When I see "channel shortening," I think of DFE coefficient calculations, regardless of the application. This is used in cases from simple DFE equalization to channel shortening for xDSL with DMT to lessen CP requirements or for RSSE in single-carrier systems. The point is not to actually do a DFE; rather, the point is to use the coefficient calculation and paradigm.
The classical DFE architecture is to have two filters: a feedforward (FF) filter and feedback (FB) filter with a slicer after the FB subtraction and decision-directed feedback passed through the FB filter. The intent is to use a FF filter to compress the residual channel response into a smaller number of taps than you started with. For DFE applications, the intent is also to transform a possibly non-mininum phase response to minimum phase to reduce error propagation. The desired structure is to have a FF filter that is (close to) all-pass and simply transforming phase, while the FB taps of the DFE represent the residual channel. That said, the concept of compressing the channel into a shortened response can generalize to the case where the FF filter is not all-pass. In this case, it looks more like a FF equalizer for a partial-response system.
I suggest investigating DFE coefficient calculation and motivations to see approaches for channel shortening. It may also be instructive to look at partial-response literature. In the case of PR, you may see descriptions of equalization to a predetermined response, but it can also be used more generally for compression of a response into a reduced number of taps.