The design and optimization of orthogonal frequency division multiplex (OFDM) systems typically take the following form: The design objective is usually to maximize the total sum rate which is the sum of individual rates in each frequency tone. The design constraints are usually linear constraints imposed across all tones. This paper explains why dual methods are ideally suited for this class of problems. The main result is the following: Regardless of whether the objective or the constraints are convex, the duality gap for this class of problems is always zero in the limit as the number of frequency tones goes to infinity. As the dual problem typically decouples into many smaller per-tone problems, solving the dual is much more efficient. This gives an efficient method to find the global optimum of non-convex optimization problems for the OFDM system. Multiuser optimal power allocation, optimal frequency planning, and optimal low-complexity crosstalk cancellation for vectored DSL are used to illustrate this point.
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