Near optimal PRT set selection algorithm for tone reservation in OFDM systems

In the tone reservation (TR) scheme, it is known that finding the optimal peak reduction tone (PRT) set is equivalent to solving the secondary peak minimization problem. However, this problem cannot be solved for the practical number of tones because it is nondeterministic polynomial-time (NP)-hard. In this paper, two efficient methods for selecting a near optimal PRT set are proposed. The first method is a random search algorithm with reduced computational complexity based on the observation that the secondary peak value of the time domain kernel, which is obtained by inverse fast Fourier transforming the characteristic sequence of the PRT set, statistically tends to decrease as the variance of the time domain kernel decreases. The second method is a deterministic selection algorithm using the cyclic difference set. The near optimality of these methods is confirmed through the numerical analysis.