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Multiple signal representation (MSR) techniques have been used to reduce the high peak-to-average power ratios (PAR) of orthogonal frequency division multiplexing (OFDM) signals. These includes partial transmit sequences (PTS), selected mapping (SLM), selective scrambling and interleaving. All MSR techniques often improve the PAR statistics and are iterative in nature. The PAR reduction obtainable depends on the number of iterations performed, which also increases the complexity of the OFDM transmitter. However, a means to estimate the achievable PAR reduction for a given number of iterations has not been reported in the literature so far. This paper derives a lower bound on the achievable PAR when a MSR technique with a given complexity is used. Our analytical results show a clear asymptotic behavior of the PAR as the number of iterations is increased. Simulation results justify the significance and accuracy of the PAR bound derived.