Energy conserving model for the channel power-gain in wireless multi-user downlink scenarios

Established models for the prediction of channel power gain in radio communication systems have got a slight drawback which grows into a real problem in a theoretical large system analysis of downlink scenarios, where the number of user terminals is allowed to grow unboundedly. The problem is that the model predictions of channel power gain do not take into account the existence of additional receivers. As the number of terminals grows unboundedly, the sum of the predicted receive powers increases unboundedly, and eventually becomes larger than the total transmit power. In a passive propagation medium - like air - such model errors conflict with the principle of conservation of energy, when applied to asymptotic large system analysis. We propose a simple generic modification which - while applicable to any of the existent channel power gain models - corrects this model error and is intended as a first step towards the provision of a channel power gain model that allows for a meaningful large system analysis. We present a fully worked out example which, besides providing interesting insight, is also intended to demonstrate that mathematical tractability is not seriously affected by the proposed modification.