The performance of multiple input single output (MISO) broadcast channels is strongly dependent on the availability of channel side information (CSI) at the transmitter. In many practical systems, CSI may be available to the transmitter only in a corrupted and incomplete form. It is natural to assume that the flaws in the CSI are random and can be represented by a probability distribution over the channel. This work is concerned with two key issues concerning MISO broadcast systems with random CSI: performance analysis and system design. First, the impact of noisy channel information on system performance is investigated. A simple model is formulated where the channel is Rayleigh fading, the CSI is corrupted by additive white Gaussian noise and a zero forcing precoder is formed by the noisy CSI. Detailed analysis of the ergodic rate and outage probability of the system is given. Particular attention is given to system behavior at asymptotically high SNR. Next, a method to construct precoders in a manner that accounts for the uncertainty in the channel information is developed. A framework is introduced that allows one to quantify the tradeoff between the risk (due to the CSI randomness) that is associated with a precoder and the resulting transmission rate. Using ideas from modern portfolio theory, the risk-rate problem is modified to a tractable mean-variance optimization problem. Thus, we give a method that allows one to efficiently find a good precoder in the risk-rate sense. The technique is quite general and applies to a wide range of CSI probability distributions.

The performance of multiple input single output (MISO) broadcast channels is strongly dependent on the availability of channel side information (CSI) at the transmitter. In many practical systems, CSI may be available to the transmitter only in a corrupted and incomplete form. It is natural to assume that the flaws in the CSI are random and can be represented by a probability distribution over the channel. This work is concerned with two key issues concerning MISO broadcast systems with random CSI: performance analysis and system design. First, the impact of noisy channel information on system performance is investigated. A simple model is formulated where the channel is Rayleigh fading, the CSI is corrupted by additive white Gaussian noise and a zero forcing precoder is formed by the noisy CSI. Detailed analysis of the ergodic rate and outage probability of the system is given. Particular attention is given to system behavior at asymptotically high SNR. Next, a method to construct precoders in a manner that accounts for the uncertainty in the channel information is developed. A framework is introduced that allows one to quantify the tradeoff between the risk (due to the CSI randomness) that is associated with a precoder and the resulting transmission rate. Using ideas from modern portfolio theory, the risk-rate problem is modified to a tractable mean-variance optimization problem. Thus, we give a method that allows one to efficiently find a good precoder in the risk-rate sense. The technique is quite general and applies to a wide range of CSI probability distributions.