On the True Cramer-Rao Lower Bound for the DA Joint Estimation of Carrier Phase and Timing Offsets

The Cramer-Rao lower bound (CRLB) plays a pivotal role in parameter estimation theory, such as timing, frequency and phase synchronization. Therefore, it receives considerable attention in the literature. This paper concerns the CRLB for data-aided (DA) timing and/or phase recovery, i.e. the parameter synchronization is aided by a training sequence known to the receiver. For DA parameter synchronization, the CRLB typically varies with the training sequence. This indicates that different training sequences offer fundamental different performance. Therefore, it is very important to be able to compute the CRLB for any particular training sequence to understand the fundamental limit that a particular training sequence has. However, in the literature, the closed-form CRLB for an arbitrary training sequence is not available. In principle, it is possible to use brute-force numerical approach to compute CRLB for any given training sequence. Such brute-force computation involves evaluation of derivatives numerically and matrix inversion. Besides the computational complexity, brute-force approach does not provide any insight on the interaction between training sequence and the resultant CRLB. In the literature, the widely cited close-form data-aided CRLB for timing and phase recovering was derived under the assumption that the training sequence is independently identical distributed (i.i.d.) and the length of the training sequence is sufficiently long. We found that the CRLB for a particular training sequence can be significantly lower than that with the long i.i.d. assumption. Therefore, the widely cited data-aided CRLB actually does not give the fundamental limit for a particular training sequence. In this manuscript, we derive a closed-form formula for data-aided CRLB for timing and phase synchronization with respect to arbitrary training sequence. The bound illustrates the close relation between the training sequence and the fundamental limit on timing and phase synchronization. This bound provides additional insights on the sequence design. 2000 IEEE International Conference on Communication

Near Optimum Low Complexity Smoothing Loops for Dynamical Phase Estimation—Application to BPSK Modulated Signals

International audience—This correspondence provides and analyzes a low complexity, near optimum, fixed-interval smoothing algorithm that approaches the performance of an optimal smoother for the price of two low complexity sequential estimators, i.e., two phase-locked loops (PLLs). Based on a linear approximation of the problem, a theoretical performance evaluation is given. The theoretical results are compared to some simulation results and to the Bayesian and hybrid Cramér–Rao bounds. They illustrate the good performance of the proposed smoothing PLL (S-PLL) algorithm. Index Terms—Dynamical phase estimation, phase-locked loop (PLL), smoothing algorithm

Synchronization Techniques for Burst-Mode Continuous Phase Modulation

Synchronization is a critical operation in digital communication systems, which establishes and maintains an operational link between transmitter and the receiver. As the advancement of digital modulation and coding schemes continues, the synchronization task becomes more and more challenging since the new standards require high-throughput functionality at low signal-to-noise ratios (SNRs). In this work, we address feedforward synchronization of continuous phase modulations (CPMs) using data-aided (DA) methods, which are best suited for burst-mode communications. In our transmission model, a known training sequence is appended to the beginning of each burst, which is then affected by additive white Gaussian noise (AWGN), and unknown frequency, phase, and timing offsets. Based on our transmission model, we derive the Cramer-Rao bound (CRB) for DA joint estimation of synchronization parameters. Using the CRB expressions, the optimum training sequence for CPM signals is proposed. It is shown that the proposed sequence minimizes the CRB for all three synchronization parameters asymptotically, and can be applied to the entire CPM family. We take advantage of the simple structure of the optimized training sequence in order to design a practical synchronization algorithm based on the maximum likelihood (ML) principles. The proposed DA algorithm jointly estimates frequency offset, carrier phase and symbol timing in a feedforward manner. The frequency offset estimate is first found by means of maximizing a one dimensional function. It is then followed by symbol timing and carrier phase estimation, which are carried out using simple closed-form expressions. We show that the proposed algorithm attains the theoretical CRBs for all synchronization parameters for moderate training sequence lengths and all SNR regions. Moreover, a frame synchronization algorithm is developed, which detects the training sequence boundaries in burst-mode CPM signals. The proposed training sequence and synchronization algorithm are extended to shaped-offset quadrature phase-shift keying (SOQPSK) modulation, which is considered for next generation aeronautical telemetry systems. Here, it is shown that the optimized training sequence outperforms the one that is defined in the draft telemetry standard as long as estimation error variances are considered. The overall bit error rate (BER) plots suggest that the optimized preamble with a shorter length can be utilized such that the performance loss is less than 0.5 dB of an ideal synchronization scenario

Improved timing recovery in wireless mobile receivers

The problem of timing recovery in wireless mobile receiver systems is critical. This is partly because timing recovery functions must follow rapid parameter changes inherent in mobile systems and partly because both bandwidth and power must be conserved in low signal to noise ratio communication channels. The ultimate goal is therefore to achieve a low bit error rate on the recovered information for improving QoS provisioning to terminal mobile users. Traditional timing recovery methods have over-relied on phase-locked loops for timing information adjustment. However, associated schemes do not exploit code properties. This leads to synchronization difficulties in digital receivers separated from transmitters by lossy channels. In this paper we present a soft timing phase estimation algorithm for wireless mobile receivers in low signal to noise ratios. In order to develop a bandwidth and power efficient timing recovery method for wireless mobile receivers, a raised cosine filter and a multilevel phase shift keying modulation scheme are implemented and no clock signals are transmitted to the receiver. In the proposed method, the receiver exploits the soft decisions computed at each turbo decoding iteration to provide reliable estimates of a soft timing signal, which in turn, improves the decoding time. The derived method, based on sequential minimization techniques, approaches the theoretical Cramer-Rao bound with unbiased estimates within a few iterations.Key Words: discrete polyphase matched filters, maximum likelihood estimators, iterative turbo receivers, log-MAP b

