Recently, MIMO systems have been considered in wireless communication systems to increase the capacity. Linear Dispersion Codes are one group of Space-Time Codes with different design methods which are used in MIMO systems. Among them, PSBLLSTCs can provide various data rate and reliable performance in uncorrelated channels. In this book, the influence of unavoidable correlation in MIMO channels on the performance of PSBLLSTCs is studied. It is shown that by applying the optimal phase shifts among transmitted symbols in one layer or between different layers, performance degradation can be reduced. It has also been shown that the optimal phase shifts achieved for uncorrelated systems would not change in presence of correlation. In studying the performance of PSBLLSTCs, high decoding complexity of Maximum Likelihood detection was noticed. In this book, the method of Polar Sphere Decoding is exploited to simplify the decoding process and to provide the possibility of using Sphere Decoding in non-lattice configuration at the receiver side for PSBLLSTCs. It is presented that this decoding process is more than 6 times faster in comparison with ML decoding process.