This paper studies a parameter estimation problem of networked linear systems with fixed-rate quantization. Under the minimum mean square error criterion, we propose a recursive estimator of stochastic approximation type, and derive a necessary and sufficient condition for its asymptotic unbiasedness. This motivates to design an adaptive quantizer for the estimator whose strong consistency, asymptotic unbiasedness, and asymptotic normality are rigorously proved. Using the Newton-based and averaging techniques, we obtain two accelerated recursive estimators with the fastest convergence speed of O(1/k), and exactly evaluate the quantization effect on the estimation accuracy. If the observation noise is Gaussian, an optimal quantizer and the accelerated estimators are co-designed to asymptotically approach the minimum Cramer-Rao lower bound. All the estimators share almost the same computational complexity as the gradient algorithms with un-quantized observations, and can be easily implemented. Finally, the theoretical results are validated by simulations. (C) 2014 Elsevier Ltd. All rights reserved.