Training Sequence Design Research Articles

A GLRT approach to data-aided timing acquisition in UWB radios-Part II: training sequence design

The overall system efficiency of impulse radio communications relies critically on judicious allocation of transmission resources, a portion of which should be used to ensure successful timing acquisition. In data-aided mode, optimum timing offset estimation depends not only on the mechanism used for energy capture and the acquisition algorithm employed to recover timing information, but also on the training sequence (TS) pattern from which the timing information is to be extracted. Furthermore, the transmission resources used for timing have to be balanced with that for conveying information messages in order to strike desirable tradeoffs between timing accuracy and information rate. In Part I of this paper, data-aided timing offset estimation is derived based on the maximum likelihood (ML) criterion, where only symbol-rate samples are needed for low-complexity receiver processing. To minimize the mean-square timing errors of these ML synchronizers while at the same time maximizing the average system capacity, TS design and transmit power allocation are investigated in this paper. The optimum training pattern and the number, placement, and power distribution between training and information-bearing symbols are formulated as a resource allocation optimization problem whose solution optimizes system-level performance with the minimum amount of resources consumed.

Adaptive frequency-domain equalization for single-carrier multiple-input multiple-output wireless transmissions

Channel estimation and tracking pose real problems in broadband single-carrier wireless communication systems employing multiple transmit and receive antennas. An alternative to estimating the channel is to adaptively equalize the received symbols. Several adaptive equalization solutions have been researched for systems operating in the time domain. However, these solutions tend to be computationally intensive. A low-complexity alternative is to adaptively equalize the received message in the frequency domain. In this paper, we present an adaptive frequency-domain equalization (FDE) algorithm for implementation in single-carrier (SC) multiple-input multiple-output (MIMO) systems. Furthermore, we outline a novel method of reducing the overhead required to train the proposed equalizer. Finally, we address the issues of complexity and training sequence design. Other computationally efficient adaptive FDE algorithms for use in SC systems employing single transmit and receive antennas, receive diversity, or space-time block codes (STBC) can be found in the literature. However, the algorithm detailed in this paper can be implemented in STBC systems as well as in broadband spatial multiplexing systems, making it suitable for use in high data rate MIMO applications.

Model-based channel estimation framework for MIMO multicarrier communication systems

The multicarrier modulation (MCM) using multiple antennas is a promising technique for broadband communications over mobile wireless channels. In this work, we investigate the channel estimation problem for the MCM system with multiple transmitter and receiver antennas. The difficulty of such a problem is that the number of the channel parameters increases proportionally with the number of transmitter antennas while the observations at the receiver do not. A model-based channel estimation framework is proposed to identify the multiple channels simultaneously. Based on this framework, we further discuss the identification condition and the training sequence design by taking into account both the model error and residual noise. Finally, we show the performance of the proposed model-based channel estimation scheme using two types of models, Fourier-transform-based model and polynomial model. We also show the system performance of two space-time codes using the proposed channel estimation algorithm.

Training Sequence Optimization in MIMO Systems With Colored Interference

We address the problems of channel estimation and optimal training sequence design for multiple-input multiple-output systems over flat fading channels in the presence of colored interference. In practice, knowledge of the unknown channel is often obtained by sending known training symbols to the receiver. During the training period, we obtain the best linear unbiased estimates of the channel parameters based on the received training block. We determine the optimal training sequence set that minimizes the mean square error of the channel estimator under a total transmit power constraint. In order to obtain the advantage of the optimal training sequence design, long-term statistics of the interference correlation are needed at the transmitter. Hence, this information needs to be estimated at the receiver and fed back to the transmitter. Obviously it is desirable that only a minimal amount of information needs to be fed back from the receiver to gain the advantage in reducing the estimation error of the short-term channel fading parameters. We develop such a feedback strategy in this paper.

On Optimal Training Sequence Design for Multiple-Antenna Systems Over Dispersive Fading Channels and Its Extensions

In this correspondence, previous work on (P,V,M) code sequences, which are sequences with a zero-correlation zone (ZCZ) that can be used to accurately and efficiently perform channel estimation in multiple-antenna communication systems, are noted. In addition, extensions of ZCZ sequence sets based on perfect sequences, almost-perfect sequences, and perfect arrays are presented. It is shown that those ZCZ sets based on perfect sequences/arrays are optimal with respect to theoretical bounds.

Training sequence design and channel estimation of ofdm-cdma broadband wireless access networks with diversity techniques

In this paper, an OFDM-CDMA system employing various diversity schemes is considered for a possible candidate of broadband wireless access networks and broadcasting applications. With an emphasis on a preamble design for multi-channel separation, we address a channel estimation based on the time-domain windowing and its imperfectness in OFDM-based multiple-antenna transmission systems. By properly designing each preamble for multiple antennas to be orthogonal in the time domain, the channel estimation can be applied to the HIPERLAN/2 and IEEE 802.11a standards in the case of more than two transmit antennas. Also, the effect of diversity techniques on the performance of OFDM-CDMA based broadband wireless access networks is investigated and the maximum achievable diversity gain for a two-path Rayleigh fading environment is evaluated. Simulation results show that the OFDM-CDMA system applying a space-time-frequency diversity with a full-rate full diversity code can give the diversity of D=4 and D=8 for both multi-user cases of maximum user and half user capacities, respectively.

