itecture. corresponding antenna. Fig. 4.63 shows a basic implementation of an analog beamforming transmitter architecture. This architecture consists of only one RF chain and multiple phase shifters that feed an antenna array. The phased arrays have been used in practical systems (e.g., radar systems) for the past several decades. Beam steering was often carried out with a selective RF switch and fixed phase shifters. This concept is still used in mod- ern communication systems using advanced hardware and improved precoding techniques. These enhancements enable separate control of the phase of each element. Unlike tradi- tional passive architectures, the beam can be steered not only to discrete but virtually any angle using active beamforming antennas. Analog beamforming is performed in the ana- log domain at RF frequencies or an intermediate frequency. However, implementing multi-stream transmission with analog beamforming is a highly complex task. In order to calculate the phase shifts, a uniformly spaced linear array with element spacing is assumed. Considering the receive scenario, the antenna array must be in the far field of the incoming signal, SO that the arriving wave front is approximately planar. If the signal arrives at an angle O relative to the antenna boresight, the wave must travel an additional distance d sin 0 to arrive at each successive element. This translates to an element specific delay which can be converted to a frequency-dependent phase shift of the signal as = 2nd(sin A) 1. The frequency dependency translates into an effect called beam unevenness. The main lobe of an antenna array at a defined frequency can be steered to a certain angle using phase offsets calculated by the latter equation (see Fig. 4.63). If the 566 Chapter 4 antenna elements are now fed with a signal of a different frequency, the main lobe will swerve by a certain angle. Since the phase relations were calculated with a certain carrier frequency in mind, the actual angle of the main lobe shifts according to the current