The minimum output energy (MOE) receiver has been developed for multiuser detection when multipath distortion is present. Its performance has been shown to be very close to the minimum mean-square-error (MMSE) receiver at high signal to noise ratio. However, due to the additive noise, the constraint vector required to construct the MOE receiver is a biased estimate of the channel vector. Thus, the MOE receiver exhibits degraded performance. To mitigate the noise effect, the constraint cost function is modified to obtain a modified MOE (MMOE) receiver in this paper, leading to a significantly improved channel estimate and detection performance. It is also revealed that the MMOE method converges to the well-known subspace method under certain conditions. In addition to the additive noise, imperfect estimation of the output data covariance matrix also causes performance loss and is studied in details based on perturbation theory.