Abstract:
Space-time codes have attracted considerable attention in the area of wireless
communications due to their ability to exploit the enormous capacity promised by the
multiple-input multiple-output(MIMO) antenna system in comparison with a single antenna
system. The main idea behind MIOMO is to establish independent parallel channels between
multiple transmit and receive antennas. But in reality, the spatial correlation and the tap
correlation in the case of frequency selective channel degrade the performance of space -time
codes. For that reason, analytically derived pair wise error probability (PEP) expressions or
bounds are of great importance in analyzing the performance of space-time codes over
different fading environments. The main contribution of this thesis is to provide a broad
mathematical framework to derive PEP bounds, which ultimately pave the way to design
good codes.
A new analytical PEP upper bound is derived in this thesis for frequency selective Rician
fading channels with dependent fading coefficients and tap coefficients. The mathematical
analysis presented in this thesis in deriving the former bound is sufficiently general to handle
any form of fading environment except Nakagami-m fading model. With this bound the
impact of correlation towards the code performance is also discussed. An exact PEP
expression is also presented in the form of a definite integral, which doesn't have a closed
form while the closed form is presented when the codewords are taken from orthogonal
designs. Since the exact PEP expressions have complicated closed forms, an approximate
expression is presented which is valid for sufficiently high signal-to-noise ratios.
Although the Nakagami-m fading model is of practical importance compared to the other
models, the mathematical complexity is very high if one follows the same classical approach,
due to the unavailability of probability density function for a linear sum of several Nakagamim
random variables. There is not much literature available related to the properties of spacetime
codes due to this complexity. The thesis provides a new way of approach to the PEP
upper bound derivation in the case of Nakagami-m fading channels employing two transmit
antennas and subsequently it is extended to a more general case. Furthermore, exact PEP
expressions are also derived in the case of orthogonal designs. Validity of the bounds is
verified by the simulations at the latter part of the thesis.
