text:
\section{Introduction}

The performance of wireless communications is severely degraded by
channel fading caused by multipath propagation and interference from
other users. Fortunately, multiple antennas can be used to increase
diversity to combat channel fading. Antenna diversity where
sufficiently separated or different polarized multiple antennas are
put at either the receiver, the transmitter, or both, has been
widely considered \cite{Paulraj}, \cite{Lek}. On the other hand,
multi-antenna channel fading can be beneficial since it can increase
the degrees of freedom of the channel and thus can provide spatial
multiplexing gain.
It is shown in \cite{FoschiniGans} that the spatial multiplexing
gain in a multi-input and multi-output (MIMO) Rayleigh fading
channel with $M$ transmit and $N$ receive antennas increases
linearly with $\min(M,N)$ if the channel knowledge is known at the
receiver. As MIMO channels are able to provide much higher spectral
efficiency and diversity gain than conventional single-antenna
channels, many MIMO schemes have been proposed, which can be
classified into two major categories: spatial multiplexing oriented
(e.g., Layered space-time architecture \cite{Foschini}), and
diversity oriented (e.g., space-time trellis coding \cite{Tarokh},
\cite{Yi}, and space-time block coding \cite{Alamouti},
\cite{Orthogonal}).

For a MIMO scheme realized by a family of codes \{$C(\rho)$\} with
signal-to-noise ratio (SNR) $\rho$, rate $R(\rho)$ (bits per channel
use), and maximum-likelihood (ML) error probability
$\mathcal{P}_e(\rho)$, Zheng and Tse defined in \cite{IEEErelay:DMT}
the spatial multiplexing gain $r$ as
$r\triangleq\lim_{\rho\rightarrow\infty} \frac{R(\rho)}{\log \rho}$
and the diversity gain $d$ as
$d\triangleq-\lim_{\rho\rightarrow\infty}
\frac{\mathcal{P}_e(\rho)}{\log \rho}$. Under the assumption of
independent and identically distributed (i.i.d.) quasi-static flat
Rayleigh fading channels where the channel state information (CSI)
is known at the receiver but not at the transmitter, for any integer
$r\leq \min(M,N)$, the optimal diversity gain $d^*(r)$ (the supremum
of the diversity gain over all coding schemes) is given by
\cite{IEEErelay:DMT}
\begin{equation}
\label{DMT} d^*(r)=(M-r)(N-r)
\end{equation}
provided that the code length $L\geq M+N-1$. The
diversity-multiplexing tradeoff (DMT) in (\ref{DMT}) provides a
theoretical framework to analyze many existing diversity-oriented
and multiplexing-oriented MIMO schemes. It indicates that the
diversity gain cannot be increased without penalizing the spatial
multiplexing gain and vice versa. This pioneering work has generated
a lot of research activities in finding DMT for other important
channel models \cite{IEEErelay:MAC}-\cite{IEEErelay:FDTCR} and
designing space-time codes that achieve the desired tradeoff of
diversity and multiplexing gain
\cite{IEEErelay:ODASC}-\cite{IEEErelay:RDTST}. The DMT analysis was
extended to multiple-access channels in \cite{IEEErelay:MAC}. The
automatic retransmission request (ARQ) scheme is shown to be able to
significantly increase the diversity gain by allowing
retransmissions with the aid of decision feedback and power control
in block-fading channels \cite{IEEErelay:ARQ}. The work in
\cite{IEEErelay:FDPRM} investigated the diversity performance of
rate-adaptive MIMO channels at finite SNRs and showed that the
achievable diversity gains at realistic SNRs are significantly lower
than those at asymptotically high SNRs. The impact of spatial
correlation on the DMT at finite SNRs was further studied in
\cite{IEEErelay:FDTCR}.

It is natural to expect that the DMT can be further enhanced through
power and/or rate adaptation if the transmitter has channel
knowledge. If the CSI at the transmitter (CSIT) is perfectly known,
there will be no outage even in slow fading channels since it is
always able to adjust its power or rate adaptively according to the
instantaneous channel conditions. For example, it can transmit with
a higher power or lower rate when the channel is poor and a lower
power or higher rate when the channel is good. However, in practice
the CSIT is almost always imperfect due to imperfect CSI feedback
from the receiver or imperfect channel estimation at the transmitter
through pilots. The work in \cite{IEEErelay:TCTT} showed that the
transmitter training through pilots significantly increases the
achievable diversity gain in a single-input
 multi-output (SIMO) link. In \cite{IEEErelay:OFT}, the authors quantified
the CSIT quality as $\alpha=-\log \sigma_{e}^2/\log \rho$, where
$\sigma_{e}^2$ is the variance of the CSIT error, and showed that
using rate adaptation, one can achieve an average diversity gain of
$\bar{d}(\alpha,\bar{r})=(1+\alpha-\bar{r})K$ in SIMO/MISO links,
where $K=\max(M,N)$ and $\bar{r}$ is the average multiplexing gain.
Note that setting $\alpha=1$ and ignoring the multiplexing gain loss
due to training symbols directly yields the result in
\cite{IEEErelay:TCTT}. For general MIMO channels, the achievable DMT
with partial CSIT  is characterized in \cite{IEEErelay:TT}, where
the partial CSIT is obtained using quantized channel feedback.

In this paper, we analyze the fundamental DMT in MIMO channels and
show that with power adaptation, imperfect CSIT provides significant
additional diversity gain over (\ref{DMT}). The imperfect CSIT
considered in this paper is due to channel estimation error at the
transmitter side. In the case of MISO/SIMO channels, we show that
with power adaptation (under an average sum power constraint), one
can achieve a higher diversity gain than that with rate adaptation
in \cite{IEEErelay:OFT}, where the authors assumed peak power
transmission and thus no temporal power adaptation is considered
therein. Specifically, we prove that with a CSIT quality $\alpha$,
the achievable diversity gain is $d(r)=K\left(1-r+K\alpha\right)$.
It has been shown in our earlier work \cite{SIMOMISO} that this is
actually the \emph{optimal} DMT in SIMO/MISO channels with CSIT
quality $\alpha$. For general MIMO channels ($M>1$, $N>1$), we show
in this paper that depending on the value of $\alpha$, different DMT
can be derived and the value of $\alpha$ has a great impact on the
achievable diversity, especially at high multiplexing gains.
Specifically, when $\alpha$ is above a certain threshold, one can
achieve a diversity gain of $d(r)=MN(1+MN\alpha)-(M+N-1)r$;
otherwise, the achievable DMT is much lower and can be described as
a collection of discontinuous line segments depending on $M$, $N$,
$r$ and $\alpha$. It is noted that an independent and concurrent
work recently reported in \cite{NoisyCSIT} shares some similar
results. However, we wish to
emphasize that
our CSIT model and the involved analysis towards the achievable DMT
are different from those in \cite{NoisyCSIT}. The noisy CSIT therein
is based on the \emph{channel mean feedback} model in
\cite{MeanFeedback} and an example of obtaining CSIT through delayed
feedback is provided, whereas the CSIT in our work is estimated from
reverse channel pilots using ML estimation at the transmitter. As
the variance of the channel estimation error is inversely
proportional to the pilots' SNR \cite{IEEErelay:SDICE}, the CSIT
quality $\alpha$ is naturally connected to the reverse channel power
consumption and any value of $\alpha$ can be achieved by scaling the
reverse channel transmit power.
In addition, our
paper provides detailed closed-form solutions to the achievable DMT,
which offers great insight and depicts directly what the DMT curve
with imperfect CSIT looks like.

