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No, you do not have to get a wireless router if you have a router already. If you are buying a wireless router, that probably means you have to buy something that is wireless for your playstation. In that case, just buy a pair of powerline adapters.

Look at them here:
There is much less latency in powerline than wifi. Again, if you already have a router (just a wired on), purchase the powerline adapters that come in pairs. After that, then you can purchase the ones that come with only 1.

Watch this video just so you can get familiar with powerline: