Optimal Training Sequences Research Articles

Optimal training sequences for MIMO systems under correlated fading

The optimal design of training sequences for channel estimation in multiple-input multiple-output (MIMO) systems under spatially correlated fading is considered. The channel is assumed to be a block-fading model with spatial correlation known at both the transmitter and the receiver. To minimize the channel estimation error, optimal training sequences are designed to exploit full information of the spatial correlation under the criterion of minimum mean square error (MMSE). It is investigated that the spatial correlation is helpful to decrease the estimation error and the proposed training sequences have good performance via simulations.

On channel estimation using optimal training sequences in Cyclic-Prefix-based Single-Carrier systems with Space-Time Block-Coding

In this paper, a new scheme that combines Space-Time Block-Coding (STBC) based on an Alamouti-like scheme and the Least Squares (LS) channel estimation using optimal training sequences in Cyclic-Prefix-based (CP)Single-Carrier (SC) systems is proposed. With two transmit antennas, based on Cramer-Rao lower bound for channel estimation, it is shown that the Periodic Complementary Set (PCS) is optimal over frequency-selective fading channels. Compared with the normal scheme without STBC, 3dB Mean Square Error (MSE) performance gains and fewer restrictions on the length of channel impulse response are demonstrated.

Optimal superimposed training for estimation of OFDM channels

We design an optimal superimposed training (SIT) scheme for orthogonal frequency division multiplexing (OFDM) systems. Linear minimum mean square error (MMSE) and least square (LS) channel estimator are developed. The proposed optimal SIT consists of two parts, optimal training sequences deduced with respect to the channel estimate's mean square error (MSE) and optimal power allocation between training and data derived by minimizing the averaged channel capacity lower bound. The relationship between bit error ratio (BER) and averaged capacity bound is investigated under the optimal SIT. Simulation results validate our optimum design.

MIMO ISI Channel Estimation Using Uncorrelated Golay Complementary Sets of Polyphase Sequences

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> In this paper, optimal training sequence design for multiple-input multiple-output (MIMO) intersymbol interference channels is addressed, and several novel low-complexity channel estimators are proposed, using uncorrelated Golay complementary sets of polyphase sequences.<footnoteref refid="fnote1"/><footnote id="fnote1"> <footnotepara>A polyphase sequence is a sequence of complex numbers, each of unit magnitude.</footnotepara> </footnote> The theoretical analysis and simulation show that, when the additive noise is Gaussian, the proposed best linear unbiased estimator achieves the minimum possible classical CramÉr–Rao lower bound (CRLB) if the channel coefficients are regarded as unknown deterministics. On the other hand, the proposed linear minimum mean-square error estimator attains the minimum possible Bayesian CRLB when the underlying channel coefficients are Gaussian and independent of the additive Gaussian noise. The proposed channel estimators not only achieve the best estimation performance but can also be implemented with low complexity via DSP or application-specified integrated circuit/field programmable gate array. This has been possible due to the special structures intrinsic to uncorrelated Golay complementary sets of polyphase sequences, which make the proposed channel estimators ready to use in the practical MIMO systems. </para>

Channel estimation for MIMO-OFDM systems in rapid fading channels

A channel estimation approach for orthogonal frequency division multiplexing with multiple-input and multiple-output (MIMO-OFDM) in rapid fading channels is proposed. This approach combines the advantages of an optimal training sequence based least-square (OLS) algorithm and an expectation-maximization (EM) algorithm. The channels at the training blocks are estimated using an estimator based on the OLS algorithm. To compensate for the fast Rayleigh fading at the data blocks, a time domain based Gaussian interpolation filter is presented. Furthermore, an EM algorithm is introduced to improve the performance of channel estimation by a few iterations. Simulations show that this channel estimation approach can effectively track rapid channel variation.

Effects of studying sequences of process-oriented and product-oriented worked examples on troubleshooting transfer efficiency

Whereas product-oriented worked examples only present a problem solution, process-oriented worked examples additionally explain the rationale behind the presented solution. Given the importance of understanding this rationale for attaining transfer, process-oriented worked examples would be expected to result in more efficient transfer. However, a previous study in the domain of electrical circuits troubleshooting suggested an expertise-reversal effect: Process information might initially impose an effective cognitive load and lead to higher efficiency but may become redundant and impose an ineffective load when training progresses, which hampers efficiency. The present study confirmed this hypothesis. The results are discussed in terms of theoretical and practical implications for the design of optimal training sequences for complex cognitive tasks.

