Asymptotic probability bounds on the peak distribution of complex multicarrier signals without Gaussian assumption

Abstract

Multicarrier signals exhibit a large peak to mean envelope power ratio (PMEPR). In this paper, we derive the lower and upper probability bounds for the PMEPR distribution when entries of the codeword, C, are chosen independently from a symmetric q-ary PSK or QAM constellation, C /spl isin/ /spl Qscr/;/sup nq/, or C is chosen from a complex n dimensional sphere, /spl Omega//sup n/ when the number of subcarriers, n, is large and without any Gaussian assumption on either the joint distribution or any sample of the multicarrier signal. Even though the worst case PMEPR is of the order of n, the main result is that the PMEPR of a random codeword C chosen from /spl Qscr/;/sup nq/ or /spl Omega//sup n/ is log n with probability one, asymptotically. A Varsharmov-Gilbert (VG) style bound for the achievable rate and minimum Hamming distance of codes chosen from /spl Qscr/;/sup nq/, with PMEPR of less than log n is obtained. It is proved that asymptotically, the VG bound remains the same for the codes chosen from /spl Qscr/;/sup nq/ with PMEPR of less than log n.