The part of the DSP chain that generates I/Q data is not the "interesting" part -- it's simply a quadrature DDS or CORDIC core, a multiplier, and some rudimentary FIR or CIC filters.
No, this is the most important part which defines technical specification of receiver (dynamic range, image rejection, spurious performance, DSP artifact presence, etc).
Simple DDC with simple CORDIC NCO and simple CIC+FIR leads to very-very dirty signal with bad spur performance, unwanted images, artefacts and dynamic range degradation.
But on the other side very good DDC and clean NCO is not simple at all, it is very hard to implement due to high speed requirements and a lot of required computational resources, in other words it requires a lot of high speed FPGA resources, such as hardware multipliers and more LE, in addition it leads to high current consumption. This is why AD936x uses simplified DSP - to reduce power consumption and simplify on-chip logic, just to get low cost at moderate output signal quality.
If you want to get the best output signal quality, to minimize unwanted spurs, images, DSP artifacts and improve dynamic range, you're needs to implement your own DSP on FPGA. Good DSP is not simple. For example, if you want to work with > 120 dB dynamic range, you will have problems with simple CORDIC NCO, because it's output will not be clean enough.
The same with filters. If you use CIC filter, you already get images. If you use simple 256-tap FIR it's not enough for 100 dB dynamic range. But 1024 and more tap filter requires much more computational resources. From my practice, FIR filter with 1024 tap and 18-bit coefficients is not enough for 120 dB dynamic range, so I'm using 24 bit coefficients, it barely covers 120 dB or even a little worse, but gives very significant improvements in comparison with 18-bit coefficients. All this eats a lot of FPGA resources.
If you working with > 120 dB dynamic range, you're needs about 24-bit data flow at full ADC speed, plus extended resolution for CIC and FIR accumulators to avoid overflow, so accumulators needs to be up to 96-bit and sometimes even more. All this is not easy at very high speed, because it involves very large amount of computation resources and they all needs to be synchronized and work in realtime at very high frequency.
If you simplify DSP it will have a lot of spurs, images and worse dynamic range, it's acceptable for cellular network, where these AD936x intended to work. But if you want to get better signal reception with less unwanted DSP artifacts and high dynamic range, it requires much more complicated DSP processing. So, AD936x is not an option and you will needs to implement your own DSP chain in a high speed FPGA which should have enough resources...
This is not simple task, because you're always need to sacrifice processing quality to keep within the available resources and processing frequency.