Training Signal Design for Estimation of Correlated MIMO Channels With Colored Interference

In this paper, we study the problem of estimating correlated multiple-input multiple-output (MIMO) channels in the presence of colored interference. The linear minimum mean square error (MMSE) channel estimator is derived and the optimal training sequences are designed based on the MSE of channel estimation. We propose an algorithm to estimate the long-term channel statistics needed for the construction of the optimal training sequences. We also design an efficient scheme to feed back the required information to the transmitter where we can approximately construct the optimal sequences. Numerical results show that the optimal training sequences provide substantial performance gain for channel estimation when compared with other training sequences

Signature sequence and training design for overloaded CDMA systems

The focus of this paper is on training and signature sequence design in an overloaded synchronous CDMA system. The channel fading gains are assumed to be unknown and are estimated using training sequences. We derive a maximum-likelihood (ML) estimator and design sequences to minimize the mean-squared error (MSE) of the estimate. Two design scenarios are considered. One case assumes that the spreading sequences are fixed due to existing system constraints and optimal training sequences are designed using an iterative algorithm in order to minimize the MSE of the estimate. Performance of the iterative algorithm is examined using Welch-bound equality (WBE) sequences as the pre-designed spreading sequences. In the other scenario, spreading sequences and training sequences are designed jointly to minimize the MSE of the estimate. The jointly designed training and spreading sequences achieve optimum performance in the sense of minimizing the MSE. It is observed that when WBE sequences are used as spreading sequences the performance of the iterative algorithm is close to optimum, or even optimum, in certain situations

Training-based estimation of correlated MIMO fading channels in the presence of colored interference

In this paper, training-based estimation of correlated block fading channels in a multiple-antenna, multi-user environment is considered. The linear minimum mean squared error (LMMSE) estimator is presented first. The problem of optimally designing the training data set, so as to minimize the mean squared channel estimation error subject to a total transmit power constraint, is then addressed. The design is based on the assumption of the availability of the channel and interference second-order statistics at the transmitter. It is shown that the optimal transmission directions are dictated jointly by the eigen-decompositions of the channel and interference covariance matrices. Their roles, in the channel estimation and interference suppression tasks, respectively, are revealed in the optimal transmit beamformer structure. The simulation results demonstrate that the gain in the estimation performance from using the optimal training sequence increases considerably with increasing spatial fading correlation, especially in strong interference environments.

Optimal design of constant-modulus training sequences with constrained length

In this letter, we consider optimal training designs for multiple-antenna cyclic-prefix-based single-carrier transmissions over frequency-selective channels. Our objective is to find optimal training sequences such that the mean-squared error of least-squares channel estimates is minimized, under constraints on the power, length, and modulus of training sequences. A sufficient design criterion is proposed, based on which two classes of optimal designs are identified. It is shown that the second class includes the existing optimal Chu sequence designs as special cases

A New Method of Constructing a Set of Optimal Training Sequences in One-Dimensional CBSE

In this paper, a new algorithm for the optimal training sequence with respect to sequence length in 1-dimensional cluster-based sequence equalizers (1-D CBSE) is presented. The proposed method not only removes the step of random training sequence selection but also shortens the length of the selected training sequences. The superiority of the new method is demonstrated by presenting several simulation results of quadrature phase shift keying (QPSK) signaling schemes and related analyses.

Optimal training for MIMO frequency-selective fading channels

High data rates give rise to frequency-selective propagation effects. Space-time multiplexing and/or coding offer attractive means of combating fading and boosting capacity of multi-antenna communications. As the number of antennas increases, channel estimation becomes challenging because the number of unknowns increases, and the power is split at the transmitter. Optimal training sequences have been designed for flat-fading multi-antenna systems or for frequency-selective single transmit antenna systems. We design a low-complexity optimal training scheme for block transmissions over frequency-selective channels with multiple antennas. The optimality in designing our training schemes consists of maximizing a lower bound on the ergodic (average) capacity that is shown to be equivalent to minimizing the mean square error of the linear channel estimator. Simulation results confirm our theoretical analysis that applies to both single- and multicarrier transmissions.

A Time-Domain Approach for Channel Estimation in MIMO-OFDM-BasedWireless Networks

This paper addresses the problem of channel estimation for multiple-input and multiple-output orthogonal frequency division multiplexing (MIMO-OFDM)-based wireless networks with frequency-reuse. Firstly, the optimal time-domain training sequences are derived for the multiple cells with the same frequency group and a set of suitable sequences are also presented for practical implementation. Secondly, a low complexity iterative algorithm is combined with the time domain channel estimation to suppress the co-channel interferences (CCIs). The channel estimation method is applied to synchronous and asynchronous cellular and the MSE performance of the estimator is also analyzed. Simulation results demonstrate that the presented channel estimation approach can substantially suppress CCIs and outperform the conventional LS MIMO-OFDM channel estimation over multipath fading channels in multicell environments.

