Wireless communications are now playing a vital role in supporting a variety of voice and data services. However, the limitation of available radio frequency poses a major challenge to these systems. Consequently, approaches for enlarging the communications capacity are of great interest. One promising solution to the problem is to use the phased array antennas (or smart antennas). Research on adaptive beamforming algorithms has been carried out and various algorithms including blind and non-blind ones have been achieved. During the time I study at Information and Communications University, my main research area is smart antenna. So far, I have proposed several adaptive beamforming algorithms for smart antennas applied to the DS-CDMA system and the Orthogonal Frequency Division Multiplexing (OFDM) system, namely, the Least Mean Square algorithm with projection (PLMS), the Minimum Mean Square Error algorithm with projection (PMMSE), the Exponential Step size Least Mean Square algorithms (ES-LMS1 and ES-LMS2) for DS-CDMA system, and the LMS and MMSE algorithms for the OFDM system. Of the proposed algorithms, PLMS and PMMSE utilize the finite alphabet property of digital signals to simultaneously estimate the weight vector and the desired user signal as well. Therefore, they are applicable not only for Binary Phase Shift Keying (BPSK) modulation but also for other modulation techniques such as Quadrature Phase Shift Keying (QPSK) and Quadrature Amplitude Modulation (QAM). In addition, the PLMS and PMMSE algorithms are also not complex in terms of computational load. Thus, these two proposed algorithms are good choices for real time applications. One may know that since LMS algorithm is a member of the family of stochastic gradient algorithms, an appropriate choice of step size parameter is very important for the algorithm to converge. A small step size will ensure small misadjustments in steady state, but the algorithm will converge slowly. On the other hand, a large step size will provide faster convergence and better tracking capabilities, but will result in higher misadjustments. In other words, there need be a trade-off between the convergence speed and the steady-state misadjustments of the conventional LMS algorithm. The proposed ES-LMS1 and ES-LMS2 algorithms employ a time-varying step size whose construction is based on the norm of the gradient estimate at each iteration. As a consequence, the two proposed algorithms have a very strong capability of tracking the signal source as the direction of arrival (DOA) of the signal source is changed. Recently, OFMD [1]-[4] has proven to be a potential solution to the demands for high bit rate and large capacity in wireless communications. For combating co-channel interferences in wireless OFDM systems, I proposed two semi-bind beamforming algorithms based on the Mean Square Error (MSE) criterion. Let us call them the OFDM-LMS and OFDM-MMSE algorithms for convenience. In the proposed algorithms, the weight vectors are updated in the time domain. All the frequencydomain signals in the receiver will be converted into the time-domain signals by using appropriate procedures. Simulation results show that the proposed algorithms are able to extract the desired signal while they suppress other undesirable co-channel interferers.
