Symbol Timing Estimation Research Articles

Joint Frequency and Symbol Synchronization Schemes for an OFDM System

This paper proposes two multi-stage joint symbol timing and carrier frequency synchronization schemes for an orthogonal frequency division multiplex (OFDM) system. Simultaneous estimation of symbol timing and frequency offset is derived from the maximum likelihood (ML) principle, assuming a cyclic prefix (guard interval) is inserted in each OFDM symbol. One of the proposed algorithms derives an initial frequency estimate in the first stage that reduces the frequency uncertainty to only two or three sub-carrier spacings. The timing information and a finer frequency estimate that has a resolution of a sub-carrier spacing are obtained in the second stage. The third stage provides an estimation for the residual fractional frequency error. The other algorithm bypasses the first stage for one can use the second stage alone to search for the timing and frequency offsets. However, the computing complexity of the second stage is higher than that of the first stage, thus the three-stage algorithm is a preferred choice unless the frequency uncertainty is small. Simulation results show that both algorithms yield excellent performance not only in white Gaussian channels but also in multipath fading channels.

Symbol timing estimation with CPM modulation

Symbol timing in continuous phase modulated signals is investigated making use of maximum likelihood estimation methods. Nondata-aided algorithms are proposed with a feedforward structure. They are suitable for digital implementation and can be employed with either full or partial response signaling. Multilevel symbol alphabets are allowed and the modulation index may be arbitrary. The performance is assessed by analysis and simulation. It turns out that full response schemes are comparatively easier to synchronize. Difficulties arise with partial response signaling especially with long frequency pulses.

A computationally efficient method of timing and phase estimation in TDMA systems using a preamble sequence

AbstractOptimum and near optimum methods of burst parameter estimation based on the discrete Fourier transform are presented. The methods are applicable to single sample per symbol demodulators when the burst preamble is chosen to be a discrete frequency component at one quarter of the symbol rate. The proposed methods do not require the squaring of the signal, and hence avoid the loss associated with squaring the noise components. The optimum method is shown to reach the Cramer‐Rao bound for symbol timing and carrier phase estimation for the chosen preamble, whereas the more computationally efficient method shows a loss of 1.0dB and yields information regarding the timing offset only. The performances of the two methods in the presence of carrier frequency offset and additive white Gaussian noise are analysed, and implementations are given together with a comparison of the respective computational complexities.

A fully digital feedforward MSK demodulator with joint frequency offset and symbol timing estimation for burst mode mobile radio

A strictly feedforward demodulator structure for minimum shift keying (MSK) modulation with joint nondata-aided symbol clock and frequency offset estimation is presented. Due to its feedforward operation, clock synchronization and frequency offset compensation are hang-up free, and the demodulator is well suited for a digital implementation. The sampled baseband signal is passed through a nonlinearity and smoothed by a digital filter. The magnitude of the filter output directly drives the clock recovery process. The phase of the smoothed signal is an estimate of the carrier frequency offset and is used for offset compensation. Following synchronization, the signal is demodulated by differentially coherent detection. The performance of the demodulator is assessed for the AWGN and the Rayleigh flat and frequency-selective fading channel by computer simulations.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

On the application of the Cramer-Rao and detection theory bounds to mean square error of symbol timing recovery

A modified Cramer-Rao bound is derived that takes account of the fact that the symbol timing estimate is restricted to a finite interval of one symbol duration. A detection theory bound is also applied to the symbol timing problem. Results obtained using the Cramer-Rao and detection theory bounds are compared. It is shown that the detection theory bound is superior to the traditionally used Cramer-Rao bound. In particular, the detection theory bound gives useful results for sharp pulse shapes and shows a dependence of the mean square error on the data sequence. It also yields meaningful results for small signal-to-noise ratios.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Low-overhead symbol timing and carrier recovery for TDMA portable radio systems

Simulation and experimental results for a hardware implementation of a low-overhead digital coherent burst demodulator for time-division multiple-access (TDMA) radio systems using short bursts are analyzed. This implementation is based on digitizing a receiving signal after a low-frequency IF amplifier and performing all demodulation functions using digital signal processing techniques. Demodulation with very low overhead for TDMA is made possible by storing a burst in memory. A novel forward loop plus backward loop structure performs carrier recovery. Symbol-timing and carrier-frequency-offset estimations are performed by block processes, using the error signal resulting from differential demodulation. Bursts as short as 32 symbols can be demodulated without overhead. Since the demodulator is entirely digital and has the potential for low-power VLSI implementation, it is suitable for a portable radio system. Other advantages of this implementation include the availability of a channel quality measure derived from symbol timing estimation and the possibility of providing differential detection when it is desirable.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Receiver Structures for Multi-h Signaling Formats

A method of utilizing the available communication bandwidth efficiently is provided by multi- h phase coding. A receiver structure for joint estimation of data, carrier phase, and symbol timing is derived based on ML estimation techniques and subsequently assessed analytically and by means of Monte Carlo simulation procedures. Results indicate that the receiver structure, although not strictly optimum, yields near-optimum performance on the additive white Gaussian noise channel.

Simultaneous Adaptive Estimation of Carrier Phase, Symbol Timing, and Data for a 49-QPRS DFE Radio Receiver

The use of adaptive decision feedback techniques in the joint estimation of data, carrier phase, and symbol timing is investigated for a 49-QPRS 90 Mbit/s digital radio. The performance of the carrier and timing recovery loops are analyzed, first in a multipathfree environment and then for the case of a multipath distorted signal and a fixed decision feedback equalizer. Finally, the joint problem of data recovery, estimation of carrier phase, and symbol timing for a

Joint Carrier Phase and Symbol Timing Recovery for PAM Systems

The detection of pulse amplitude modulation (PAM) carrier signals requires accurate symbol timing and carrier phase references. In most cases, it is desired to estimate these parameters directly from measurements on the received data signal. This paper adds to and unifies the theory of maximum likelihood [ML] estimation as applied to PAM timing and phase recovery. Several different estimation strategies are considered. Data-aided [DA] estimators are found which assume the transmitted data symbols are known at the receiver. Nondata-aided [NDA] estimators are found which require only knowledge of the statistics of the transmitted data symbols. Structures for estimation of symbol timing, carrier phase, and joint estimation of timing and phase are presented. The estimators are evaluated on the basis of their error variances. Relatively simple approximate expressions for these error variances are presented. These expressions allow the comparison of the effects of excess bandwidth, different modulation schemes, DA versus NDA recovery, and joint estimation versus estimation of only one parameter. A practical implementation of the ML estimator, termed a pseudo-maximum likelihood (PML) estimator, is proposed and analyzed. The performance of the PML estimator is shown to include a noise-independent, data-dependent jitter which dominates in many cases of practical interest.

Carrier and Bit Synchronization in Data Communication - A Tutorial Review

This paper examines the problems of carrier phase estimation and symbol timing estimation for carrier-type synchronous digital data signals, with tutorial objectives foremost. Carrier phase recovery for suppressed-carrier versions of double sideband (DSB), vestigial sideband (VSB), and quadrature amplitude modulation (QAM) signal formats is considered first. Then the problem of symbol timing recovery for a baseband pulse-amplitude modulation (PAM) signal is examined. Timing recovery circuits based on elementary statistical properties are discussed as well as timing recovery based on maximum-likelihood estimation theory. A relatively simple approach to evaluation of timing recovery circuit performance in terms of rms jitter of the timing parameters is presented.