In this paper, we propose two auxiliary beam pair (ABP) schemes, i.e., auxiliary-half (AH) and auxiliary-full (AF) to improve the initial access (IA) mechanism in a millimeter wave (mmWave) device-to-device (D2D) network. In AH, a uniform linear array (ULA) is split equally to form two simultaneous beams at both transmitter (TX) and receiver (RX) for device detection. The detection process takes place through the generation of antenna scan sequences. On the other hand, AF utilizes the full antenna array to form one beam at a time at RX and TX and searches the same sector twice in a time division manner. We also employ beamforming (BF) technique in the already existing schemes in literature, i.e., oblivious directional neighbor discovery (ODND) and Polya’s Necklaces. We compare all the schemes and it is shown that both AH and AF exhibit a high dependence on the separation between the beam pair. We also prove the dependence of discovery delay (DD) on the signal-to-noise ratio (SNR) which is contrary to the worst-case DD upper-bound given by ODND. For a reasonable value of beam separation, high SNR threshold and high TX–RX separation, AH achieves a lower DD than all other schemes. Moreover, AF outperforms all other schemes in terms of probability of miss detection (PMD) and for a considerable beam separation, low SNR threshold and low RX–TX separation, it also achieves a lower DD than ODND, Polya’s Necklaces and AH.