FPGA Frequency Domain Based Beidou-3 B2a Coarse Acquisition Processor Using FFT
Not immediately an answer but I can't get a picture in comments. It may give you an idea of what it takes to implement a 32K point FFT. I just pushed a 32K streaming FFT through Vivado. These are the result for a xc7z020clg400-1 (synthesis only):


Vivado could not fit all memory in block rams so it started using LUTs as memories. 

As a background: the $40K was a quote from an IP provider to the company I worked for.