Maximum Likelihood Frequency Offset Estimation Algorithms for OFDM Systems

• Main Authors: JiunHung Yu, 余俊宏
• Other Authors: Yu T. Su
• Format: Others
• Language: zh-TW
• Published: 2003
• Online Access: http://ndltd.ncl.edu.tw/handle/73794105001352323694

碩士 === 國立交通大學 === 電信工程系 === 91 === The frequency uncertainty associated with an orthogonal frequency division multiplexing (OFDM) signal, depending on the application, can be as large as many tens subcarrier spacings. This carrier frequency offset (CFO) uncertainty is usually partitioned into an integer part and a fractional part and must be compensated for before other synchronization and demodulation operations take place. This thesis presents complete optimal (in the generalized maximum likelihood sense) and near-optimal solutions for the above CFO compensation problem. Based on the generalized maximum likelihood (ML) principle and assuming the availability of pilot symbols, we derive efficient algorithms for estimating either the fractional part or the integer part of the CFO, assuming a fractional-then-integer frequency synchronization procedure. By deriving the ML fractional CFO estimates based on repetitive identical training symbols, we show that all previous correlation-based algorithms use only a part of the sufficient statistic. We then convert the problem of obtaining the ML solution from searching exhaustively over the entire uncertainty range to that of solving a spectrum polynomial whence greatly reduce the computational load. By properly truncating the spectrum polynomial, we obtain a closed-form expression for the corresponding zeros so that the root-searching procedure is much simplified. The complexity of locating the desired root is further reduced at almost no expense of performance degradation by an alternate algorithm that uses the fact that the solution is related to the root of a special factor of the polynomial. This alternate method is very attractive for its simplicity and excellent performance that, even at low signal-to-noise ratios (SNRs), is very close to the corresponding Cram\''r-Rao lower bound. We also present detailed analysis of the mean-squared error (MSE) performance and validate our analysis by simulations. The frequency ambiguity due to the presence of an integer CFO should be resolved once the fractional part has been estimated. We propose a special pilot symbols structure that can be used in both fractional and integer CFO estimations. A class of new ML integer CFO estimation algorithms is derived and the associated performance is presented. The pilot structure is a generalization of some earlier proposals and our derivation gives these proposal a unified theoretical foundation. To reduce the estimation complexity, we examine some variations of the ML estimate and suggest a two-stage method whose performance is almost as good as that of the optimal estimate.