As the 3GPP Long Term Evolution (LTE) systems mature and more LTE mobiles become ubiquitous the Random Access Channel (RACH) will experience higher load. Understanding RACH capacity is of high importance for the 4G system planners. Capacity of the LTE RACH was analyzed in the past under the assumption of the ideal receiver with zero missed detection probability. In this work we assume realistic PRACH receiver under the assumption of AWGN channel which is specified as one of the test cases in the standard. We derive the expression for the preamble detection probability when r UEs are transmitting. Using this quantity we compute normalized RACH throughput for a single cell. We experiment with different parameters to illustrate their impact on RACH capacity. We show that the Gaussian channel can degrade ideal receiver capacity significantly (13%-66%) depending on the choice of system parameters.