First, we need to find a convenient way to model the changes in channel over time. In the description above, the matrix calculation and properties apply to a single tone in an OFDM system. For simplicity, we will continue to express the discussion in matrix framework. In a real OFDM system, every tone can be considered independently. To model the variation in a given channel, we choose an initial value and a final value for the channel matrix and linearly “morph” from the initial to the final channel over a selected period of time. This allows us to assess the quality of precoding for a changing channel. The approach is illustrated in FIG. 4A. The first channel realization is a 1×4 matrix shown on the left by circles. The final channel realization is shown on the right by squares. The lines indicate what the value of the channel is at any intermediate point in time. A similar approach can be used for high-dimensional matrices and complex-valued matrices.
FIG. 4A shows two 1×4 channels and their intermediate realizations as the channel moves from its initial to its final state. Using this approach for changing channels, the simulation tries to mimic the typical behavior of a MU system. Specifically: The system performs a channel sounding at an initial time and derives MU precoding matrices “Q” based on the channel state at this time. These precoding matrices are used for subsequent transmissions, even as the channel changes continuously. At any time, we can calculate the SINR from the knowledge of the channel and the precoding matrix that are in use at that time. The signal strength for user i can be calculated as:
Si=trace(Qi+Hi+HiQi)??(4)
While the interference experienced by user i can be calculated as:
