| The research of this dissertation focuses on efficient carrier and symbol synchronization methods for digital receivers. We first deal with correcting sampling mismatches between the received samples and the transmitted symbols. An interpolation method using a trigonometric polynomial is devised for this purpose. Our analysis and simulations demonstrate that this trigonometric interpolation attains better performance than “conventional” interpolators employing algebraic polynomials, such as a Lagrange polynomial, while simultaneously reducing the required hardware. In addition, with just a slight modification to this method, the interpolator can achieve an arbitrary frequency response. To recover a synchronized sample from existing samples, given a timing offset, we can optimize this method such that the interpolation error in the recovered sample is minimized for that specific timing offset value. Using this optimization technique, the overall interpolation error is reduced. As for the implementation, the optimal interpolator does not require additional hardware when a lookup table is used for sine and cosine values. When high precision, high speed and a small table are desired, the trigonometric interpolator can be implemented using an anglerotation processor, which is also developed in this research. By decomposing the rotation into coarse and fine rotations, and by balancing the internal wordlength, based on the overall precision requirement, very good performance can be achieved using a very small ROM table and a few small array-multipliers. This structure also provides an efficient implementation of a phase derotator to compensate for carrier phase errors. Next, we present an efficient method for symbol timing and carrier phase estimation used in burst modems that transmit and receive packet data. A feedforward structure is proposed. A rectangular-to-polar convertor, which forms the bulk of the timing and phase estimator, is discussed. |
