While original network coding is proposed over the data link layer, recent work suggests that it can also be implemented on the physical layer. In fact it is more natural for wireless networks because of its omnidirectional transmission. In this paper, we investigate the symbol-error-rate (SER) for binary phase-shift keying (BPSK) and quadrature phase-shift keying (QPSK), but the approaches can be generalized to other constellation schemes. The closed-form SER results are derived for physical layer network coding over AWGN channels. The theoretical analysis is also validated by numerical simulation.