\emph{Notations}: $\mathcal{R}^N$ denotes the the set of real
$N$-tuples, and $\mathcal{R}^{N+}$ denotes the set of non-negative
$N$-tuples. Likewise, $\mathcal{C}^{N\times M}$ denotes the set of
complex $N\times M$ matrices. For a real number $x$, $(x)^+$ denotes
$\max(x,0)$, while for a set $\mathcal{O}\subseteq \mathcal{R}^N$,
$\mathcal{O}^+$ denotes $\mathcal{O}\cap\mathcal{R}^{N+}$.
${\mathcal{O}}^c$ denotes the complementary set of $\mathcal{O}$ and
$\emptyset$ denotes the empty set. $|\mathcal{O}|$ denotes the
cardinality of set $\mathcal{O}$. $x\in (a, b]$ denotes that the
scalar $x$ belongs to the interval $a < x \leq b$. Likewise, $x\in
[a, b]$ is similarly defined. $\mathcal{CN}(0,\sigma^2)$ denotes the
complex Gaussian distribution with mean 0 and variance $\sigma^2$.
The superscripts $^*$ and $^{\dag}$ denote the complex conjugate and
conjugate transpose, respectively. $\|\cdot\|_F^2$ denotes the
matrix Frobenius norm and $\textbf{I}_N$ denotes the $N\times N$
identity matrix. $E\{\cdot\}$ denotes the expectation operator and
$\log(\cdot)$ denotes the base-2 logarithm. $f(\rho)\doteq \rho^b$
denotes that $b$ is the exponential order of $f(\rho)$, i.e.,
$\lim_{\rho\rightarrow\infty} {\log(f(\rho))}/{\log(\rho)}=b$.
Likewise, $\buildrel \textstyle .\over \leq$ is similarly defined. Finally, for matrix
$\mathbf{A}$, $\mathbf{A} \succeq 0$ denotes that $\mathbf{A}$ is
positive semidefinite; if $\succeq$ is used with a vector, it
denotes the componentwise inequality.

The rest of this paper is organized as follows. In section II,  we
describe the channel model. In section III, we propose a power
adaptation scheme based on imperfect CSIT and present the main
result on the achievable DMT. The achievability proof of the
presented DMT is given in Section IV. Section V provides some
discussions. Finally, Section VI concludes this paper.

\section{Channel Model}

We consider a point-to-point TDD wireless link with $M$ transmit and
$N$ receive antennas, where the downlink and uplink channels are
reciprocal. Without loss of generality, we assume $M\geq N$ in this
paper. As shown in \cite{IEEErelay:DMT}, this assumption does not
affect the DMT result. We also consider quasi-static Rayleigh fading
channels, where the channel gains are constant within one
transmission block of $L$ symbols, but change independently from one
block to another. We assume that the channel gains are independently
complex circular symmetric Gaussian with zero mean and unit
variance. The channel model, within one block, can be written as
\begin{equation}
\label{SIMO_channel}
\textbf{Y}=\sqrt{{P}/M}\textbf{H}\textbf{X}+\textbf{W}
\end{equation}
where $\textbf{H}=\{h_{n,m}\}\in\mathcal{C}^{N\times M }$ with
$h_{n,m}$, $m=1,2,\ldots,M$, $n=1,2,\ldots,N$, being the channel
gain from the $m$-th transmit antenna to the $n$-th receive antenna;
$\textbf{X}=\{X_{m,l}\} \in \mathcal{C}^{M\times L}$ with $X_{m,l}$,
$m=1,2,\ldots,M$, $l=1,2,\ldots,L$, being the symbol transmitted
from antenna $m$ at time $l$; $\textbf{Y}=\{Y_{n,l}\}\in
\mathcal{C}^{N\times L}$ with $Y_{n,l}$, $n=1,2,\ldots,N$,
$l=1,2,\ldots,L$, being the received signal at antenna $n$ and time
$l$; the additive noise $\textbf{W}\in \mathcal{C}^{N\times L}$ has
i.i.d. entries $W_{n,l}\sim \mathcal{CN}(0,\sigma^2)$; $P$ is the
instantaneous transmit power while the average energy of $X_{m,l}$
is normalized to be 1. Letting $\bar{P}$ denote the average sum
power constraint, we have $E\{P\}=\bar{P}$. So, the average SNR at
the receive antenna is given by $\rho=\bar{P}/\sigma^2$.

