To run the Windows Phone 8.x SDK on your PC, you'll have to upgrade to Windows 8. If you're looking to get started with the latest 8.1 SDK, you'll need the Windows 8.1 update with Visual Studio 2013 Update 2.
To run the emulators, you'll need to have Hyper-V active on your machine as it is required. If your machine doesn't support Hyper-V, the only options are to upgrade your device or run a Virtual Machine hosted in the cloud. Microsoft Azure provide great hosting for developer VMs at a relatively cheap cost.
The other option is to buy a Windows Phone 8 device as you don't require Hyper-V to debug your applications straight to a device. At the cost of some mid-range device, you'd be better actually getting a device.
I hope that helps :)