Ambient backscatter system (ABS) is a newly rising communication mechanism which enables battery-free devices to communicate with each other. Based on the ABS model, we use the energy detection method to detect the information bits transmitted from tag under the unknown source. It is known that for an ambient source with complex constellation, the outage probability of the asymptotic bit error rate (BER) is very hard to compute. Nevertheless, we here show that when source is restricted to real, such outage probability can be derived in closed form and would reflect certain insight for system design. Simulations are provided to corroborate the theoretical studies.