We assume that the receiver has perfect CSI $\textbf{H}\in
\mathcal{C}^{N\times M}$, but the transmitter has imperfect CSIT
$\hat{\textbf{H}}\in \mathcal{C}^{N\times M}$, which is estimated
from reverse channel pilots using ML estimation. Thus,
$\hat{\textbf{H}}$ can be modeled as
\cite{IEEErelay:SDICE}-\cite{IEEErelay:SDVA}
\begin{equation}
\hat{\textbf{H}}=\textbf{H}+\textbf{E}
\end{equation}
where the channel estimation error $\textbf{E}\in
\mathcal{C}^{N\times M}$ has i.i.d. entries $E_{n,m}\sim
\mathcal{CN}(0,\sigma_{e}^2)$, $n=1,2,\ldots,N$, $m=1,2,\ldots,M$,
and is independent of $\textbf{H}$. The quality of
$\hat{\textbf{H}}$ is thus characterized by $\sigma_{e}^2$. If
$\sigma_{e}^2 = 0$, the transmitter has perfect channel knowledge;
if $\sigma_{e}^2$ increases, the transmitter has less reliable
channel knowledge. We follow \cite{IEEErelay:OFT} to quantify the
channel quality at the transmitter. The transmitter is said to have
a \emph{CSIT quality} $\alpha$, if $\sigma_{e}^2\doteq
\rho^{-\alpha}$. The definition of $\alpha$ builds up a connection
between the imperfect channel knowledge at transmitters and the
forward channel SNR, $\rho$. Since the variance of the channel
estimation error is inversely proportional to the pilots' SNR, i.e.,
$\sigma_{e}^2\propto (SNR_{pilot})^{-1}$ \cite{IEEErelay:SDICE}, any
value of $\alpha$ can be achieved by scaling the reverse channel
power such that $SNR_{pilot}\doteq\rho^{\alpha}$. One can see that
the selection of
 $\alpha$ value actually determines the cost of obtaining
 CSIT in terms of the reverse channel power consumption. When $\alpha=0$,
 the reverse channel SNR does not
 scale with $\rho$, which means that the pilot power is fixed or limited; when $0<\alpha<1$,
 the reverse channel SNR relative
 to $\rho$ is asymptotically zero; when $\alpha=1$, the
 reverse channel SNR scales with $\rho$ at the same rate; when $\alpha>1$,
 the reverse channel SNR as compared to the forward channel SNR, $\rho$, is asymptotically unbounded \cite{IEEErelay:OFT}.
In the sequel, we will study how the pilot power, or equivalently
the CSIT quality $\alpha$, affects the fundamental tradeoff of
diversity and multiplexing in the considered channel. Before
presenting our main results, we give the following probability
density function (pdf) expressions and some preliminary results that
will be used later.

For an $N\times M$ ($N\leq M$) random matrix $\textbf{A}$ with
i.i.d. entries $\sim \mathcal{CN}(0,1)$, let $0<\lambda_1 \leq
\lambda_2 \leq ... \leq \lambda_N$
 denote the ordered nonzero eigenvalues of $\textbf{A}\textbf{A}^{\dag}$. Letting $v_n$ denote the exponential order of
$1/\lambda_n$ for all $n$, the pdf of the random vector
$\textbf{v}=[v_1,...,v_N]$ is given by \cite{IEEErelay:Eigen}
\begin{equation}
\label{eqnpv2}
\begin{split}
p(\textbf{v})&=\lim_{\rho\rightarrow\infty}\xi^{-1}(\log \rho)^N\prod_{n=1}^N \rho^{-(M-N+1)v_n} \prod_{j>n}^N (\rho^{-v_n}-\rho^{-v_j})^2\exp\left(-\sum_{n=1}^N \rho^{-v_n}\right)\\
&\doteq
\begin{cases}
0,\ \text{for any $v_n<0$}\\
\prod_{n=1}^N \rho^{-(2n-1+M-N)v_n},\  \text{for all $v_n\geq0$}
\end{cases}
\end{split}
\end{equation}where $\xi$ is a normalizing constant. Hence, the probability $\mathcal{P}_\mathcal{O}$ that
$(v_1,...,v_N)$ belongs to set $\mathcal{O}$ can be characterized by
\begin{equation}
\label{bb} \mathcal{P}_\mathcal{O}\doteq \rho^{-d_{\mathcal{O}}},\
\text{for}\ d_{\mathcal{O}}= \inf_{(v_1,...,v_N)\in \mathcal{O}^+}
\sum_{n=1}^N (2n-1+M-N)v_n
\end{equation}provided that $\mathcal{O}^+$ is not empty.

Letting $\textbf{a}=[a_1,a_2...,a_N]$, $0<a_1\leq a_2\leq...\leq
a_N$, $\textbf{b}=[b_1,b_2...,b_N]$, $0<b_1\leq b_2\leq...\leq b_N$,
and $\textbf{c}=[c_1,c_2...,c_N]$, $0<c_1\leq c_2\leq...\leq c_N$,
denote the eigenvalue vectors of $\textbf{H}\textbf{H}^{\dag}$,
$\hat{\textbf{H}}\hat{\textbf{H}}^{\dag}$ and $
\textbf{E}\textbf{E}^{\dag}$, respectively, the pdfs of
$\textbf{a}$, $\textbf{b}$, and $\textbf{c}$ can be shown to be
\begin{eqnarray}
\label{eqn_9}
&&p(\textbf{a})=\xi^{-1}\prod_{n=1}^N a_n^{M-N} \prod_{n<j}^N (a_n-a_j)^2\exp\left(-\sum_{n=1}^N a_n\right)\\
&&p(\textbf{b})=\hat{\xi}^{-1}
\prod_{n=1}^N b_n^{M-N} \prod_{n<j}^N (b_n-b_j)^2\exp\left(-\frac{1}{1+\sigma_e^2}\sum_{n=1}^N b_n\right) \\
\label{eqn_11} &&p(\textbf{c})=\tilde{\xi}^{-1} \prod_{n=1}^N
c_n^{M-N} \prod_{n<j}^N
(c_n-c_j)^2\exp\left(-\frac{1}{\sigma_e^2}\sum_{n=1}^N c_n\right)
\end{eqnarray}
where $\hat{\xi}^{-1}=\xi^{-1} (1+\sigma_e^2)^{-MN}$ and
$\tilde{\xi}^{-1}=\xi^{-1} (\sigma_e^2)^{-MN}$.

\section{Main Result on DMT}
The ML error probability $\mathcal{P}_e(\rho)$ of the channel
described in (\ref{SIMO_channel}) is closely related to the
associated packet outage probability $\mathcal{P}_{out}$, which is
defined as the probability that the instantaneous channel capacity
falls below the target data rate $R(\rho)$. In fact, the error
probability of an ML decoder which utilizes a fraction of the
codeword such that the mutual information between the received and
transmitted signals exceeds $LR(\rho)$ (no outage), averaged over
the ensemble of random Gaussian codes, can be made arbitrarily small
provided that the codeword length $L$ is sufficiently large
\cite{IEEErelay:OAD}. We will thus leverage on the outage
probability to examine the achievable diversity gain. If the
transmitter has perfect CSIT, it may adopt the optimal power
adaptation according to the actual instantaneous channel gain such
that no outage will occur. With only the imperfect CSIT, in order to
mitigate the channel uncertainty, we propose the following power
adaptation scheme.

