A Training-Based Mutual Information Lower Bound for Large-Scale Systems

We provide a mutual information lower bound that can be used to analyze the effect of training in models with unknown parameters. For large-scale systems, we show that this bound can be calculated using the difference between two derivatives of a conditional entropy function. We provide a step-by-step process for computing the bound, and apply the steps to a quantized large-scale multiple-antenna wireless communication system with an unknown channel. Numerical results demonstrate the interplay between quantization and training.