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This study proposes a new technique for communicating over multiple-input multiple-output (MIMO) frequency selective channels. This approach operates by calculating the QR decomposition of the polynomial channel matrix at the receiver on the basis of channel state information, which in this work is assumed to be perfectly known. This then enables the frequency selective MIMO system to be transformed into a set of frequency selective single-input single-output systems without altering the statistical properties of the receiver noise, which can then be individually equalised. A like-for-like comparison with the orthogonal frequency division multiplexing scheme, which is typically used to communicate over channels of this form, is provided. The polynomial matrix system is shown to achieve improved performance in terms of average bit error rate results, as a consequence of time-domain symbol decoding.