The technology of smart antennas for mobile communication systems has received much interest in the last couple of years. A smart antenna combines antenna arrays with digital signal processing units in order to improve reception and emission radiation patterns dynamically in response to the signal environment. It can increase channel capacity, extend range coverage, steer multiple beams to track many mobiles, compensate aperture distortion or reduce multipath fading and co-channel interference. Of course, such a system is much more complex than traditional Omni-directional base station systems because it must include very powerful numeric processors. Even with the most powerful signal processors available today it is a very challenging task because the computational complexity of the operations involved becomes very large if the number of array elements increases. There will be a growing need for developing efficient algorithms.