Robust synchronization for PSK (DVB-S2) and OFDM systems

The advent of high data rate (broadband) applications and user mobility into modern wireless communications presents new challenges for synchronization in digital receivers. These include low operating signal-to-noise ratios, wideband channel effects, Doppler effects and local oscillator instabilities. In this thesis, we investigate robust synchronization for DVB-S2 (Digital Video Broadcasting via Satellite) and OFDM (Orthogonal Frequency Division Multiplexing) systems, as these technologies are well-suited for the provision of broadband services in the satellite and terrestrial channels respectively.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Data-Aided ML Parameter Estimators of PSK Burst Modems and Their Systolic VLSI Implementations

A high performance Universal Modem ASIC that supports several modulation types and burst mode frame formats is under development. Powerful and generic data-aided (DA) parameter estimators are necessary to accommodate many modes. In this paper we present an approximated maximum likelihood (ML) carrier frequency offset estimator, ML joint carrier phase and timing offsets estimator and their systolic VLSI implementations for PSK burst modems. The performances are close to the Cramer-Rao lower bounds (CRLB) at low SNRs. Compared with theoretical solutions, the estimators proposed here are much simpler and easier to implement by the current VLSI technology. The CRLB for DA estimations is discussed in some depth, some issues on training sequence design is also addressed in this work.Globecomm99</i

MIMO-OFDM communication systems: channel estimation and wireless location

In this new information age, high data rate and strong reliability features our wireless communication systems and is becoming the dominant factor for a successful deployment of commercial networks. MIMO-OFDM (multiple input multiple output-orthogonal frequency division multiplexing), a new wireless broadband technology, has gained great popularity for its capability of high rate transmission and its robustness against multi-path fading and other channel impairments. A major challenge to MIMO-OFDM systems is how to obtain the channel state information accurately and promptly for coherent detection of information symbols and channel synchronization. In the first part, this dissertation formulates the channel estimation problem for MIMO-OFDM systems and proposes a pilot-tone based estimation algorithm. A complex equivalent base-band MIMO-OFDM signal model is presented by matrix representation. By choosing equally-spaced and equally-powered pilot tones from sub-carriers in one OFDM symbol, a down-sampled version of the original signal model is obtained. Furthermore, this signal model is transformed into a linear form solvable for the LS (least-square) estimation algorithm. Based on the resultant model, a simple pilot-tone design is proposed in the form of a unitary matrix, whose rows stand for different pilot-tone sets in the frequency domain and whose columns represent distinct transmit antennas in the spatial domain. From the analysis and synthesis of the pilot-tone design in this dissertation, our estimation algorithm can reduce the computational complexity inherited in MIMO systems by the fact that the pilot-tone matrix is essentially a unitary matrix, and is proven an optimal channel estimator in the sense of achieving the minimum MSE (mean squared error) of channel estimation for a fixed power of pilot tones. In the second part, this dissertation addresses the wireless location problem in WiMax (worldwide interoperability for microwave access) networks, which is mainly based on the MIMO-OFDM technology. From the measurement data of TDOA (time difference of arrival), AOA (angle of arrival) or a combination of those two, a quasi-linear form is formulated for an LS-type solution. It is assumed that the observation data is corrupted by a zero-mean AWGN (additive white Gaussian noise) with a very small variance. Under this assumption, the noise term in the quasi-liner form is proved to hold a normal distribution approximately. Hence the ML (maximum-likelihood) estimation and the LS-type solution are equivalent. But the ML estimation technique is not feasible here due to its computational complexity and the possible nonexistence of the optimal solution. Our proposed method is capable of estimating the MS location very accurately with a much less amount of computations. A final result of the MS (mobile station) location estimation, however, cannot be obtained directly from the LS-type solution without bringing in another independent constraint. To solve this problem, the Lagrange multiplier is explored to find the optimal solution to the constrained LS-type optimization problem

A Useful Form of the Abel Bound and Its Application to Estimator Threshold Prediction

International audienceThis correspondence investigates the Abel bound in order to predict the estimators mean square error (mse) threshold effect. A tractable and computationally efficient form of this bound is derived. This form combines the Chapman–Robbins and the Cramér–Rao bounds. This bound is applied to a data-aided carrier frequency estimation problem for which a closed-form expression is provided. An indicator of the signal-to-noise ratio threshold is proposed. A comparison with recent results on the Barankin bound (Chapman–Robbins version) shows the superiority of the Abel-bound version to predict the mse threshold without increasing the computational complexity

Performance analysis of symbol timing estimators for time-varying MIMO channels

The purpose of this thesis is to derive and analyze the theoretical limits for estimatingthe symboltiming delayof Multiple-Input Multiple-Output (MIMO)systems. Two main N X M system models are considered, where N represents the number of transmit antennas and M denotes the number of receive antennas, the 2 X 2 system used by S.-A. Yangand J. Wu and the 4 X 4system used by Y.-C. Wu and E. Serpedin. The second model has been extended to take into account the symbol time-varying fading. The theoretical estimation limits are shown by several bounds: modified Cramer-Rao bound (MCRB), Cramer-Rao bound (CRB) and Barankin bound (BB). BB will be exploited to obtain accurate information regarding the necessary length of data to obtain good estimation. Two scenarios for synchronization are presented: data-aided (DA) and non-data-aided (NDA). Two models for the fading process are considered: block fading and symbol time-varying fading, respectively, the second case being assumed to be Rayleigh distributed. The asymptotic Cramer-Rao bounds for low signal-to-noise ratio (low-SNR) and for high-SNR are derived and the performance of several estimators is presented. The performance variation of bounds and estimators is studied byvarying different parameters, such as the number of antennas, the length of data taken into consideration during the estimation process, the SNR, the oversampling factor, the power and the Doppler frequency shift of the fading