See : https://en.m.wikipedia.org/wiki/Secure_voice

It's all about bandwidth. At a minimum cellular voice signals have 4.7 kilobits of bandwidth per second.

Plus the cell phone network and the cell phones themselves, work really really hard, at compressing that data stream for human voices only.

So if you're going to use some acoustic coupling to send data acoustically over the cellular network, you're not going to get 4.7 kilobits per second, you're going to get less than that.

Encrypting your voice stream, is going to take some bandwidth, so let's say there's a 10% overhead, so we're at about 4 kilobits per second of total voice bandwidth after encryption.

http://www.whence.com/minimodem/ is a neat program that does software audio encoding and decoding so you could run a virtual modem from your desktop or phone.

Here is a demonstration of the general concept: https://www.youtube.com/watch?v=uQqWHLZjOjA

https://spectrum.ieee.org/why-mobile-voice-quality-still-stinksand-how-to-fix-it

Here is some secure voice modulation demonstrations that you could use as a starting point: https://www.youtube.com/watch?v=BLKHf40K0Wk

This program does exactly what you want. Implement secure voice in software. You would just have to transmit this over your cell phone. It's possible this could be built out for Android for your specific use case, but right now it's built for generalized radio transmission. So you could build two of these, for either party. And connect via audio call over the cell phone. You just might not get as much bandwidth, and call quality as you want. You'd have to keep reducing the settings until it worked

https://github.com/aarmono/crypto_transceiver_instructions

One big obstacle, is you're going to have to do physical key exchange for your endpoints. If you use the internet for that key exchange, you might as well use encrypted voip.

Signal is a great example of this but I don't think you'll find any ways to do it non-VoIP.

https://en.wikipedia.org/wiki/Acoustic_coupler

Slap your phone in one of those bad boys and go to town with your TST 3550 or whatever.

As for cell phones, I don't think it's really supported. I'd recommend using a separate encrypted calling app, or getting a dedicated encrypted phone device.

non voip

I think this is not doable. You don't have access to the voice codec to start with, and the phone at the other end generally won't receive the bit stream coming out of it anyway. With a non-rooted phone it's hard to even get to the voice stream. You might be able to send subliminal encrypted text messages through a voice channel and that could be kind of cool, and hard to detect. That idea has been around for a while but I don't know of existing software that does it.

With VOIP, of course there are many encrypted systems available.

Added: also I assumed throughout that you meant present day mobile phones. With land phones at both ends, it may still be doable using dialup modems, but that was a 1990s thing and was pretty awful when you got down to it. It existed though.

Instead of fiddling with the limitation on Android set by Google, I think a custom crypto DAC/ADC would be far eaiser, though you need both hard and software knowledge to accomplish this. It also came with the added benefit of not processing cryptographic operations on a black box.

Still, I don't know what goal you want to achieve and threat model is. If you are just curious if this possible, the answer will be ye with tons of hops amd hacks. If you really want security, I will advise you go another route.

My understanding of the way a phone call works leads me to believe the data would not survive the dynamic compression done at the various transmission points like towers, relays, or the occasional satellite. If neither party is moving and the towers in use do not change in load, it might be possible, but at that point you're more tethered down than if you used a VPN.

there are some obscure hardware options for this but hardware based audio encryption is mostly just enterprise stuff, it's very difficult for a consumer to obtain

This should be possible to do it software, but I don't know about any apps or something else that deals with this. You would probably also need a rooted phone for it to work.

Not that I'm aware of phone calls traversed the cellular network and are uncrypted. Okay, well that's not exactly true. They are encrypted, but the cellular network has the decryption key. That way nobody on the air can listen to the call, but the cell company can record it.