Highest rate achievable by current DSP and A/D chips?
This is a pretty benign requirement. The Open Source software defined radio community does significantly more than 100 MS/s complex samples in software running on stock PC hardware. The samples come from stock SDR hardware.

However, you wouldn't be doing a 100s of taps long channel estimator / LMS filter at that rate.

It's impossible to estimate the computational complexity of your problem without at least knowing what kind of interferer you want to cancel. However, 10 MS/s really doesn't sound dramatic at all.