Switching level optimization for adaptive modulation

Two formulations that are commonly used in the determination of the switching levels are the Torrance cost function and the Lagrangian optimization. From the Lagrangian optimization, it can be seen that the switching levels can be each separately related to the target bit error rate with the constraint that the average bit error satisfies the target bit error requirement. This provides a search direction for the optimum solution of the Torrance formulation. Also, it is verified that if the target bit error is neglected, the Torrance formulation can find the optimum solution for the possible lowest bit error rate. In this case, each switching level is only related to two adjacent modulation modes. Based on this relation, we approximate the Torrance formulation with a two-mode one-dimensional search problem. From this decomposition, we further develop a one mode cost function to evaluate the cost of using one specific modulation mode as a function of instantaneous SNR. Switching levels can be determined by simply comparing these one mode cost functions.