On multicarrier signals where the PMEPR of a random codeword is asymptotically logn

Multicarrier signals exhibit a large peak-to-mean envelope power ratio (PMEPR). In this correspondence, without using a Gaussian assumption, we derive lower and upper probability bounds for the PMEPR distribution when the number of subcarriers n is large. Even though the worst case PMEPR is of the order of n, the main result is that the PMEPR of a random codeword C=(c₁,...,c_n) is logn with probability approaching one asymptotically, for the following three general cases: i) c_i´s are independent and identically distributed (i.i.d.) chosen from a complex quadrature amplitude modulation (QAM) constellation in which the real and imaginary part of c_i each has i.i.d. and even distribution (not necessarily uniform), ii) c_i´s are i.i.d. chosen from a phase-shift keying (PSK) constellation where the distribution over the constellation points is invariant under π/2 rotation, and iii) C is chosen uniformly from a complex sphere of dimension n. Based on this result, it is proved that asymptotically, the Varshamov-Gilbert (VG) bound remains the same for codes with PMEPR of less than logn chosen from QAM/PSK constellations.