Multidimensional lattice constellations which present signal space diversity
(SSD) have been extensively studied for single-antenna transmission over fading
channels, with focus on their optimal design for achieving high diversity gain.
In this two-part series of papers we present a novel combinatorial geometrical
approach based on parallelotope geometry, for the performance evaluation of
multidimensional finite lattice constellations with arbitrary structure,
dimension and rank.

A complete evaluation of the benefits of cooperative diversity schemes does
not only include the outage and error rate performance but also the
second-order statistics of the achievable informationtheoretic capacity. In a
non-ergodic fading channel, the system is in outage when the destination cannot
decode the fixed-rate transmitted signal with negligible error probability.
Because of the Doppler effect, which is induced by the mobility of the wireless
nodes, these outage capacity events are correlated.

Monotonicity criteria are established for the generalized Marcum Q-function,
$\emph{Q}_{M}$, the standard Nuttall Q-function, $\emph{Q}_{M,N}$, and the
normalized Nuttall Q-function, $\mathcal{Q}_{M,N}$, with respect to their real
order indices M,N. Besides, closed-form expressions are derived for the
computation of the standard and normalized Nuttall Q-functions for the case
when M,N are odd multiples of 0.5 and $M\geq N$. By exploiting these results,
novel upper and lower bounds for $\emph{Q}_{M,N}$ and $\mathcal{Q}_{M,N}$ are
proposed.

Second order statistics provides a dynamic representation of a fading channel
and plays an important role in the evaluation and design of the wireless
communication systems. In this paper, we present a novel analytical framework
for the evaluation of important second order statistical parameters, as the
level crossing rate (LCR) and the average fade duration (AFD) of the
amplify-and-forward multihop Rayleigh fading channel.

We present novel exact expressions and accurate closed-form approximations
for the level crossing rate (LCR) and the average fade duration (AFD) of the
double Nakagami-m random process. These results are then used to study the
second order statistics of multiple input multiple output (MIMO) keyhole fading
channels with space-time block coding. Numerical and computer simulation
examples validate the accuracy of the presented mathematical analysis and show
the tightness of the proposed approximations.