Study Of Parameter Estimation Algorithm Of Multidimensional Sinusoidal Signal

The problem of multidimensional frequency estimation has received extensive attention for its widespread applications in numerous fields such as MIMO wireless channel sounding, mobile communications, radar, sonar, seismology and nuclear magnetic resonance spectroscopy. In this thesis, several frequency estimation algorithms are developed for two-dimensional (2-D) and multidimensional sinusoids. The main work can be summarized as:1. In chapter 2, some classical frequency estimation algorithms in the literature are discussed.2. In chapter 3, a new method for two-dimensional (2-D) frequency estimation of multiple damped sinusoids is proposed. The key idea is to combine the subspace-based technique and projection separation approach. The frequency parameters in the first dimension are estimated by the MUSIC-based method, and then a set of projection separation matrices are constructed by the estimated frequency parameters. In doing so, the frequency parameters in the second dimension can be separated by the constructed projection separation matrix. Finally, each frequency parameter in the second dimension is estimated by multiple 1-D MUSIC-based methods. The estimated frequency parameters in two dimensions are automatically paired.3. In chapter 4, a computationally efficient method that combines the subspace and projection separation approaches is proposed for multidimensional frequency estimation of multiple sinusoids. Without loss of generality, rearranging the multidimensional data as a series of two-dimensional (2-D) sliced matrices X1.2, frequency parameters in the first dimension are firstly estimated by using the conventional MUSIC method based on the covariance of the slice series. Subsequently, a set of projection separation matrices is constructed to separate and estimate the frequency parameters in the rth (r≥2) dimension through the 2-D sliced matrices X1.2. The estimated frequencies in the rth dimension are connected with the associated projection separation matrix derived from the frequency estimates in the first dimension, and thus the frequency pairing is automatically achieved.4. In chapter 5, a simple method based on the HOSVD decomposition that combines the subspace and projection separation approaches is proposed for multidimensional frequency estimation of multiple sinusoids. Frequency parameters in the first dimension are obtained by using signal subspace of the first dimension which is extracted by the HOSVD decomposition. Subsequently, a set of projection separation matrices is constructed to project the measure tensor and separate the components of the received tensor into single ones. And then, the signal subspace of each dimension of separated measure tensor is estimated by the HOSVD decomposition and the desired multidimensional frequency pairings are automatically obtained.5. Finally, a conclusion is drawn in chapter 6.