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Adaptive beamforming using sparse arrays can alleviate system burden with a sub-Nyquist sampling rate while achieving high resolution. To process multi-dimensional signals without losing structural information, tensor models can be incorporated in the beamformer design. Unfortunately, existing tensor beamformers are only suitable for uniform arrays and cannot handle ambiguous sidelobes caused by sparse sensor deployment. In this article, we propose a sub-Nyquist tensor beamformer based on a coprimality constraint. Specifically, the signals received by the sparse subarrays of a coprime planar array are modeled as two sub-Nyquist tensors. To enhance the desired component of the sub-Nyquist tensor signals, we formulate a pair of tensor beamformer weights and investigate the principle of tensorial signal filtering. A coprimality-based combined distortionless response constraint is then imposed to jointly …