Training sequence design for frequency offset and frequency-selective channel estimation

We consider the problem of data-aided frequency-offset and channel estimation in the case of frequency-selective channels. More precisely, we address the problem of training sequence selection with the goal of providing accurate frequency offset and channel estimates. Toward this end, we consider the Crame/spl acute/r-Rao bound (CRB), for which we derive a closed-form expression. Since the CRB is a complicated function of the training sequence and the channel parameters, a much simpler asymptotic CRB is derived. Two criteria for training sequence design based on the asymptotic CRB are proposed, and a minmax approach is presented to optimize them. Our main contribution is to show that a white sequence is minmax optimal for both criteria considered, and that the quest for a generally optimal sequence is hardly motivated.

Training-based channel estimation for multiple-antenna broadband transmissions

This paper addresses the problem of training sequence design for multiple-antenna transmissions over quasi-static frequency-selective channels. To achieve the channel estimation minimum mean square error, the training sequences transmitted from the multiple antennas must have impulse-like auto correlation and zero cross correlation. We reduce the problem of designing multiple training sequences to the much easier and well-understood problem of designing a single training sequence with impulse-like auto correlation. To this end, we propose to encode the training symbols with a space-time code, that may be the same or different from the space-time code that encodes the information symbols. Optimal sequences do not exist for all training sequence lengths and constellation alphabets. We also propose a method to easily identify training sequences that belong to a standard 2/sup m/-PSK constellation for an arbitrary training sequence length and an arbitrary number of unknown channel taps. Performance bounds derived indicate that these sequences achieve near-optimum performance.

Orthogonal space-time block codes: maximum likelihood detection for unknown channels and unstructured interferences

Space-time coding (STC) schemes for communication systems employing multiple transmit and receive antennas have been attracting increased attention. The so-called orthogonal space-time block codes (OSTBCs) have been of particular interest due to their good performance and low decoding complexity. In this paper, we take a systematic maximum-likelihood (ML) approach to the decoding of OSTBC for unknown propagation channels and unknown noise and interference conditions. We derive a low-complexity ML decoding algorithm based on cyclic minimization and assisted by a minimum amount of training data. Furthermore, we discuss the design of optimal training sequences and optimal information transfer to an outer decoder. Numerical examples demonstrate the performance of our algorithm.

Optimal binary training sequence design for multiple-antenna systems over dispersive fading channels

Accurate and efficient channel estimation is important in multiple-antenna communication systems in order to effectively reduce the mutual interference among different transmitting antennas. For a nondispersive channel that is modeled by a single tap for each transmitting and receiving antenna pair, the well-known Hadamard sequences can be applied to estimate the channel coefficients. However, for a dispersive channel that has multipath problem and is modeled by multiple taps, the optimal sequences must have both good autocorrelations and cross correlations. The existence of binary sequences with such good property is an open problem. In this paper, we devise an algorithm to find these sequence sets. These codes can be applied in multiple-antenna systems.

Regularity and strict identifiability in MIMO systems

We study finite impulse response (FIR) multi-input multi-output (MIMO) systems with additive noise, treating the finite-length sources and channel coefficients as deterministic unknowns, considering both regularity and identifiability. In blind estimation, the ambiguity set is large, admitting linear combinations of the sources. We show that the Fisher information matrix (FIM) is always rank deficient by at least the number of sources squared and develop necessary and sufficient conditions for the FIM to achieve its minimum nullity. Tight bounds are given on the required source data lengths to achieve minimum nullity of the FIM. We consider combinations of constraints that lead to regularity (i.e., to a full-rank FIM and, thus, a meaningful Cramer-Rao bound). Exploiting the null space of the FIM, we show how parameters must be specified to obtain a full-rank FIM, with implications for training sequence design in multisource systems. Together with constrained Cramer-Rao bounds (CRBs), this approach provides practical techniques for obtaining appropriate MIMO CRBs for many cases. Necessary and sufficient conditions are also developed for strict identifiability (ID). The conditions for strict ID are shown to be nearly equivalent to those for the FIM nullity to be minimized.

Multiuser channel estimation for detection of cochannel signals

Estimation of the channel impulse responses of multiple cochannel users is a key requirement of all multiuser detection and interference cancellation techniques, though little attention has been paid to the subject in the context of time-division multiple-access (TDMA) systems. This paper addresses a pilot-based MMSE technique for multiuser channel estimation in a TDMA system, and makes two key contributions. Firstly, it allows for time variation of the channels within and between training sequences, an essential feature in a multiuser environment even at moderate fading rates. Secondly, it addresses the design of training sequences for the multiple cochannel users.