\begin{proposition}
Given $\hat{\textbf{H}}$, the transmitter
 transmits with power
 \begin{equation}
 \label{PA}
P(\hat{\textbf{H}})=\frac{ \kappa\bar{P}}{\left(\prod_{n=1}^N
b_n^{2n-1+M-N}\right)^t}
\end{equation}where $\kappa=\hat{\xi}\prod_{n=1}^N \left[(2n-1+M-N)(1-t)\right]$ and
 $t$ ($0\leq t<1$) can be chosen arbitrarily close to $1$.
\end{proposition}

It is shown in Appendix A that the above power adaptation scheme
satisfies the sum power constraint $E\{P(\hat{\textbf{H}})\}=
\bar{P}$. We believe that given the CSIT quality of $\alpha$, this
power adaptation scheme is the optimal power adaptation scheme that
maximizes the achievable diversity gain of a MIMO fading channel.

\begin{theorem}

Consider a MIMO channel with $M$ transmit and $N$ receive antennas
($M\geq N$) and CSIT quality of $\alpha$. If the block length $L\geq
M+N-1$, the achievable DMT using the power adaptation scheme in
Proposition 1 is characterized by

Case 1: If $N=1$ or $\alpha \geq \frac{1}{M-1}$, then
\begin{equation}
\begin{split}
d(r)=MN(1+MN\alpha)-(M+N-1)r.
\end{split}
\label{eq14}
\end{equation}

Case 2: Otherwise, the achievable DMT is a collection of
discontinuous line segments, with the two end points of line segment
$d_k(r)$ ($k\in \mathcal{B}$) given by
\begin{equation}
\label{eqn_446}
\begin{split}
\text{Left end: }&d_k(r)=k(M-N+k){\tau}(k),\  \text{for}\ r=(N-k){\tau}(k)\\
\text{Right end: }&d_k(r)=((N-k)(k-N-1)+MN){\tau}(k)-(2k-1+M-N)(N-{\mathcal{I}}(k)){\tau}({\mathcal{I}}(k)),\\
&\ \ \ \ \ \ \ \ \ \ \text{for}\
r=(N-{\mathcal{I}}(k)){\tau}({\mathcal{I}}(k))
\end{split}
\end{equation}where
\begin{equation}
\mathcal{B}=\left\{k\middle | (M-N+k)(N-k)<1/\alpha,
(N-k){\tau}(k)<(N-\bar{k}){\tau}(\bar{k}), \forall \bar{k}<k,
k=1,...,N\right\}, \nonumber
\end{equation}
${\tau}(k)=1+k\alpha(M-N+k)$ and ${\mathcal{I}}(k)= \max_{\bar{k}\in
{\mathcal{B}},\bar{k}<k} \bar{k}$.
\end{theorem}

For example, when $M=N=2$ and $\alpha<1$, the DMT curve consists of
two discontinuous line segments which are
$(0,16\alpha+4)$---$(1+\alpha,13\alpha+1)$ and
$(1+\alpha,1+\alpha)$---$(2,2\alpha)$. When $r=1+\alpha$, the
achievable diversity gain is $d(r)=1+\alpha$ instead of
$13\alpha+1$. From Theorem 1, we can get $d(0)=MN(1+MN\alpha)$ and
$d(N)=p\alpha(M-N+p)(MN+(p-N)(N-p+1)))-p^2+p$ where $p=\min_{k\in
{\mathcal{B}}} k$. If $\alpha <\frac{1}{(N-1)(M-N+1)}$, which
indicates $1\in {\mathcal{B}}$, we will have $d(N)=\alpha
N(M-N+1)^2$.

\section{Proof of Theorem 1}
The proof involves the computation of the asymptotic ML  error
probability at high SNRs. We will first derive a lower bound of the
SNR exponent of the outage probability, denoted as
$d_\mathcal{O}(r)$, and then show that using a random coding
argument the SNR exponent of the error probability is no less than
$d_\mathcal{O}(r)$ if $L\geq M+N-1$.

\subsection{Derivation of $d_{\mathcal{O}}(r)$}
Optimizing over all input distributions, which  can be assumed to be
Gaussian with a covariance matrix $\textbf{Q}$ without loss of
optimality, the outage probability of a MIMO channel with transmit
power $P(\hat{\textbf{H}})$ is given by
\begin{equation}
\label{OutageProb} \mathcal{P}_{out}=\inf_{\textbf{Q}\succeq0,
tr(\textbf{Q})\leq M}\mathcal{P}\left(\log
\text{det}\left(\textbf{I}_N+\frac{P(\hat{\textbf{H}})}{M\sigma^2}\textbf{H}\textbf{Q}\textbf{H}^{\dag}\right)<R(\rho)
\right)
\end{equation}
where $\mathcal{P}(\cdot)$ denotes the probability of an event. It
is shown in \cite{IEEErelay:DMT} that one can get an upper bound and
a lower bound on the outage probability by picking
$\textbf{Q}=\textbf{I}_{M}$ and $\textbf{Q}=M\textbf{I}_M$,
respectively, and the two bounds converge in the high SNR regime.
Therefore, without loss of generality, we consider
$\textbf{Q}=\textbf{I}_M$. Substituting (\ref{PA}) in
(\ref{OutageProb}), we have
\begin{equation}
\begin{split}
\mathcal{P}_{out}&=\mathcal{P}\left(\log \text{det}\left(\textbf{I}_N+\frac{\rho \kappa}{M\prod_{n=1}^N b_n^{(2n-1+M-N)t}}\textbf{H}\textbf{H}^{\dag}\right)<R(\rho) \right)\\
&=\mathcal{P}\left(\log\prod_{n=1}^N\left(1+\frac{\rho \kappa
a_n}{M\prod_{n=1}^N b_n^{(2n-1+M-N)t}}\right)<R(\rho) \right).
\end{split}
\end{equation}

