLSE equalizers

A fast channel-estimation scheme for adaptive maximum-likelihood sequence-estimation (MLSE) equalizers called the orthogonal-transformed variable-gain least mean squares (OVLMS) algorithm is proposed. This algorithm requires only as many operations as the least mean squares algorithm in spite of its excellent performance. Furthermore, an operational complexity reduction method is proposed in which the orthogonal matrix is reconfigured as eigenvectors with valid eigenvalues. The OVLMS algorithm is theoretically analyzed and is shown to have both a fast acquisition and a good tracking performance. An equalizer using OVLMS (OVLMS-MLSE) experimentally attains a 5-dB improvement in bit-error rate (BER) performance at BER of 1.0×10 ^-4 over coherent detection. The OVLMS-MLSE is found to be free of the degradation caused by sampling phase error. Finally, the OVLMS-MLSE equalizer is experimentally verified to synchronize within five symbols     

An efficient implementation of the harmonic balance technique for solving nonlinear microwave problems

An efficient implementation of the harmonic balance method, using novel numerical algorithms, that are both robust and efficient, coupled with analytical expressions developed for the elements of the Jacobian matrix, is presented. The approach possesses excellent convergence property and speed. Simulated performances using the developed approach for a 10-GHz GaAs MESFET amplifier are found in good agreement with the measured results.     

MLSE for correlated diversity sources and unknown time-varyingfrequency-selective Rayleigh-fading channels

Yu and Pasupathy (see ibid., vol.43, p. 1534-44, 1995) derived a maximum-likelihood sequence estimation (MLSE) receiver structure for unknown time varying frequency-selective Rayleigh-fading channels and uncorrelated diversity sources. This receiver design is extended to the case of correlated diversity sources. Correlated diversity sources typically arise with space diversity, where constraints on antenna volume require that diversity antennae be placed too closely together. Analytic and simulated bit-error rate (BER) curves are presented for receivers which exploit and ignore the correlation. In the former case, we find a small BER improvement that reduces with decreasing correlation. However, for a fixed receiver complexity, superior performance is achieved when the correlation is ignored     

Adaptive combined DFE/MLSE techniques for ISI channels

By embedding a decision-feedback equalizer (DFE) into the structure of a maximum-likelihood sequence estimator (MLSE), an adaptive combined DFE/MLSE scheme is proposed. In this combined DFE/MLSE, the embedded DFE has three functions: (i) prefiltering the received signals and truncating the equivalent channel response into the desired one, (ii) compensating for channel distortions, and (iii) providing the MLSE detector with predicted values of input signals. Since the embedded MLSE detector operates on the predicted signals the detected symbols at the output of the DFE/MLSE do not suffer any delay and can be directly fed back into the embedded DFE so that the error propagation, which usually takes place in a conventional DFE, can be greatly reduced. Analytical and simulation results indicate that the performance is significantly improved by the DFE/MLSE compared to the conventional DFE while its computation complexity is much less than that of the conventional MLSE receiver. The combined DFE/MLSE can use different adaptive structures (block-updating, sliding window updating or symbol-by-symbol updating) to meet different performance objectives. Moreover, the proposed DFE/MLSE provides a trade-off between performance and complexity with a parameter m representing the MLSE detection depth as well as the number of predicting steps of the embedded DFE. For some particular values of m, this scheme is capable of emulating the conventional DFE, MLSE-VA, adaptive LE-MLSE equalizer, adaptive DDFSE, and adaptive BDFE without detection delay     

A low-complexity lattice-based low-PAR transmission scheme for DSL channels

This paper presents a new low-complexity multicarrier modulation (MCM) technique based on lattices which achieves a peak-to-average power ratio (PAR) as low as three. The scheme can be viewed as a "drop in" replacement for the discrete multitone (DMT) modulation of an asymmetric digital subscriber line modem. We show that the lattice-MCM retains many of the attractive features of sinusoidal-MCM, and does so with lower implementation complexity, O(N), compared with DMT, which requires O(NlogN) operations. We also present techniques for narrowband interference rejection and power profiling. Simulation studies confirm that performance of the lattice-MCM is superior, even compared with recent techniques for PAR reduction in DMT.     

Design of nonuniformly spaced tapped-delay-line equalizers for sparse multipath channels

Analytical expressions that explicitly indicate the tap values and tap positions of infinite-length, T-spaced tapped-delay-line (TDL) equalizers for sparse multipath channels are derived. Simple design rules for allocating taps to finite-length, minimum mean-square error, nonuniformly spaced TDL equalizers (NU-Es) are formulated based on the derived results. The design-rule-based methodology demonstrates a better tradeoff between accuracy and efficiency than existing tap-allocation schemes. The resultant NU-Es also achieve a lower overall computational complexity than conventional, uniformly spaced TDL equalizers (U-Es) of the same span for both directly adaptive and channel-estimate-based implementations. Moreover, a square-root raised cosine (SRRC) receive filter matched to a SRRC transmit filter is better than a matched filter when used to precede a NU-E.