Cross-Entropy-Based Sign-Selection Algorithms for Peak-to-Average Power Ratio Reduction of OFDM Systems

Sign-selection uses a set of subcarrier signs to reduce the peak-to-average power ratio (PAR) of orthogonal-frequency-division multiplexing (OFDM). However, the computational complexity (worst-case) is exponential in N, the number of subcarriers. Suboptimal sign-selection algorithms, achieving different tradeoffs between the PAR reduction and complexity, have thus been developed. For example, the derandomization method achieves high PAR reduction of O(log N) with relatively high complexity of O(N²). On the other hand, selective mapping (SLM) and partial transmit sequences (PTS) sacrifice the achievable PAR reduction for lower complexity. In this paper, we develop two new cross-entropy (CE)-based sign-selection algorithms. Our algorithms simultaneously updates the probabilities of the signs of all subcarriers. The first algorithm obtains a PAR lower than the above methods with a complexity level of O(N²). However, if the number of iterations is fixed, this algorithm obtains the same PAR reduction as derandomization, but with O(N log N) complexity. Practical PAR reduction algorithms require that the extra cost of PAR reduction must be small. Therefore, we propose the second algorithm, which adaptively adjusts the probability of "elite" samples, and stops whenever a PAR threshold is reached. Our second algorithm achieves up to 95 % complexity savings over the first (with only a 0.4-dB PAR reduction loss). The simulations confirm the complexity advantages of the proposed algorithms compared to SLM and derandomization.