\begin{lemma}The eigenvalues of $\hat{\textbf{H}}\hat{\textbf{H}}^{\dag}$,
$\textbf{H}\textbf{H}^{\dag}$ and $\textbf{E} \textbf{E}^{\dag}$
have the following relationship
\begin{equation}
\label{bac} b_n \leq 2 (a_n+c_N), \  n=1,2,...,N.
\end{equation}
\end{lemma}
\begin{IEEEproof}
We obviously have the following equality
\begin{equation}
(\textbf{H}+\textbf{E})(\textbf{H}+\textbf{E})^{\dag}+(\textbf{H}-\textbf{E})(\textbf{H}-\textbf{E})^{\dag}=2 (\textbf{H}\textbf{H}^{\dag}+\textbf{E}\textbf{E}^{\dag})
\end{equation}where both $(\textbf{H}+\textbf{E})(\textbf{H}+\textbf{E})^{\dag}$
and $(\textbf{H}-\textbf{E})(\textbf{H}-\textbf{E})^{\dag}$ are
positive semidefinite matrices. We denote the vector of eigenvalues
of $(\textbf{H}\textbf{H}^{\dag}+\textbf{E}\textbf{E}^{\dag})$ as
$\textbf{d}=[d_1,...,d_N]$ with $d_1\leq d_2\leq...\leq d_N$. Since
the eigenvalues of the sum of two positive semidefinite matrices are
at least as large as the eigenvalues of any one of the positive
semidefinite matrices \cite{IEEErelay:Math}, we have $ b_n\leq 2
d_n,\  n=1,2,...,N$. Further, using the relationship of the
eigenvalues of the sum of Hermitian matrices, we get $a_n + c_1 \leq
d_n \leq a_n +c_N,\  n=1,2,...,N$. It thus directly leads to
(\ref{bac}).
 \end{IEEEproof}

With Lemma 1, the outage probability is upper bounded by
\begin{equation}
\label{out} \mathcal{P}_{out}\leq
 \mathcal{P}\left[\log\prod_{n=1}^N \left(1+ \frac{\rho \kappa
a_n}{M\prod_{n=1}^N (2a_n+2c_N)^{(2n-1+M-N)t}}
\right)<R(\rho)\right] .
\end{equation}

Let $v_n$ and $u_n$ denote the exponential orders of $1/{a_n}$ and
$1/{c_n}$, respectively, i.e.,
$v_n=-\lim_{\rho\rightarrow\infty}\frac{\log(a_n)}{\log(\rho)}$,
$u_n=-\lim_{\rho\rightarrow\infty}\frac{\log(c_n)}{\log(\rho)}$.
Using (\ref{eqnpv2}), (\ref{eqn_9}) and (\ref{eqn_11}), the pdfs of
the random vector $\textbf{v}=[v_1,...,v_N]$ and
$\textbf{u}=[u_1,...,u_N]$ can be shown to be
\begin{eqnarray}
&&p(\textbf{v})\doteq
\begin{cases}
0,\ \text{for any $v_n<0$}\\
\prod_{n=1}^N \rho^{-(2n-1+M-N)v_n},\  \text{for all $v_n\geq0$}
\end{cases}\label{pvn1}\\
&&p(\textbf{u})\doteq
\begin{cases}
0,\ \text{for any $u_n<\alpha$}\\
\prod_{n=1}^N \rho^{-(2n-1+M-N)(u_n-\alpha)},\  \text{for all
$u_n\geq \alpha$}.
\end{cases}\label{pun1}
\end{eqnarray}

At high SNRs, with (\ref{pvn1}) and (\ref{pun1}), (\ref{out})
becomes
\begin{equation}
\label{eqn29} \mathcal{P}_{out}\leq \mathcal{P}\left[\sum_{n=1}^N
\left(1-v_n+\sum_{n=1}^N t(2n-1+M-N)\min(v_n,u_N)\right)^+
<r\right].
\end{equation}

So, the outage event $\mathcal{O}$ in (\ref{eqn29}) is the set of
$\{v_1,\ldots,v_N,u_1,\ldots,u_N\}$ that satisfies
\begin{equation}
\label{eqn28} \sum_{n=1}^N \left(1-v_n+\sum_{n=1}^N
t(2n-1+M-N)\min(v_n,u_N)\right)^+ <r
\end{equation}
where $ v_n\geq 0, u_n\geq \alpha\geq0, n=1,2,...,N$.

According to (\ref{bb}), we have
\begin{equation}
\mathcal{P}_{out}\leq \mathcal{P}_\mathcal{O}\doteq
\rho^{-d_{\mathcal{O}}(r)}
\end{equation}
where $d_\mathcal{O}(r)$ serves as a lower bound of the SNR exponent
of $\mathcal{P}_{out}$ and is given by
\begin{equation}
\label{DMTNEW} d_\mathcal{O}(r)= \inf_{(v_1,...,v_N,u_1,...,u_N)\in
\mathcal{O}} \sum_{n=1}^N (2n-1+M-N) \left(v_n+u_n-\alpha\right).
\end{equation}

Next, we work on the explicit expression of $d_\mathcal{O}(r)$.
Since the left hand side (LHS) of (\ref{eqn28}) is a non-decreasing
function of $u_N$, decreasing $u_N$ will not violate the outage
condition in (\ref{eqn28}) while enjoying a reduced SNR exponent
$\sum_{n=1}^N (2n-1+M-N) \left(v_n+u_n-\alpha\right)$. Combining
with the fact $u_n\geq \alpha, \ n=1,2,...,N$, the solution of
$\textbf{u}$ is found to be $u_1^*=...=u_N^*=\alpha$. Therefore,
(\ref{eqn28}) can be rewritten as
 \begin{equation}
 \mathcal{O}=\left\{v_n\middle|\sum_{n=1}^N \left(1-v_n+\sum_{n=1}^N t(2n-1+M-N)\min(v_n,\alpha)\right)^+ <r, v_n\geq 0 \right\}.
 \end{equation}

To solve the optimization problem of (\ref{DMTNEW}), we need to solve the subproblems
\begin{equation}
\label{eqn33} d_k(r)\triangleq \inf_{(v_1,...,v_N)\in \mathcal{O}_k}
\sum_{n=1}^N (2n-1+M-N) v_n,\ k=0,1,...,N
\end{equation}
where subset $\mathcal{O}_k$ $(0\leq k \leq N)$ is defined as
\begin{equation}
\begin{split}
\mathcal{O}_k  =&\left\{v_n\middle|\sum_{n=1}^N
\left(1-v_n+\sum_{n=1}^k t(2n-1+M-N)\alpha + \sum_{n=k+1}^N
t(2n-1+M-N)v_n\right)^+ <r,\right.\nonumber\\ &\left.v_1\geq...\geq
v_k\geq \alpha \geq v_{k+1}\geq...\geq v_N \right\} .
 \end{split}
\end{equation}

So, $d_\mathcal{O}(r)$ is given by
\begin{equation}
\label{eqn_29} d_\mathcal{O}(r)=\min\left( d_0(r),
d_1(r),...,d_N(r)\right).
\end{equation}
In other words, among all the DMT curves $d_0(r)$,...,$d_N(r)$,
corresponding to the outage subsets
$\mathcal{O}_1$,...,$\mathcal{O}_N$, the lowest one will be the DMT
curve for the entire outage event. Since $t$ can be made arbitrarily
close to 1, it is without loss of accuracy to set $t=1$ in the rest
of this paper.

