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The 60 GHz unlicensed frequency band has been adopted to support high data rate WLAN applications. The problem of this frequency band is that the wireless signal is vulnerable to the shadowing of objects. Especially in indoor scenarios, humans may frequently block the signal paths that cause disconnections of devices. This problem can be mitigated by using multiple antennas that can create rich signal paths between the devices. The idea presented in this paper is to employ a distributed antenna system (DAS) architecture enabled by radio-over-fiber technology to alleviate the shadowing problem. In the DAS architecture, multiple remote antenna units (RAUs), each of them equipped with an antenna array, are connected with the same WLAN access points via optical fibers. But there are questions that need to be answered, including the beamforming strategy with multiple RAUs, and the placement and the required number of the RAUs. These questions are related to factors like room size, population density, etc. We discuss these questions in this paper and present our findings through theoretical models and extensive simulations, which can be referred to for practical implementations. We find that the proposed 60 GHz DAS can significantly improve the link connectivity. Even when only two RAUs are used, the signal coverage can be improved to an acceptable percentage in heavy shadowing scenarios.