Minimization of PAPR for DFT-Spread OFDM With BPSK Symbols

In this paper, the problem of reducing the peak-to-average power ratio (PAPR) of a discrete Fourier transform spread orthogonal frequency-division multiplexing signal is considered for the transmission of BPSK symbols. In particular, a joint optimization of the constellation-rotation angle and the pulse-shaping vector is conducted with or without the allocation of additional sub-carriers. To avoid the exponential complexity required to evaluate the PAPR, a computationally efficient upper bound on the worst-case PAPR is derived and adopted as the objective function. Unlike conventional upper bounds, the proposed upper bound exploits the structure in the relative phase among symbol waveforms and incorporates the constellation-rotation effect. The signal-to-interference-plus-noise ratio (SINR) at the output of a constellation-derotating matched filter is also derived along with a generalized Nyquist criterion and adopted as the inequality constraint function. Then, joint optimizations are conducted through numerical search for various signal parameters and target SINRs. Surprisingly, the optimal rotation angle is neither 0 nor π/2. It is shown that the proposed combinations significantly outperform the existing combinations of the rotation angle and the shaping vector when the signal is amplified by a nonlinear power amplifier.