Firstly, we derive $d_0(r)$.
It is easy to show
 \begin{equation}
 \label{eqn_30}
\sum_{n=1}^N \left(1-v_n+\sum_{n=1}^N (2n-1+M-N)v_n\right)^+\geq
N-\sum_{n=1}^N v_n +N\sum_{n=1}^N (2n-1+M-N)v_n \geq N
\end{equation}
which suggests that it is possible to operate at spatial
multiplexing gain $r\in[0,N]$ reliably without any outage, i.e.,
$d_0(r)=\infty$. So we can exclude $d_0(r)$ from the optimization
problem in (\ref{eqn_29}).

Secondly, we derive $d_k(r)$ ($1\leq k \leq N$). Note that the function
 $\sum_{n=1}^N \left(1-v_n+\sum_{n=1}^k (2n-1\right.$ $\left.+M-N)\alpha + \sum_{n=k+1}^N (2n-1+M-N)v_n\right)^+$
  is an increasing function of $v_{k+1},v_{k+2},...,v_N$. That is,
  decreasing $v_{k+1},v_{k+2}...,v_N$ does not violate the outage condition for
  $\mathcal{O}_k$, while reducing the SNR exponent $\sum_{n=1}^N (2n-1+M-N)v_n$.
  Therefore, the optimal solutions of $v_{k+1},v_{k+2},...,v_N$ are
  $v_{k+1}^*=v_{k+2}^*=...=v_N^*=0$. Consequently, the
  optimization problem in (\ref{eqn33}) can be reformulated as
 \begin{equation}
 d_k(r)=\inf_{(v_1,...,v_k)\in \tilde{\mathcal{O}}_k} \sum_{n=1}^k (2n-1+M-N) v_n,\
 k=1,...,N.
 \end{equation}
Here the modified outage subset $\tilde{\mathcal{O}}_k$ is defined
as
\begin{equation}
\label{eqn35}
\begin{split}
\tilde{\mathcal{O}}_k
=\left\{v_1,...,v_k\middle|N\tau(k)-\sum_{n=1}^k v_n<r, \alpha\leq
v_k\leq...\leq v_1 \leq \tau(k) \right\}.
\end{split}
\end{equation}
where $\tau(k)=1+k\alpha(M-N+k)$. Careful observation of
(\ref{eqn35}) reveals that
\begin{equation}
\label{rr}
\begin{split}
 N\tau(k)-\sum_{n=1}^k v_n \geq (N-k)\tau(k).
\end{split}
\end{equation}
It implies that there will be no outage ($d_k(r)=\infty$), if $r
\leq (N-k)\tau(k)$ or $(N-k)\tau(k) \geq N$. Note that $(N-k)\tau(k)
\geq N \Rightarrow (M-N+k)(N-k)\geq 1/\alpha$. So, if $(M-N+k)(N-k)<
1/\alpha$, there will be nonzero outage ($d_k(r)<\infty$), for $r\in
\Omega_k$, where $\Omega_k$ is defined as
\begin{equation}
\label{ome} \Omega_k\triangleq \left((N-k)\tau(k),\ N\right].
\end{equation}

For any $r\in \Omega_k$, we are able to explicitly calculate the
optimal solutions of $v_1,...,v_k$ that minimize the SNR exponent
$\sum_{n=1}^k (2n-1+M-N)v_n$. The results are summarized in the
following.

\begin{enumerate}
    \item If $r=(N-k')\tau(k)-(k-k')\alpha,\
k'=1,2,...,k$, then the achievable diversity for outage event
$\tilde{\mathcal{O}}_k$ is
\begin{equation}
\label{eqn_35} d_k(r)=k'(M-N+k')\tau(k)+(k-k')(k+k'+M-N)\alpha.
\end{equation} The corresponding optimal solutions of $v_1,...v_k$ are
$v_1^*=...=v_{k'}^*=\tau(k)$, $v_{k'+1}^*=...=v_k^*=\alpha$.
Specifically, $d_k(r)=k(M-N+k)\tau(k)$ for $r=(N-k)\tau(k)$.

\item  If
$(N-k')\tau(k)-(k-k')\alpha<r<(N-k'+1)\tau(k)-(k-k'+1)\alpha,\
k'=1,2,...,k$,  the achievable diversity for outage event
$\tilde{\mathcal{O}}_k$ is
\begin{equation}
\label{eqn_38}
d_k(r)=((N-k')(k'-N-1)+MN)\tau(k)+(k-k'+1)(k-k')\alpha-(2k'-1+M-N)r.
\end{equation}
The corresponding optimal solutions of $v_1,...,v_k$ are
$v_1^*=...=v_{{k'-1}}=\tau(k)$,
$v_{k'}^*=(N-k'+1)\tau(k)-(k-k')\alpha-r$,
$v_{k'+1}^*=...=v_k^*=\alpha$.
 \end{enumerate}

For a particular $k'$, when spatial multiplexing gain $r$ is
 between $(N-k')\tau(k)-(k-k')\alpha$ and
 $(N-k'+1)\tau(k)-(k-k'+1)\alpha$, only one singular value
 of $\textbf{H}$, corresponding to the typical outage event, needs to be adjusted
 to be barely large enough to support the data rate. (\ref{eqn_38}) further shows that
 $d_k(r)$ is a continuous line segment between these two points. It is thus obvious that curve $d_k(r)$ is piecewise-linear with
$(r,d_k(r))$ specified in (\ref{eqn_35}) being its corner points.

After calculating $d_1(r),...,d_N(r)$, we remain to solve
$d_{\mathcal{O}}(r)=\min_k d_k(r),\ k=1,...,N$. Since
$d_k(r)=\infty$ if $(M-N+k)(N-k)\geq 1/\alpha $, we only need to
consider $k\in \mathcal{A}$, where set $\mathcal{A}$ is defined as
\begin{equation}
\mathcal{A}=\left\{k\middle | (M-N+k)(N-k)< 1/\alpha,
k=1,...,N\right\}.
\end{equation}

Note that we always have $k=N \in \mathcal{A}$. We consider the
following two cases.

