Grassmann quantization for precoded MIMO systems
It is projected that future mobile cellular networks will carry traffic that is Internet intensive and capacity hungry. A bottleneck in providing such capacity is the limited availability of spectrum and power along with the random fluctuations in the propagation medium. Using antenna arrays at the transmitter and at the receiver and creating a multiple-input multiple-output (MIMO) wireless channel for data transmission has emerged as a candidate for improving the performance of wireless networks. The wireless propagation medium for a signal transmitted from an antenna array may be modelled as a matrix, called the channel matrix. The knowledge of the channel matrix may be used at the transmitter to signifi- cantly improve system performance. Unfortunately, in many wireless systems, the transmitter may not have access to this channel knowledge and will rely on feedback of quantized channel information from the receiver. This feedback consumes a part of the capacity available for data transmission from the receiver, thereby assigning a cost to the system performance. The objective of this dissertation is to analytically quantify the system performance as a function of this feedback cost. This dissertation formulates the problem of quantization of channel information in a non-Euclidean space called the complex Grassmann manifold. This formulation is novel and traditional signal processing tools and techniques do not extend naturally to the Grassmann manifold since it is not a vector space. The fidelity of channel information is then characterized as a function of the number of quantization levels. Using these results, the achievable signal-to-noise ratio and the outage probability of a MIMO beamforming system are expressed in terms of the feedback rate. In the general case of a precoded spatial multiplexing system or a space-time block coded system, the received signal strength is quantified as a function of the feedback rate. The bounds and approximations derived herein are validated to be tight under practical circumstances using simulation results, thus providing a performance benchmark. A sufficient condition is derived that will guarantee no loss in the diversity performance of precoded MIMO systems due to quantization of channel information.