Enhanced-Accuracy, Low-Complexity Doppler-Shift and Doppler-Rate Estimators in Packet Transmission

Packet transmission of digital data is nowadays adopted in several wireless communications systems such as satellite time-division multiple access (TDMA) and terrestrial mobile cellular radio, just to mention a few. In those scenarios, the received signal may suffer from significant time-varying Doppler distortion due to relative motion between transmitter and receiver. This occurs, for instance, in the last-generation mobile-satellite communication systems based on a constellation of nongeostationary low-earth-orbit (LEO) satellites [1] and in millimeter-wave mobile communications for traffic control and assistance [2]. In such situations, carrier Doppler shift and Doppler rate estimation must be performed at the receiver for correct demodulation of the received signal. A number of efficient digital signal processing (DSP) algorithms have already been developed for the estimation of the Doppler shift affecting the received carrier [3], and a few algorithm for Doppler rate estimation are also available in the open literature [4], [5]. The issue of joint Doppler shift/rate estimation has been addressed as well, although to a lesser extent [6], [7]. In all of the papers above, the observed signal is either an unmodulated carrier, or contains pilot symbols known at the receiver. The most common burst format is the conventional preamble-payload arrangement, wherein all pilots are consecutive and they are placed at the beginning of the data burst. Other formats are the midamble as in the GSM system [8], wherein the preamble is moved to the center of the burst, or the so-called pilot symbol assisted modulation (PSAM) paradigm [9], where the set of pilot symbols is regularly multiplexed with data symbols in a given ratio (the so-called burst overhead). Data Aided (DA) algorithms, which exploit the information contained in the pilot symbols, are normally employed to attain good performance with small burst overhead. The recent introduction of efficient channel coding with iterative detection [10] has also placed new and more stringent requirements on receiver synchronization. The carrier synchronizer is requested to operate at a lower signal to noise ratio (SNR) than it used to be with conventional coding. In this work, we consider a different, non-conventional pilot arrangement that allows to achieve good carrier synchronization a low SNR. Specifically, the preamble is split in two sections of equal length that are placed at the beginning (preamble) and at the end (postamble) of each burst. As will be apparent in the sequel, this arrangement allows to increase the carrier synchronization parameter estimation accuracy for a pre-assigned burst overhead. This idea can be traced back to [9], although its full development has not, to the authors’ knowledge, been pursued as yet. We first outline the received signal model affected by Doppler distortions. Next, we present and analyze a low-complexity DA Doppler shift estimator. Two extensions of this algorithm for joint Doppler shift and Doppler rate estimation are then introduced, and finally, some conclusions are drawn. Expressions of the joint Cramér-Rao bounds for carrier phase/frequency offset and carrier phase/frequency offset/frequency rate-of-change are also given for the special preamble-postamble burst format.