Parameter Acquisition Techniques for Multiuser Detection with ISI Cancellation in a Quasi-Synchronous Reverse Link MC-CDMA System

In a quasi-synchronous reverse link multicarrier code division multiple access system, the signal detection is vulnerable to the interference due to the insufficient guard interval. A multiuser detection with intersymbol interference cancellation is a potential solution to overcome this problem. In this paper, we proposes a parameter acquisition technique based on a specially designed training sequence for the receiver. The concerned parameters are the transformed signature sequences and the ISI generation sequences. We analyze a criterion for the training sequences to achieve the minimum mean square error and propose the systematic generation of the optimum training sequences. We also propose the noise variance estimator for providing information about noise variance to some classes of multiuser detection. Simulation results prove relevant benefits of the proposed techniques and give useful insights into the system designs.

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.

Symbol timing estimation in MIMO correlated flat‐fading channels

AbstractIn this paper, the data aided (DA) and non‐data aided (NDA) maximum likelihood (ML) symbol timing estimators and their corresponding conditional Cramer–Rao bound (CCRB) and modified Cramer–Rao bound (MCRB) in multiple‐input‐multiple‐output (MIMO) correlated flat‐fading channels are derived. It is shown that the approximated ML algorithm in References [4,13] is just a special case of the DA ML estimator; while the extended squaring algorithm in Reference [14] is just a special case of the NDA ML estimator. For the DA case, the optimal orthogonal training sequences are also derived. It is found that the optimal orthogonal sequences resemble the Walsh sequences, but present different envelopes. Simulation results under different operating conditions (e.g. number of antennas and correlation between antennas) are given to assess and compare the performances of the DA and NDA ML estimators with respect to their corresponding CCRBs and MCRBs. It is found that (i) the mean square error (MSE) of the DA ML estimator is close to the CCRB and MCRB, (ii) the MSE of the NDA ML estimator is close to the CCRB but not to the MCRB, (iii) the MSEs of both DA and NDA ML estimators are approximately independent of the number of transmit antennas and are inversely proportional to the number of receive antennas, (iv) correlation between antennas has little effect on the MSEs of DA and NDA ML estimators and (v) DA ML estimator performs better than NDA ML estimator at the cost of lower transmission efficiency and higher implementation complexity. Copyright © 2004 John Wiley &amp; Sons, Ltd.

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.

A Two-Dimensional Multipath Channel Estimator for CDMA Systems With Timing-Offset Errors

This letter proposes a two-dimensional pilot-aided channel estimator for multicarrier and single carrier cyclic prefix assisted code division multiple access systems in the presence of timing-offset errors. Using optimal training sequences with special cyclic correlation properties can minimize the timing offset errors. Optimal and binary sub-optimal training sequences are designed in this context. Both theoretic analysis and simulation studies demonstrate significant performance improvement for the proposed method over conventional frequency domain channel estimation methods.

Channel Estimation Using Implicit Training

In this paper, a new method to perform channel estimation is presented. It is shown that accurate estimation can be obtained when a training sequence is actually arithmetically added to the information data as opposed to being placed in a separate empty time slot: hence, the word implicit. A closed-form solution for the estimation variance is derived, as well as the Cramer-Rao lower bound. Conditions are derived for the training sequences that result in a channel estimation performance that is independent of the channel characteristics. In addition, estimation performance is shown to be independent of the modulation format. A procedure to synthesize optimal training sequences is presented, and the problem of synchronization is solved. The performance of the algorithm is then compared with other methods that use explicit training under GSM-like environmental conditions, and the new algorithm is shown to be competitive with these. Finally, comparisons are also carried out against blind methods over realistic bandlimited channels, and these show that the new method exhibits good performance.

Optimal training for block transmissions over doubly selective wireless fading channels

High data rates give rise to frequency-selective propagation, whereas carrier frequency-offsets and mobility-induced Doppler shifts introduce time-selectivity in wireless links. To mitigate the resulting time- and frequency-selective (or doubly selective) channels, optimal training sequences have been designed only for special cases: pilot symbol assisted modulation (PSAM) for time-selective channels and pilot tone-assisted orthogonal frequency division multiplexing (OFDM) for frequency-selective channels. Relying on a basis expansion channel model, we design low-complexity optimal PSAM for block transmissions over doubly selective channels. The optimality in designing our PSAM parameters consists of maximizing a tight lower bound on the average channel capacity that is shown to be equivalent to the minimization of the minimum mean-square channel estimation error. Numerical results corroborate our theoretical designs.