In wireless communications, spectrum is a scarce resource and hence imposes a high cost on the high data rate transmission. Fortunately, the emergence of multiple antenna system has opened another very resourceful dimension – space, for information transmission in the air. It has been demonstrated that multiple antenna system provides very promising gain in capacity without increasing the use of spectrum, hence leading to a breakthrough in the data rate of wireless communication systems. Since then, multiple-input multiple-output (MIMO) system has become one of the major focuses in the research community of wireless communications and information theory. The study of the performance limits of MIMO system becomes very important since it gives a lot of insights in understanding and design...[ Read more ]

In wireless communications, spectrum is a scarce resource and hence imposes a high cost on the high data rate transmission. Fortunately, the emergence of multiple antenna system has opened another very resourceful dimension – space, for information transmission in the air. It has been demonstrated that multiple antenna system provides very promising gain in capacity without increasing the use of spectrum, hence leading to a breakthrough in the data rate of wireless communication systems. Since then, multiple-input multiple-output (MIMO) system has become one of the major focuses in the research community of wireless communications and information theory. The study of the performance limits of MIMO system becomes very important since it gives a lot of insights in understanding and designing the practical MIMO systems.

There has been lots of literature studying the performance limits of MIMO system. Most of them are investigated in terms of channel capacity. However, channel capacity only characterizes the system performance when the block length of the code is infinite. While it sheds some light on how the ultimate throughput of the system vary with different system parameters, it does not tell us the error probability when the block length is finite, which is an important measure of interest in practical system design. On the other hand, the study on the error probability or performance limits of MIMO system for finite block length is however relatively less extensive.

In this thesis, we aim to study on the performance limits of some MIMO systems, in terms of achievable throughput subject to a given error probability and a given finite block length. The achievable throughput is sort of an extension of capacity to the finite block length case. We focus in MIMO system with continuous channel inputs, i.e. the modulation is not discrete. To obtain the achievable throughput, we study the error probability of the optimal code, given the data rate, the finite block length and the channel condition, by deriving its upper bounds and lower bounds. These bounds correspondingly give us the bounds on the achievable throughput. The bounds we obtain not only tell us the achievable throughput numerically, but also exhibit some relations analytically and provide some insights to us.

We will focus mainly on the MIMO system with channel state information (CSI) at both transmitter (CSIT) and receiver (CSIR). The system with CSIR only will also be addressed in terms of capacity and achievable throughput, but less extensive on in-depth investigation and performance analysis. We study the achievable throughout in both single user and multiuser scenarios. During our derivation of the achievable throughput, we also obtain some interesting finding on the geometrical interpretation of the capacity of a single user MIMO Gaussian channel, by extending Shannon’s sphere packing approach to MIMO channel. To study the achievable throughput of the multiuser MIMO system, we choose a specific kind of system to investigate – namely, MIMO-Orthogonal Frequency Division Multiple Access (MIMO-OFDMA) system with zero-forcing space division multiple access (ZF-SDMA). The motivation of studying this particular type of system is its potential in the practical application, due to its significant capacity gain using multiuser diversity at the relatively low expense of complexity.