To overcome spectrum congestion, a promising approach is to integrate sensing and communication (ISAC) functions in one hardware platform. Recently, metamaterial antennas, whose tunable radiation elements are arranged more densely than those of traditional multiple-input-multiple-output (MIMO) arrays, have been developed to enhance the sensing and communication performance by offering a finer controllability of the antenna beampattern. In this paper, we propose a holographic beamforming scheme, which is enabled by metamaterial antennas with tunable radiated amplitudes, that jointly performs sensing and communication. However, it is challenging to design the beamformer for ISAC functions by taking into account the unique amplitude-controlled structure of holographic beamforming. To address this challenge, we formulate an integrated sensing and communication problem to optimize the beamformer, and design a holographic beamforming optimization algorithm to efficiently solve the formulated problem. A lower bound for the maximum beampattern gain is provided through theoretical analysis, which reveals the potential performance enhancement gain that is obtained by densely deploying several elements in a metamaterial antenna. Simulation results substantiate the theoretical analysis and show that the maximum beamforming gain of a metamaterial antenna that utilizes the proposed holographic beamforming scheme can be increased by at least 50% compared with that of a traditional MIMO array of the same size. In addition, the cost of the proposed scheme is lower than that of a traditional MIMO scheme while providing the same ISAC performance.
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