  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.
