This paper presents the optimum physical random access channel (PRACH) structure in terms of the number of control signaling bits accommodated and the transmission bandwidth based on the link budget in order to satisfy the coverage requirement for the single-carrier (SC)-FDMA based E-UTRA uplink. First, we present the design concept of the PRACH structure considering the purposes of the random access procedure in the E-UTRA. Simulation evaluations including a system-level simulation show that a PRACH comprising a 0.5-msec preamble sequence can convey a 6-bit control signal at the cell edge when the inter-site distance (ISD) is 500m under full channel load conditions with one-cell frequency reuse. It is also shown, however, that a PRACH longer than one-sub-frame, e.g., 1.0msec, is necessary to support the ISD of 1732m assuming the same conditions. We also show that the best transmission bandwidth for the PRACH is approximately 1.08-4.5MHz from the viewpoint of the misdetection probability, and a 1.08-MHz transmission bandwidth is suitable considering other aspects such as flexible resource assignment in the time domain and a small number of options in the transmission bandwidth.