On bounds and algorithms for frequency synchronization for collaborative communication systems

Cooperative diversity systems are wireless communication systems designed to exploit cooperation among users to mitigate the effects of multipath fading. In fairly general conditions, it has been shown that these systems can achieve the diversity order of an equivalent MISO channel and, if the node geometry permits, virtually the same outage probability can be achieved as that of the equivalent MISO channel for a wide range of applicable SNR. However, much of the prior analysis has been performed under the assumption of perfect timing and frequency offset synchronization. In this paper, we derive the estimation bounds and associated maximum likelihood estimators for frequency offset estimation in a cooperative communication system. We show the benefit of adaptively tuning the frequency of the relay node in order to reduce estimation error at the destination. We also derive an efficient estimation algorithm, based on the correlation sequence of the data, which has mean squared error close to the Cramer-Rao Bound.Comment: Submitted to IEEE Transaction on Signal Processin

Optimal pilot placement for frequency offset estimation and data detection in burst transmission systems

In this letter, we address the problem of pilot design for Carrier Frequency Offset (CFO) and data detection in digital burst transmission systems. We consider a quasi-static flat-fading channel. We find that placing half of the pilot symbols at the beginning of the burst and the other half at the end of the burst is optimal for both CFO estimation and data detection. Our findings are based on the Cram´er-Rao bound and on empirical evaluations of the bit error rate for different pilot designs. The equal-preamble-postamble pilot design is shown to provide a significant gain in performance over the conventional preambleonly pilot design

Carrier Frequency Offset Estimation for OFDM Systems using Repetitive Patterns

This paper deals with Carrier Frequency Offset (CFO) estimation for OFDM systems using repetitive patterns in the training symbol. A theoretical comparison based on Cramer Rao Bounds (CRB) for two kinds of CFO estimation methods has been presented in this paper. Through the comparison, it is shown that the performance of CFO estimation can be improved by exploiting the repetition property and the exact training symbol rather than exploiting the repetition property only. The selection of Q (number of repetition patterns) is discussed for both situations as well. Moreover, for exploiting the repetition and the exact training symbol, a new numerical procedure for the Maximum-Likelihood (ML) estimation is designed in this paper to save computational complexity. Analysis and numerical result are also given, demonstrating the conclusions in this paper

Scattered Pilots and Virtual Carriers Based Frequency Offset Tracking for OFDM Systems: Algorithms, Identifiability, and Performance Analysis

In this paper, we propose a novel carrier frequency offset (CFO) tracking algorithm for orthogonal frequency division multiplexing (OFDM) systems by exploiting scattered pilot carriers and virtual carriers embedded in the existing OFDM standards. Assuming that the channel remains constant during two consecutive OFDM blocks and perfect timing, a CFO tracking algorithm is proposed using the limited number of pilot carriers in each OFDM block. Identifiability of this pilot based algorithm is fully discussed under the noise free environment, and a constellation rotation strategy is proposed to eliminate the c-ambiguity for arbitrary constellations. A weighted algorithm is then proposed by considering both scattered pilots and virtual carriers. We find that, the pilots increase the performance accuracy of the algorithm, while the virtual carriers reduce the chance of CFO outlier. Therefore, the proposed tracking algorithm is able to achieve full range CFO estimation, can be used before channel estimation, and could provide improved performance compared to existing algorithms. The asymptotic mean square error (MSE) of the proposed algorithm is derived and simulation results agree with the theoretical analysis