We should be able to build a complete, simple direct conversion receiver on a chip using current IC technology. The possible receive frequency would be limited by the IC technology used for the mixers. Every day, it seems, operating frequencies move a little higher, so we can count on regular improvements.
In an article published 11 years ago in QEX Magazine, Gerald Youngblood shows us that putting a whole radio on a chip would be easy.
In a conventional superhetrodyne receiver, you mix the local oscillator signal with the incoming RF to produce an intermediate frequency (IF). Then you amplify that as needed and detect the result. This is applicable to the detection of AM, FM, or SSB signals. In a software-defined radio (SDR), one technique uses a direct conversion (no IF), so the output of the mixer is the baseband signal. Here's an example that uses a low-pass filter to limit the passband to no more than 1.5kHz. Thus, the received signal bandwidth is 14MHz to 14.0015MHz
Unfortunately, this simple receiver would also receive 13.9985MHz to 14MHz just as well. This is the image frequency (band). To work around this and to avoid the need for super selective tunable filter networks at the front end or an IF amplifier section, an IQ converter section provides an excellent solution. IQ stands for in-phase and quadrature (shifted by 90° or sine and cosine signals). Using this quadrature sampling mixer section and two low-pass filters, we can get baseband signals that can be fed to two ADCs.
Once the signals are in the digital domain, further processing is done. In the original QEX article, Youngblood makes use of the sound card on a PC and available software to do the fast Fourier transform and inverse fast Fourier transform.
As an example of how simple some of this circuitry can be, Youngblood shows the front-end sampling quadrature detector.
There aren't very many parts, and the ones that are there are dirt cheap. Youngblood was using this as the basis for a SDR that could operate from 100kHz to 54MHz. He was also making a transmitter to go with it, but that part is easy — just a simple frequency synthesizer for the ham bands from 160m through 6m.
Here's one more look at a block diagram of an SDR, this time from an article in the March/April 2012 edition of QEX Magazine.
Again, we see that it's pretty simple. The whole thing calls out for fabrication on a chip.
Have you done any work on SDRs? How well did they work?