We derive a jointly optimum space-time linear precoder and decoder for a multi-input multi-output (MIMO) channel with delay-spread, using the weighted MMSE criterion. We show that our solution provides a unified framework, from which several well-known designs as well as new designs can be developed. As an example, we show how to design a QoS based precoder and decoder that can optimally transmit and receive independent data streams, each with a different coding, modulation and target BER requirements.