In this paper, we mainly study the symbol detection of the ambient backscatter, a novel communication mechanism that utilizes ambient radio frequency signals as both the power source and the symbol carrier to enable communications between devices. We derive the optimal detector with its closed-form bit error rate (BER), and thus give the detection that yields the balanced BER. We next design a suboptimal detector with a relatively simple BER expression that tells more insight of the system parameters. For the practical application, we propose a method to estimate the required parameters of the detectors, which heuristically derives another detection threshold. Simulations are then provided to corroborate the theoretical studies.