This type of simple power supply is unsuitable for a radio transceiver.
You do not mention the current requirements for the radio, but from experience I expect that on receive it will be a couple of hundred milli-amps and on transmit several amps, depending on the transmitter power.
15 volts is rather high for a "12volt" radio, any fluctuations due to the mains supply could cook the radio.
You will need a lot of smoothing capacitance to eliminate the mains hum on transmit.
All in all, you need a proper stabilised power supply, not a simple capacitor filtered supply.
JimB