Necessary and sufficient conditions for perfect channel shortening and implications for interference mitigation

We explore the shortening of multiple channels arising from either over-sampling or from using multiple antennas between a single transmitter and receiver. Using terminology we develop, we give new necessary and sufficient conditions for perfect channel shortening (PCS). In an example, the perfect channel shortener's robustness against wide-band noise, narrow-band interferers and received signal SNR mismeasurement is compared to that of an imperfect channel shortener. The work concludes with a list of possible extensions of the results and future work.