## Detection and Precoding for Multiple Input Multiple Output Channels

### Detektion und Vorcodierung für die Mehrkanalübertragung

Band 9, Erlanger Berichte aus Informations- und Kommunikationstechnik, Herausgeber: A. Kaup, W. Koch, J. Huber. Shaker Verlag, Aachen, 2004. ISBN 3-8322-2916-7

Thesis PDF file,
Slides used in the presentation (German)
PDF file

### Abstract

New communication services continue to demand higher and higher data rates from the digital transmission system supporting them. The electromagnetic bandwidth available and the maximum radiated power are subject to fundamental physical constraints as well as regulations and therefore limited. The only way for the digital transmission system to increase the data rate available for reliable communications within these limitations is by using increasingly sophisticated signal processing and channel coding techniques.

In particular, in recent years it was realized that designing wireless
digital communication systems to more efficiently exploit the
*spatial domain* of the transmission medium, i.e., free space,
allows for a significant increase of spectral
efficiency [Foschini96,Foschini98,Telatar99]. This can be
done by employing several transmitting and receiving elements to
realize a single communication link. In other words, at the expense of
more advanced signal processing (and, obviously, more transmission
hardware, since several receive- and transmit-signal processing chains
have to be set up), the amount of information that can be transmitted
reliably in a fixed amount of electromagnetic spectrum and with fixed
total transmit power can be significantly increased. In principle this
increase is linear in the number of parallel physical subchannels that
can be established, which is equal to either the number of transmit or
the number of receive elements, whichever is smaller.

The signal processing and channel coding schemes underlying these techniques form the basis for several types of advanced communication systems, all of which can be described by a linear vector-valued model.

In this thesis we develop signal processing methods that can be applied for such ``multiple input multiple output channels'' (``MIMO channels'' for short).

In particular we only consider ``full-rate'' space-time transmission,
i.e., we strive to use all spatial dimensions in all time instants, as
in the scheme of [Golden99,Foschini99]. If some form of
redundancy is used in the spatial dimensions, one speaks of space-time
codes, which achieve so-called space-time-coding gain by spreading the
information to be transmitted over space *and* time, e.g.,
space-time trellis codes [Tarokh98] or space-time block codes
from orthogonal designs [Alamouti98,Tarokh99]. The exchange
enabled with these methods is known as the diversity-multiplexing
tradeoff [Zheng03], and in this terminology we only consider
schemes that achieve the full multiplexing gain.

Chapter 3 introduces some of the transmission systems for which the methods to be described later are applicable. In the subsequent chapters we concentrate on the wireless multiple antenna transmission system. A fundamental distinction can be made regarding whether channel state information is available to the receiver only, to the transmitter only, or to both. Another fundamental distinction, somewhat connected to the availability of channel state information, is whether joint processing of the signals is possible for receiving elements, the transmitting elements, or both. In particular, in so-called ``broadcast MIMO'' systems the receiving elements belong to physically seperate users of the communication system, which makes receiver-side cooperation impossible. In this case all processing is required to be performed at the transmitter.

The first strategies to be discussed in Chapter 4 are the so-called detection strategies, i.e., how the receiving side in the transmission system obtains estimates of the transmitted data. Apart from the traditional linear and nonlinear equalization techniques, for which some details to enhance performance are discussed, we will elaborate on the recently introduced lattice reduction-aided precoding scheme [Yao02]. We show how the latter scheme can be generalized in order to be applicable to MIMO systems with arbitrary numbers of dimensions, and discuss possible improvements to closer reach the performance of the optimum approach, maximum-likelihood estimation.

Following this discussion of receiver concepts, in Chapter 5 we look at transmitter-side processing options in order to simplify detection at the receiver. After a look at two linear schemes, we present an information-theoretic discussion of a nonlinear transmitter side concept for interference mitigation by precoding, and show how this concept can be implemented by a spatial variant of the well-known Tomlinson-Harashima [Tomlinson71,Harashima72] precoding method. This scheme allows for very power-efficient communication over the already mentioned MIMO broadcast channels. A generalization of the Tomlinson-Harashima approach leads us to ``vector precoding'', for which we can again use concepts similar to lattice reduction-aided detection to obtain a low-complexity transmitter architecture.

Whenever transmitter-side processing is studied, immediately the question of imperfect channel state information arises. Therefore, in Chapter 6 we take a closer look at the performance degradation of both the receiver-side as well as the transmitter-side methods when channel state information is unreliable.