The PlayStation Gold headset is probably the only wireless headset which is directly compatible with PS3, PS4, PS5, Android, PC, Switch (Personally tested) Get hold of them before they are super rare. :
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Sony PlayStation Gold Wireless Stereo Headset 20th Anniversary Edition (3001078) | eBay
PS4 software update adds support for Sony's wireless 7.1 virtual surround headsets - CNET
PlayStation Gold Wireless Headset Review (2018): Finally Golden | WIRED
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PS3 PULSE Wireless Stereo Headset Elite Edition Unboxing (New PlayStation 3 Wireless Gaming Headset) - YouTube
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Leaked: Gold Wireless Stereo Headset for PlayStation 4, PlayStation 3, and PlayStation Vita
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Amazon.com: Gold Wireless Stereo Headset - PlayStation 4 : Wireless Stereo Headset: Video Games
Amazon.com: Gold Wireless Stereo Headset - PlayStation 4 : Wireless Stereo Headset: Video Games
Sony Gold PS4 Wireless Stereo Headset Review — Gadgetmac
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Comparison: Gold Wireless Headset vs Pulse Elite Edition Headset PS3/PS4 - YouTube
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Amazon.com: Gold Wireless Stereo Headset - PlayStation 4 : Wireless Stereo Headset: Video Games
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Sony Gold PS4 Wireless Stereo Headset Review — Gadgetmac