Case 1: $\mathcal{A}$ has only one element, i.e.,
$\mathcal{A}=\{k=N\}$. In this case, we have
$d_{\mathcal{O}}(r)=d_N(r)$. If $N=1$, this condition is naturally
satisfied, since there is only one element in $\mathcal{A}$ that is
$k=1$. If $N>1$, we must require $(M-N+k)(N-k) \geq 1/\alpha$ for
$k=1,...,N-1$, which leads to
\begin{equation}
\label{eqn42} \alpha  \geq \frac{1}{M-1},\ \ N>1.
\end{equation}

We now examine the corner points of $d_N(r)$. From (\ref{eqn_35}),
we have $r=(N-k')(1+\alpha MN-\alpha)> 1+MN\alpha-\alpha$ for corner
point $k'$ ($k'=1,2,...,N-1$). Since $1+MN\alpha-\alpha$ is a
non-decreasing function of $\alpha$, we easily get $r>
1+\frac{MN}{M-1}-\frac{1}{M-1} >N$. Thus we conclude that there is
only one corner point ($0,d_N(0)$) on curve $d_N(r)$ over region
$r\in \Omega_{N}$. Therefore, $d_{\mathcal{O}}(r)=d_N(r)$ is a
straight line between corner points ($0,d_N(0)$) and ($N,d_N(N)$).
From (\ref{eqn_38}), we have $d_N(N)=MN(1+MN\alpha)-(M+N-1)N$, so
$d_{\mathcal{O}}(r)$ can be described as
\begin{equation}
d_{\mathcal{O}}(r)=MN(1+MN\alpha)-(M+N-1)r \ \ \text{for}\ 0\leq
r\leq N.
\end{equation}

Case 2: $\mathcal{A}$ has more than one element. Since $N\in
\mathcal{A}$ and $\Omega_N=[0, N]$, $\Omega_k$ ($k\neq N,k\in
\mathcal{A}$) overlaps with $\Omega_N$. That is, there are some
regions of spatial multiplexing gain $r$, leading to finite
diversity gains on different DMT curves. A straightforward method to
find $d_{\mathcal{O}}(r)$ is to numerically calculate $d_k(r)$ for
all $k\in \mathcal{A}$, and choose the minimum value among them.
However, this makes $d_{\mathcal{O}}(r)$ implicit and hardly
insightful. To find the closed-form solution of
$d_{\mathcal{O}}(r)$, we wish to find out if there is any
relationship among $d_1(r),...,d_N(r)$. This motivates the birth of
the following Lemma, the proof of which is given in Appendix B.

\begin{lemma}
For any spatial multiplexing gain $r\in \Omega_{k_1} \bigcap \Omega_{k_2}$ ($1\leq k_1, k_2\leq N$), if $k_1<k_2$, we have $d_{k_1}(r)<d_{k_2}(r)$.
\end{lemma}

This Lemma tells us if a spatial multiplexing gain $r$ leads to
finite diversity gains on two DMT curves, we only need to select the
curve with lower diversity gain. For example, if $r\in
\Omega_1\bigcap\Omega_2\bigcap...\bigcap\Omega_N$, then
$d_{\mathcal{O}}(r)=d_1(r)$ since $d_1(r)<d_2(r)<...<d_N(r)<\infty$.
Therefore, we can further expurgate bad $k$ (s.t. $\Omega_k\subseteq
\Omega_{\bar{k}}$, for $\bar{k}<k \in \mathcal{A} $) from
$\mathcal{A}$ and only take into account $k\in {\mathcal{B}}$ for
the optimization problem, where
\begin{equation}
{\mathcal{B}}=\left\{k\middle |
(N-k)\tau(k)<(N-\bar{k})\tau(\bar{k}),\  \forall \bar{k}<k,
\bar{k},k \in \mathcal{A}\right\}.
\end{equation}

Letting $|{\mathcal{B}}|$ denote the cardinality of ${\mathcal{B}}$,
we further divide $r\in[0,N]$ into $|{\mathcal{B}}|$ non-overlapping
regions with region $\tilde{\Omega}_k$ ($k\in {\mathcal{B}}$)
defined as
\begin{equation}
\begin{split}
\tilde{\Omega}_k&=\Omega_k\bigcap \tilde{\Omega}_{\bar{k}}^c,\  \forall \bar{k}<k\&\bar{k}\in {\mathcal{B}}\\
&=
[(N-k)\tau(k), (N-\mathcal{I}(k))\tau(\mathcal{I}(k)))\\
\end{split}
\end{equation}
where $\mathcal{I}(k)$ indicates the immediately preceding element
of $k$ in ${\mathcal{B}}$, i.e.,
$\mathcal{I}(k)=\max_{\bar{k}<k,\bar{k}\in {\mathcal{B}}} \bar{k}$.
From Fig. 1, which illustrates the relationship between $\Omega_{k}$
and $\tilde{\Omega}_k$, we get $d_{\mathcal{O}}(r)=d_k(r)$ for any $
r\in \tilde{\Omega}_k$.

Next we examine the corner points on curve $d_k(r)$ over $r\in
\tilde{\Omega}_k$ and give the following Lemma, the proof of which
is given in Appendix C.
\begin{lemma}
For $k\in {\mathcal{B}}$, there is only one corner point, $\left(
(N-k)\tau(k), k(M-N+k)\tau(k)\right)$, making $r\in
\tilde{\Omega}_k$.
\end{lemma}

As a result, $d_k(r)$ over $r\in \tilde{\Omega}_k$ is just a single
line segment connecting the following two end points
\begin{equation}
\label{eqn_44}
\begin{split}
\text{Left end: }&d_k(r)=k(M-N+k)\tau(k),\  \text{for}\ r=(N-k)\tau(k)\\
\text{Right end: }&d_k(r)=((N-k)(k-N-1)+MN)\tau(k)-(2k-1+M-N)(N-\mathcal{I}(k))\tau(\mathcal{I}(k)),\\
&\ \ \ \ \ \ \ \ \ \text{for}\
r=(N-\mathcal{I}(k))\tau(\mathcal{I}(k)).
\end{split}
\end{equation}

Finally, since $d_{\mathcal{O}}(r)$ is the union of $d_k(r)$ over
$r\in \tilde{\Omega}_k$ for all $k\in {\mathcal{B}}$,
 the DMT curve over the entire outage event is the collection of all the involved
line segments and the two end points of line segment $d_k(r)$ ($k\in
{\mathcal{B}}$) are described in (\ref{eqn_44}). It should be noted
that these line segments are discontinuous though $r$ is continuous
between $0$ and $N$. Combining the above Cases 1 and 2 directly
leads to (\ref{eq14}) and (\ref{eqn_446}) in Theorem 1.

