s with bit loading. the dominant path without any scattering. The condition number of this rank-one channel matrix equals infinity. However, the equivalent cross-polarized channel is a unitary matrix with entries - sin (11.1) The condition number of the unitary matrix in Equation (11.1) is one. This transformation of condition is the key argument for usage of XPD antennas in cellular systems. In reality, factors such as azimuth displacement make the XPD channel matrix nonunitary but still considerably reduce the condition number of the channel. Figure 11.27 shows a comparison of the measured condition numbers between XPD and copolarized antenna measurements. It is observed that, on median, the condition number of the channel reduces from 4 to approximately 2.5 with XPD antennas. 11.4.3.3 SVD Precoding SVD precoding of the MIMO channel matrix is known to be a simple capacity- achieving strategy for a MIMO channel with fixed transmit power constraint. We show the results with this precoding technique in Figure 11.28 and compare them to dual-stream equal power allocation (EPA). In the result, we first observe that for MMSE EPA, XPD antennas always outperform copolarized antennas by approxi- mately 20% at 30 dB. The gains with SVD precoding gains are also consistent at all © 2009 by Taylor & Francis Group, LLC Early Real-Time Experiments and Field Trial Measurements SNRs. With SVD precoding, XPD antennas are better than copolarized antennas by 10%. 11.4.3.4 Spatial Water Filling SVD precoding, along with spatial water-filling power allocation, has been shown to be the capacity achieving strategy for a transmitter with sum transmit power constraint. Here, prior to the SVD operation, optimum power allocation for each stream is performed according to the water-filling solution [9]. This solution inher- ently includes adaptive single-stream or dual-stream mode selection. With SVD spatial water filling, we observe a crossover point at approximately 6 dB between XPD and copolarized antennas. Below this SNR, copolarized ant