MPhil Thesis Presentation
Minimum Distance Based Linear MIMO Precoding: A Lattice Theoretic Approach

by Mr Victor Hei CHENG

 :  11 Jan 2013 (Fri)
 :  2:30pm
Venue  :  Room 2463, 2/F (Lifts 25-26), HKUST

Examination Committee
Prof Daniel PALOMAR, ECE/HKUST (Chairman)
Prof Wai Ho MOW, ECE/HKUST (Thesis Supervisor)
Prof Shenghui SONG, ECE/HKUST
Linear precoding is a practical scheme for improving the performance of a point-to-point multiple-input-multiple-output (MIMO) system, and has been studied intensively during the last few decades. In practical applications, the symbols to be transmitted are taken from a discrete alphabet, such as quadrature amplitude modulation (QAM), and it is of interest to find the optimal linear precoder for a certain performance measure of the MIMO channel.
In this thesis we study linear precoders for non-singular MIMO channel with additive white Gaussian noise, with lattice-type inputs where the transmitted symbols are crafted from an infinite lattice. The objective is to maximize the minimum distance of the received lattice points, where the precoder is subject to an energy constraint.

Using lattice theoretic tools, it is shown that the optimal precoder only produces a finite number of different lattices, namely perfect lattices, at the receiver. The well-known densest packing lattices are instances of perfect lattices. However it is analytically shown that the densest lattices are not always the solution. This is a counter-intuitive result at first sight, since previous work in the area showed a tight connection between densest packing lattices and minimum distance. Since there are only finitely many different perfect lattices, they can theoretically be enumerated off-line. A new upper bound on the optimal minimum distance is derived, which significantly improves upon a previously reported bound. Based on this bound, we propose an algorithm that finds the optimal precoders in the asymptotic case.
Finally the asymptotic result is applied to the finite alphabet cases to construct precoders and we improve upon them by adding lower rank perfect forms to generate a finite codebook. Simulation results showed that the proposed precoders perform extremely close to the optimal in the finite alphabet case as well and outperform all other competing schemes.

*** ALL ARE WELCOME !! ***