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Multi-carrier-based waveform design for directional modulation (DM) is studied, where simultaneous data transmission over multiple frequencies can be achieved, with given phase distribution at the main lobe and as random as possible over sidelobe regions for each frequency. The design can be implemented efficiently by the inverse discrete Fourier transform (IDFT) structure. However, the problem of multi-carrier design is the high peak-to-average-power ratio (PAPR) of the resultant signals, leading to non-linear distortion when signal peaks pass through saturation regions of a power amplifier. To solve the problem, the  $\text {PAPR}\leq \rho ~(\rho \geq 1)$  constraint is considered in the design, and a solution called wideband beam and phase pattern formation by Newton’s method (WBPFN) is proposed. The resultant beam patterns, phase patterns, and complementary cumulative distribution function (CCDF) of PAPR are presented to demonstrate the effectiveness of the proposed design.

Multi-Carrier Waveform Design for Directional Modulation Under Peak to Average Power Ratio Constraint