Drawing inspiration from the advantages of intelligent reflecting surfaces (IRS) in wireless networks,this paper presents a novel design for intelligent omni surface (IOS) enabled integrated sensing and communications (ISAC). By harnessing the power of multi antennas and a multitude of elements, the dual-function base station (BS) and IOS collaborate to realize joint active and passive beamforming, enabling seamless 360-degree ISAC coverage. The objective is to maximize the minimum signal-tointerference-plus-noise ratio (SINR) of multi-target sensing, while ensuring the multi-user multi-stream communications. To achieve this, a comprehensive optimization approach is employed, encompassing the design of radar receive vector, transmit beamforming matrix, and IOS transmissive and reflective coefficients. Due to the non-convex nature of the formulated problem, an auxiliary variable is introduced to transform it into a more tractable form. Consequently, the problem is decomposed into three subproblems based on the block coordinate descent algorithm. Semidefinite relaxation and successive convex approximation methods are leveraged to convert the sub-problem into a convex problem, while the iterative rank minimization algorithm and penalty function method ensure the equivalence. Furthermore,the scenario is extended to mode switching and time switching protocols. Simulation results validate the convergence and superior performance of the proposed algorithm compared to other benchmark algorithms.

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