Principles of Linear MIMO Receivers

Abstract

As depicted in the block diagram of Fig. 18.1, we consider a MIMO system with frequency flat and in general time-varying channel with channel matrix $\varvec{\mathrm {H}}(k)\,\epsilon \,\mathbb {C}^{N\mathrm {x}M}$, input signal vector $\varvec{\mathrm {s}}(k)\,\epsilon \,\mathbb {C}^{M\mathrm {x}1}$, noise vector $\varvec{\mathrm {n}}(k)\,\epsilon \,\mathbb {C}^{N\mathrm {x}1}$, and receive vector $\varvec{\mathrm {r}}(k)\,\epsilon \,\mathbb {C}^{N\mathrm {x}1}$. At the receiver, a linear filter described by a matrix $\varvec{\mathrm {W}}(k)\,\epsilon \,\mathbb {C}^{M\mathrm {x}N}$ is employed to obtain at its output a good replica $\varvec{\mathrm {y}}(k)$ of the transmit signal vector $\mathrm {\varvec{s}}(k)$. We assume that a channel estimator not shown in Fig. 18.1 has provided perfect channel state information so that the instantaneous channel matrix $\mathbf {H}(k)$ is known for every discrete-time instant k at the receiver.