This paper investigates the outage probability of a wireless system with linear constrained minimum variance (LCMV) beamforming using a uniform linear array beamformer. LCMV beamforming is able to perfectly cancel a number of dominant interferers while other interferers remain. A simplified beamforming model is used to derive closed-form outage probability expressions considering the impact of LCMV beam patterns on various interferers. Fading statistics of Rayleigh, Rician, and Nakagami are used to characterize the desired signal, whereas interferers are assumed to be subject to Rayleigh fading. One important aspect of this paper is the consideration of the directions of arrivals (DOA) of the dominant interferers and the exact beam patterns in the outage performance evaluations of LCMV beamforming systems. Numerical results of the outage probability are presented to illustrate the impact of DOA's of the dominant interferers and the impact of different fading scenarios. The paper also presents performance comparison between LCMV beamforming and conventional beamforming considering different interference scenarios (DOA's of dominant interferers).