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In free-space optical communications that use both amplitude and phase data modulation (for example, in quadrature amplitude modulation (QAM)), the data are typically recovered by mixing a Gaussian local oscillator with a received Gaussian data beam. However, atmospheric turbulence can induce power coupling from the transmitted Gaussian mode to higher-order modes, resulting in a significantly degraded mixing efficiency and system performance. Here, we use a pilot-assisted self-coherent detection approach to overcome this problem. Specifically, we transmit both a Gaussian data beam and a frequency-offset Gaussian pilot tone beam such that both beams experience similar turbulence and modal coupling. Subsequently, a photodetector mixes all corresponding pairs of the beams’ modes. During mixing, a conjugate of the turbulence-induced modal coupling is generated and compensates the modal …