MIMO Systems with Precoding

Abstract

In Chap. 18, we have investigated the zero-forcing and the minimum mean squared error (MMSE) receiver, which are able to remove or at least minimize the inter-channel interference to the expense of a potential increase of the mean noise power at the receiver output. To maximize the channel capacity, we have already investigated a prefilter in Chap. 21, which acts as a power allocation filter at the transmitter. Now, we are going to consider prefilters also denoted as precoders to reduce inter-channel interference and thus move the receive filter in principle to the transmitter. As for single input single output wire-line and wireless systems, one motivation is to relocate the hardware complexity of the receiver to some extend to the transmitter, Fischer (Precoding and Signal Shaping for Digital Transmission. Wiley, New York, 2002 [1]), Joham (IEEE Trans. Signal Process. 53:2700–2712, 2005 [2]), Vu and Paulraj (IEEE Signal Process Mag 24:86–105, 2007 [3]). This strategy is advantageous in the downlink scenario from the base station to the user, where the receivers are the individual user terminals, which then could be less complex. In most cases, the resulting hardware increase of the base station transmitter can be afforded, because its cost is shared among the large number of the users. However, there is a significant burden, because precoding requires knowledge about the channel parameters at the transmitter side to be able to adjust the precoder. Consequently, the channel estimator, which is located at the receiver, has to sent appropriate channel parameters, e.g., the full channel matrix $\mathbf {H}$ to the transmitter via a feedback channel. This arrangement is thus denoted as closed loop scheme. Precoding is also used in the downlink of multi-user scenarios and described in Chap 24. Precoders, which do not require channel knowledge, are called space-time encoders, are open loop schemes, and discussed in Chap. 23.