1.5G Wireless Receiver and Transmitter 1.5W JBA-515

Yes, you can. Unless the bluetooth is built into a PA system, you will run into problems (see below). Anytime you use a wireless device with a guitar, you rob your precious tone. Your problem arises when your bluetooth device changes the EQ of your signal: you will not get true bypass like you get when you plug your guitar into a cable straight to an amp. You will also run into problems with the "input" side of things. Your bluetooth devices are set up to receive up to a limit of an electrical signal. ---Ever heard someone yell into a microphone or a telephone? Notice the distorted sound it makes? Same thing here. You will most likely have a distorted signal (especially if you use effects pedals). The range you are looking for might also run you into problems. The range on most bluetooth devices is 15 to 20ft. The longer the range, the more expensive.

The theoretical maximum bit rate can be calculated by solving for R from Eb/No = SW/NR where Eb is the energy per bit, No is the noise power per bit, S is the signal strength, W is the bandwidth, N is the noise power spectral density, and R is the bit rate. In practice, as Tigger also notes, it's a lot more complicated! For example, in a noisy or low signal environment, you might use error detecting/error correcting encoding (i.e. Viterbi or Reed/Solomon) to get a lower bit error rate, but you would then transmit more bits (the encoding bits) than you would for unencoded -- thus a lower effective bit rate. Entire books are devoted to this subject. Sklar's is one of the best, see first reference. To simplistically answer your question, power received is related to the gain of the receiving antenna, the power transmitted, the gain of the transmitting antenna, the distance, the wavelength, and the gain of the receiving antenna. See equation 5.13 in second reference. Pr = (PtGt/4piR^2)(lamda^2/4pi)Gr. In your example, all are constant except R^2. So received power decreases by the square of the distance. Since bit error rate is determined by Eb/No, insist that Eb/No, in the first equation, be held constant. Thus, your bit rate also decreases by the square of the distance.

The best way to do this is with remote control modules. This would save you a lot time and money on FCC certification fees. You can get modules for 420 MHz, 920MHz. depending on your location would determine the frequency.