In this chapter, we describe a compact array antenna. Beamforming is achieved by tuning the load reactances at parasitic elements surrounding the active central element. The existing beam forming algorithms for this reactively controlled parasitic array antennas require long training time. In comparison with these algorithms, a faster beamforming algorithm, based on simultaneous perturbation stochastic approximation (SPSA) theory with a maximum cross-correlation coefficient (MCCC) criterion, is proposed in this chapter. The simulation results validate the algorithm. In an environment where the signal-to-interference ratio (SIR) is 0 dB, the algorithm converges within 50 iterations and achieves an output SINR of 10 dB. With the fast beamforming ability and its low power consumption attribute, the antenna makes the mass deployment of smart antenna technologies practical. To give a comparison of the beamforming algorithm with one of the standard beamforming algorithms for a digital beamforming (DBF) antenna array, we compare the proposed algorithm with the least mean square (LMS) beamforming algorithm. Since the parasitic array antenna is in nature an analog antenna, it cannot suppress correlated interference. Here, we assume that the interferences are uncorrelated.