A low complexity multicarrier PAR reduction approach based on subgradient optimization

We introduce a novel subgradient optimization-based framework for iterative peak-to-average power ratio (PAR) reduction for multicarrier systems, such as wireless orthogonal frequency division multiplexing (OFDM) and wireline discrete multitone (DMT) very high-speed digital subscriber line (DMT-VDSL) systems. The proposed approach uses reserved or unused tones to minimize the peak magnitude of the DMT symbol vector where these tone values are iteratively updated through a subgradient search. The algorithms obtained through this framework have very simple update rules, and therefore, low computational complexities in general. Since the approach is based on the direct update of some frequency domain parameters, the power spectral density (PSD) level constraints that exist in the communications standards can easily be incorporated into the algorithms. This feature also enables simple compensation for the effects of transmit filter on PAR. Furthermore, we can locate the Active Set PAR reduction method for real baseband signals as a special case of the subgradient approach and provide its natural extension to handle complex baseband DMT signals. In addition to the peak level cost function, we also introduce the K-peak energy cost function which is also used to develop effective subgradient algorithms as illustrated by the simulation examples.

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