A deterministic algorithm that achieves the PMEPR of c log n for multicarrier signals

Multicarrier signals often exhibit large peak to mean envelope power ratios (PMEPR) which can be problematic in practice. In this paper, we study adjusting the sign of each subcarrier in order to reduce the PMEPR of a multicarrier signal with n subcarriers. Considering that any randomly chosen codeword has PMEPR of log n with probability one and for large values of n, randomly choosing signs should lead to the PMEPR of log n in the probability sense. Based on the derandomization algorithm suggested in Spencer (1994), we propose a deterministic and efficient algorithm to design signs such that the PMEPR of the resulting codeword is less than c log n for any n where c is a constant independent of n. By using a symmetric q-ary constellation, this algorithm in fact constructs a code with rate 1 - log_q 2, PMEPR of c log n, and with simple encoding and decoding. We then present simulation results for our algorithm.