This paper investigates the antenna selection scheme choosing the antenna with the largest channel gain to the the cellular user for device-to-device (D2D) communication underlaying cellular networks. We derive an exact closed-form expression of the ergodic achievable rate and examine its asymptotic behavior in the high signal-to-noise ratio (SNR) regime. It is demonstrated that the high SNR approximation can be much improved by a higher transmit power ratio between the base station (BS) and the D2D transmitter in the small cell setting where all users are closely located. However, in the macro cell setting in which only the D2D terminals are fairly close, the influence of the transmit power ratio becomes insignificant. In addition, we present upper and lower bounds of the ergodic achievable rate. Based on these results, we illustrate that the D2D communication cannot help in the cellular network for elevating the rate when the transmit SNR at the BS grows high. If the BS SNR is lower, then the D2D communication can effectively increase the ergodic achievable rate. Numerical results are provided to justify the correctness of the expressions and the relevant performance analysis.