How to program a keyless entry for your miata?

I just bought a keyless remote for a 2002 Mazda Miata. I bought the car from a dealer and the remotes were missing. The keyless remote came with instructions as follows. However they did not work for me and I never got the buzz sound at the end of step 4 d. I am now wondering if my Miata actually has the remote module system installed? If anyone can tell me how to verify or test the remote module system it would be appreciated. Anyway, if the folloing works for anyone I would be pleased to learn of it. 1. Begin with all keys out of the ignition. 2. Close all doors. 3. Open drivers door and leave open. 4. Perform the following steps within 24 seconds. a. Insert key into ignition and turn to ON (without cranking the engine). b. Turn key to OFF and remove from ignition. c. Repeat steps a. and b. two more times. d. Push driver door frame button three times. 5. Buzz sound or chime should be heard at this point signalling that the vehicle is now in programming mode. If not, then wait 40 seconds and return to step 4. 6. All transmitters need to be programmed at this time, including the old ones. Push any button on the first transmitter two times. A chime should sound signalling that the vehicle has accepted the new transmitter code. a. IF THERE IS ONLY ONE TRANSMITTER, press any button on the same transmitter twice until a chine sounds. Repeat this step one last time with the single transmitter for a total of three programmings. b. IF THERE ARE TWO TRANSMITTERS, press any button on the second transmitter twice until a chine sounds. Repeat this step one last time with the second transmitter for a total of three programmings. c. IF THERE ARE THREE TRANSMITTERS, press any button on the second and third transmitters twice (one after the other) until the chime has sounded for each of the three transmitters. 7. Push driver frame button one time. Two buzz sounds or chimes should be heard at this point signalling successful progamming. 8. Test transmitter(s) for function. Good luck.