Synthesizing Low Autocorrelation and Low PAPR OFDM Sequences Under Spectral Constraints Through Convex Optimization and GS Algorithm

Sequences with low autocorrelation (AC) and low peak to average power ratio (PAPR) are desired in many communication or signal processing applications. This work investigates the synthesis of OFDM sequences with the desired low AC and low PAPR under spectral constraints. The spectral constraints limit the maximum allowable power on each subcarrier to avoid interference on particular reserved bands and undesirable DC-offset. The first part of this work discusses the design of sequences with periodic AC property under spectral constraints. Specifically, we present a convex optimization method for synthesizing OFDM sequences with minimized peak sidelobe level (PSL) or weighted sum of sidelobe levels (WSSL) of the periodic AC function within specified time lags. The design objective to be minimized can also be a certain convex function of the sequence AC sidelobes. Furthermore, we present methods based on Gerchberg-Saxton (GS) algorithm to decrease the PAPR of the sequences, while maintaining the optimized AC characteristic. The second part of this work investigates the aperiodic AC under spectral constraints. In this case, the optimal sequence design problem is nonconvex. By relaxing the nonconvex problem to a convex problem, we provide lower bounds for PSL and WSSL of the aperiodic AC function. Based on the optimal solution for the relaxed convex problem, we present an efficient algorithm to find sequences with low PAPR and near-optimal aperiodic AC property while the spectral constraints are satisfied.