We present the joint maximum likelihood (ML) symbol-time and carrier-frequency offset estimator in orthogonal frequency-division multiplexing (OFDM) systems. Redundant information contained within the cyclic prefix enables this estimation without additional pilots. Simulations show that the frequency estimator may be used in a tracking mode and the time estimator in an acquisition mode.

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ML estimation of time and frequency offset in OFDM systems

The design and optimization of multicarrier communications systems often involve a maximization of the total throughput subject to system resource constraints. The optimization problem is numerically difficult to solve when the problem does not have a convexity structure. This paper makes progress toward solving optimization problems of this type by showing that under a certain condition called the time-sharing condition, the duality gap of the optimization problem is always zero, regardless of the convexity of the objective function. Further, we show that the time-sharing condition is satisfied for practical multiuser spectrum optimization problems in multicarrier systems in the limit as the number of carriers goes to infinity. This result leads to efficient numerical algorithms that solve the nonconvex problem in the dual domain. We show that the recently proposed optimal spectrum balancing algorithm for digital subscriber lines can be interpreted as a dual algorithm. This new interpretation gives rise to more efficient dual update methods. It also suggests ways in which the dual objective may be evaluated approximately, further improving the numerical efficiency of the algorithm. We propose a low-complexity iterative spectrum balancing algorithm based on these ideas, and show that the new algorithm achieves near-optimal performance in many practical situations

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Dual methods for nonconvex spectrum optimization of multicarrier systems

We present and analyze low-rank channel estimators for orthogonal frequency-division multiplexing (OFDM) systems using the frequency correlation of the channel. Low-rank approximations based on the discrete Fourier transform (DFT) have been proposed, but these suffer from poor performance when the channel is not sample spaced. We apply the theory of optimal rank-reduction to linear minimum mean-squared error (LMMSE) estimators and show that these estimators, when using a fixed design, are robust to changes in channel correlation and signal-to-noise ratio (SNR). The performance is presented in terms of uncoded symbol-error rate (SER) for a system using 16-quadrature amplitude modulation (QAM).

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OFDM channel estimation by singular value decomposition

Channel estimation techniques for OFDM systems based on a pilot arrangement are investigated. Channel estimation based on a comb type pilot arrangement is studied through different algorithms for both estimating the channel at pilot frequencies and interpolating the channel. Channel estimation at pilot frequencies is based on LS and LMS methods while channel interpolation is done using linear interpolation, second order interpolation, low-pass interpolation, spline cubic interpolation, and time domain interpolation. Time-domain interpolation is obtained by passing to the time domain by means of IDFT (inverse discrete Fourier transform), zero padding and going back to the frequency domain by DFT (discrete Fourier transform). In addition, channel estimation based on a block type pilot arrangement is performed by sending pilots in every sub-channel and using this estimation for a specific number of following symbols. We have also implemented a decision feedback equalizer for all sub-channels followed by periodic block-type pilots. We have compared the performances of all schemes by measuring bit error rates with 16QAM, QPSK, DQPSK and BPSK as modulation schemes, and multipath Rayleigh fading and AR based fading channels as channel models.

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Channel estimation techniques based on pilot arrangement in OFDM systems

The QRS complex is the most striking waveform within the electrocardiogram (ECG). Since it reflects the electrical activity within the heart during the ventricular contraction, the time of its occurrence as well as its shape provide much information about the current state of the heart. Due to its characteristic shape it serves as the basis for the automated determination of the heart rate, as an entry point for classification schemes of the cardiac cycle, and often it is also used in ECG data compression algorithms. In that sense, QRS detection provides the fundamentals for almost all automated ECG analysis algorithms. Software QRS detection has been a research topic for more than 30 years. The evolution of these algorithms clearly reflects the great advances in computer technology. Within the last decade many new approaches to QRS detection have been proposed; for example, algorithms from the field of artificial neural networks genetic algorithms wavelet transforms, filter banks as well as heuristic methods mostly based on nonlinear transforms. The authors provide an overview of these recent developments as well as of formerly proposed algorithms.

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The principles of software QRS detection

The use of multi-amplitude signaling schemes in wireless OFDM systems requires the tracking of the fading radio channel. The paper addresses channel estimation based on time-domain channel statistics. Using a general model for a slowly fading channel, the authors present the MMSE and LS estimators and a method for modifications compromising between complexity and performance. The symbol error rate for a 18-QAM system is presented by means of simulation results. Depending upon estimator complexity, up to 4 dB in SNR can be gained over the LS estimator.

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On channel estimation in OFDM systems

We present a multiuser synchronization scheme for tracking the mobile's uplink time and frequency offsets. It uses the redundancy introduced by the cyclic prefix and does not need additional pilots. We show performance results of an orthogonal frequency division multiplexing (OFDM)-based radio interface based on the universal mobile telecommunication system (UMTS) parameters. For a UMTS-typical mobile channel environment, the performance of a coherent system employing the scheme is virtually indistinguishable from the performance of a perfectly synchronized system. In a differentially modulated system, synchronization errors decrease the system performance by about 0.7 dB compared to a perfectly synchronized system.

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A time and frequency synchronization scheme for multiuser OFDM

In this paper we analyze the performance of three low-complexity channel estimators, based on the discrete Fourier transform (DFT), for orthogonal frequency-division multiplexing (OFDM) systems. Estimators of this type have been analyzed for discrete-time channels, and we extend this analysis to continuous-time channels. We present analytical expressions for their mean-squared error (MSE) and evaluate their complexity vs. symbol-error rate (SER) for 16-QAM. The analysis shows that this type of estimators may experience an irreducible error floor at high SNRs. However, in one of the three estimators the error floor can be eliminated while the complexity stays low and the performance is maximized.

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Analysis of DFT-Based Channel Estimators for OFDM

Simple analytical upper bounds, approximations and lower bounds on the error function Q(x) are presented and analyzed. A class of functions are given, where the choice of two parameters result in good upper bounds, lower bounds and approximations on Q(x) . The results are given in formulas, parameter tables and graphs. The approximations are suitable for programmable pocket calculators.

Per Ola Börjesson

Papers

ML estimation of time and frequency offset in OFDM systems

On channel estimation in OFDM systems

A time and frequency synchronization scheme for multiuser OFDM

Analysis of DFT-Based Channel Estimators for OFDM

Simple Approximations of the Error Function Q(x) for Communications Applications