New Algorithms for Peak-to-Mean Envelope Power Reduction of OFDM Systems through Sign Selection

It has been shown that for multi-carrier signals with n subcarriers, the peak-to-mean envelope power ratio (PMEPR) of a random codeword generated from a symmetric spherical, QAM or PSK constellation is log(n) asymptotically. Motivated by this result, recently a coding scheme with a rate of 1-log_q(2) over a symmetric q-ary constellation has been proposed that achieves a PMEPR less than c log(n), where c is a constant. The idea of this coding scheme is to adjust the sign of subcarriers using so-called Chernoff bound-based derandomization algorithm. In this paper, using Chernoff bound and second order exponential Markov bound in conjunction with Gaussian approximation, two new variations of the derandomization algorithm are presented that yield roughly the same statistical PMEPR at the same rate. Moreover, it is rigorously established that the asymptotic PMEPR of both these algorithms is exactly the same as that of the original derandomization algorithm. Given a fixed amount of memory, our new algorithms can reduce the complexity up to one order, i.e. from O(n³) to O(n²). On the other hand, given a fixed computational complexity, our algorithms can reduce the required memory down to half.