This is quite easy to do, but don't expect a high bit-rate. If it is a string then make sure it's not a long one (the longer the higher is the error probability ). Lets assume we're working with the vital part of the ASCII code, namely up to character number 127, then all you need is 7 bits per character. Transform this character into bits and modulate those bits using QFSK (there are several modulations to choose from, frequency shift based ones have turned out to be the most robust I've tried from the conventional ones... I've created my own modulation scheme for this use case). Select the carrier frequencies as 18.5,19,19.5, and 20 kHz (if you want to be mathematically strict in your design, select frequency values that assure you both orthogonality and phase continuity at symbol transitions, if you can't, a good workaround to avoid abrupt symbols transitions is to multiply your symbols by a window of the same size, eg. a Gaussian or Bartlet ). In my experience you can move this values in the range from 17.5 to 20.5 kHz (if you go lower it will start to bother people using your app, if you go higher the average type microphone frequency response will attenuate your transmission and induce unwanted errors).
On the receiver side implement a correlation or matched filter receiver (an FFT receiver works as well, specially a zero padded one but it might be a little bit slower, I wouldn't recommend Goertzel because frequency shift due to Doppler effect or speaker-microphone non-linearities could affect your reception). Once you have received the bit stream make characters with them and you will recover your message
If you face too many broadcasting errors, try selecting a higher amount of samples per symbol or band-pass filtering each frequency value before giving them to the demodulator, using an error correction code such as BCH or Reed Solomon is sometimes the only way to assure an error free communication.
One topic everybody always forgets to talk about is synchronization (to know on the receiver side when the transmission has begun), you have to be creative here and make a lot a tests with a lot of phones before you can derive an actual detection threshold that works on all, notice that this might also be distance dependent
If you are unfamiliar with these subjects I would recommend a couple of great books:
- Digital Modulation Techniques from Fuqin Xiong
- DIGITAL COMMUNICATIONS Fundamentals and Applications from BERNARD SKLAR
- Digital Communications from John G. Proakis
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