Cyclostationarity: half a century of research

A simple algorithm for detection of timing error of a synchronous, band-limited, BPSK or QPSK data stream is proposed. The algorithm requires only two samples per symbol for its operation. One of the two samples is also used for the symbol decision. Derivation of the s curve reveals a sinusoidal shape.

A BPSK/QPSK Timing-Error Detector for Sampled Receivers

A new class of fast-converging timing recovery methods for synchronous digital data receivers is investigated. Starting with a worst-case timing offset, convergence with random binary data will typically occur within 10-20 symbols. The input signal is sampled at the baud rate; these samples are then processed to derive a suitable control signal to adjust the timing phase. A general method is outlined to obtain near-minimum-variance estimates of the timing offset with respect to a given steady-state sampling criterion. Although we make certain independence assumptions between successive samples and postulate ideal decisions to obtain convenient analytical results, our simulations with a decision-directed reference and baud-to-baud adjustments yield very similar results. Convergence is exponential, and for small loop gains the residual jitter is proportional and convergence time is inversely proportional to the loop gain. The proposed algorithms are simple and economic to implement. They apply to binary or multilevel PAM signals as well as to partial response signals.

Timing Recovery in Digital Synchronous Data Receivers

The digital realization of timing recovery circuits for digital data transmission is considered. A digital algorithm is proposed that can be implemented very efficiently even at high data rates. The resulting timing jitter has been computed and verified by simulations. In contrast to other known algorithms, the one presented here allows free-running sampling oscillators and a novel planar filtering method that prevents synchronization hangups. >

Digital filter and square timing recovery

Many communication and control systems employ signal formats that involve some form of periodic processing operation. Signals produced by samplers, scanners, multiplexors, and modulators are familiar examples. Often these signals are appropriately modeled by random processes that are cyclostationary (CS), i.e., processes with statistical parameters, such as mean and autocorrelation, that fluctuate periodically with time. In this paper we examine two methods for representing nonstationary processes that reveal the special properties possessed by CS processes. These representations are the harmonic series representation (HSR) and the translation series representation (TSR). We show that the HSR is particularly appropriate for characterizing the structural properties of CS processes and that the TSR provides natural models for many types of communication signal formats. The advantages gained by modeling signals as CS processes rather than stationary processes is illustrated by consideration of the optimum filtering problem. We present general solutions for filters that minimize mean-square error for continuous-waveform estimation, and we discuss several specific examples for the particular case of additive noise. These examples demonstrate improvement in performance over that of filter designs based on stationary models for the signal processes.

Characterization of cyclostationary random signal processes

A new technique is presented for evaluating the performance of a popular type of timing recovery circuit for baseband synchronous pulse amplitude modulation (PAM) data signals. The timing circuit consists of a square-law device followed by a narrowband filter tuned to the pulse repetition frequency along with provision for reshaping the pulses entering the timing path (prefiltering). The output of the timing circuit is a nearly sinusoidal timing wave whose zero crossings indicate the appropriate sampling instants for demodulation of the PAM signal. For a random data sequence, the timing wave exhibits phase fluctuations which are strongly dependent on the pulse shapes entering the timing path and the passband shape of the narrow-band filter. Expressions for rms phase fluctuation in the timing wave as a function of the prefiltering and postfiltering characteristics of the filters preceding and following the square-law device are presented. These expressions have a form which is especially suitable for studying the case where the baseband PAM signal is band-limited to frequencies less than the pulse repetition frequency. A condition on prefiltering and postfiltering which gives error-free timing recovery is presented. Results obtained from some specific examples serve to illustrate several aspects of the timing recovery problem.

J. Bubrouski

Papers

Statistical Properties of Timing Jitter in a PAM Timing Recovery Scheme

Statistical properties of timing jitter in a PAM timing recovery scheme