# Bit loading and precoding for MIMO communication systems

HTML clipboardThis thesis considers the joint design of bit loading, precoding and receive filters for a multiple-input multiple-output (MIMO) digital communication system. Both the transmitter and the receiver are assumed to know the channel matrix perfectly. It is well known that, for linear MIMO transceivers, orthogonal transmission (i.e., diagonalization of the channel matrix) is optimal for some criteria such as maximum mutual information. It has been shown that if the receiver uses the linear minimum mean squared error (MMSE) detector, the optimal transmission strategy is to perform bit loading on orthogonal subchannels.

In the first part of the thesis, we consider the problem of designing the transceiver in order to minimize the probability of error given maximum likelihood (ML) detection. A joint bit loading and linear precoder design is proposed that outperforms the optimal orthogonal transmission. The design uses lattice invariant operations to transform the channel matrix into a lattice generator matrix with large minimum distance separation at a low price in terms of transmit power. With appropriate approximations, it is shown that this corresponds to selecting lattices with good sphere-packing properties. An algorithm for this power minimization is presented along with a lower bound on the optimization. Apparently, given the optimal ML detector, orthogonal subchannels are (in general) suboptimal.

The ML detector may suffer from high computational complexity, which motivates the use of the suboptimal but less complex MMSE detector. An intermediate detector in terms of complexity and performance is the decision feedback (DF) detector. In the second part of the thesis, we consider the problem of joint bit loading and precoding assuming the DF detector. The main result shows that for a DF MIMO transceiver where the bit loading is jointly optimized with the transceiver filters, orthogonal transmission is optimal. As a consequence, inter-symbol interference is eliminated and the DF part of the receiver is actually not required, only the linear part is needed. The proof is based on a relaxation of the discrete set of available bit rates on the individual subchannels to the set of positive real numbers. In practice, the signal constellations are discrete and the optimal relaxed bit loading has to be rounded. It is shown that the loss due to rounding is small, and an upper bound on the maximum loss is derived. Numerical results are presented that confirm the theoretical results and demonstrate that orthogonal transmission and the truly optimal DF design perform almost equally well. An algorithm that makes the filter design problem especially easy to solve is presented.

As a byproduct from the work on decision feedback detectors we also present some work on the problem of optimizing a Schur-convex objective under a linearly shifted, or skewed, majorization constraint. Similar to the case with a regular majorization constraint, the solution is found to be the same for the entire class of cost functions. Furthermore, it is shown that the problem is equivalent to identifying the convex hull under a simple polygon defined by the constraint parameters. This leads to an algorithm that produces the exact optimum with linear computational complexity. As applications, two unitary precoder designs for MIMO communication systems that use heterogenous signal constellations and employ DF detection at the receiver are presented.

Advisor:

School:Kungliga Tekniska högskolan

School Location:Sweden

Source Type:Doctoral Dissertation

Keywords:TECHNOLOGY; Information technology; Telecommunication

ISBN:978-91-7415-359-0

Date of Publication:01/01/2009