\subsection{Achievability Proof}

To complete the proof of the Theorem 1, we need to show that
$\mathcal{P}_e(\rho)\buildrel \textstyle .\over \leq \rho^{-d_{\mathcal{O}}(r)}$ if $L\geq
M+N-1$. With the ensemble of i.i.d. complex Gaussian random codes at
the input, the ML error probability is given by \cite{IEEErelay:DMT}
\begin{equation}
\label{eqn41}
\mathcal{P}_e(\rho)=\mathcal{P}_{\mathcal{O}}\mathcal{P}(\text{error}
|\mathcal{O})+\mathcal{P}(\text{error},\mathcal{O}^c)\leq
\mathcal{P}_{\mathcal{O}}+\mathcal{P}(\text{error},\mathcal{O}^c)
\end{equation}where $\mathcal{O}$ and $\mathcal{P}_{\mathcal{O}}$ are given by (\ref{eqn28}) and (\ref{DMTNEW}), respectively.

$\mathcal{P}(\text{error},\mathcal{{O}}^c)$ can be upper-bounded by
a union bound. Assume that $\textbf{X}(0)$, $\textbf{X}(1)$ are two
possible transmitted codewords, and that $\Delta
\textbf{X}=\textbf{X}(1)-\textbf{X}(0)$. Suppose $\textbf{X}(0)$ is
transmitted, the probability that an ML receiver will make a
detection error in favor of $\textbf{X}(1)$, conditioned on a
certain realization of the channel, is
\begin{equation}
\mathcal{P}\left(\textbf{X}(0)\rightarrow \textbf{X}(1)\middle |
\textbf{H},\hat{\textbf{H}}\right)=\mathcal{P}\left(\frac{P(\hat{\textbf{H}})}{M
\sigma^2}\left\| \frac{1}{2}\textbf{H}(\Delta \textbf{X})\right
\|_F^2\leq \|\textbf{w}\|^2\right)
\end{equation}where $\textbf{w}$ is the additive noise on the direction of $\textbf{H}(\Delta \textbf{X})$, with variance $1/2$. With the standard approximation of the Gaussian tail function, $Q(x)\leq 1/2 \exp(-x^2/2)$, we have
\begin{equation}
\mathcal{P}\left(\textbf{X}(0)\rightarrow \textbf{X}(1)\middle |
\textbf{H},\hat{\textbf{H}}\right)\leq \exp
\left(-\frac{P(\hat{\textbf{H}})}{4M \sigma^2}\|\textbf{H}(\Delta
\textbf{X})\|^2\right).
\end{equation}

Averaging over the ensemble of random codes, we have the average
pairwise error probability conditioned on the channel realization
\begin{equation}
\mathcal{P}\left(\textbf{X}(0)\rightarrow \textbf{X}(1)\middle |
\textbf{H},\hat{\textbf{H}}\right)\leq \det
\left(\textbf{I}_N+\frac{P(\hat{\textbf{H}})}{2M
\sigma^2}\textbf{H}\textbf{H}^{\dag}\right)^{-L}.
\end{equation}

With a data rate $R=r\log(\rho)$ (bits per channel use), we have in total $\rho^{Lr}$ codewords. Applying the union bound, we have
\begin{equation}
\begin{split}
\mathcal{P}(\text{error} | \textbf{H},\hat{\textbf{H}})&\leq\rho^{Lr} \det \left(\textbf{I}_N+\frac{P(\hat{\textbf{H}})}{2M \sigma^2}\textbf{H}\textbf{H}^{\dag}\right)^{-L}\\
&= \rho^{Lr} \prod_{n=1}^N \left(1+ \frac{\rho \kappa
a_n}{2M\prod_{n=1}^N b_n^{2n-1+M-N}} \right)^{-L}
\\
&\leq \rho^{Lr}  \prod_{n=1}^N \left(1+ \frac{\rho \kappa
a_n}{M\prod_{n=1}^N (2a_n+2c_N)^{2n-1+M-N}}
\right)^{-L}\\
&\doteq \rho^{-L\left(\sum_{n=1}^N \left(1-v_n+\sum_{n=1}^N
(2n-1+M-N)\min(v_n,u_N)\right)^+-r\right)}.
\end{split}
\end{equation}

Averaging over the distributions of $\textbf{H}$ and $ \hat{\textbf{H}}$, or equivalently
 $\textbf{v}$ and $\textbf{u}$, we have
\begin{equation}
\begin{split}
&\mathcal{P}(\text{error}, \mathcal{{O}}^c)=\int_{\mathcal{O}^c}p(\textbf{u})p(\textbf{v}) \mathcal{P}(\text{error} | \textbf{H},\hat{\textbf{H}})d\textbf{u} d\textbf{v}\\
&\buildrel \textstyle .\over \leq \int_{\mathcal{{O}}^c}\rho^{-\sum_{n=1}^N(2n-1+M-N)(v_n+u_n-\alpha)} \rho^{-L\left(\sum_{n=1}^N \left(1-v_n+\sum_{n=1}^N (2n-1+M-N)\min(v_n,u_N)\right)^+-r\right)} d\textbf{u} d\textbf{v}\\
&\doteq \rho^{-d_G(r)}
\end{split}
\end{equation}
where
\begin{equation}
\label{eqn_48}
\begin{split}
d_G(r)
=&\inf_{\textbf{u}, \textbf{v} \in \mathcal{O}^c}\sum_{n=1}^N(2n-1+M-N)(v_n+u_n-\alpha)\\
&+L\left(\sum_{n=1}^N \left(1-v_n+\sum_{n=1}^N
(2n-1+M-N)\min(v_n,u_N)\right)^+-r\right).
\end{split}
\end{equation}

When $L\geq M+N-1$, $d_G(r)$ has the same monotonicity as
$\sum_{n=1}^N \left(1-v_n+\sum_{n=1}^k (2n-1+M\right.$
$\left.-N)\alpha + \sum_{n=k+1}^N (2n-1+M-N)v_n\right)^+$ with
respect to $v_n$ or $u_n$, $n=1,...,N$. Therefore, the minimum
always occurs when $\sum_{n=1}^N \left(1-v_n+\sum_{n=1}^N
(2n-1+M-N)\min(v_n,u_N)\right)^+=r$. Hence
\begin{equation}
\begin{split}
d_G(r)&=\inf_{\sum_{n=1}^N \left(1-v_n+\sum_{n=1}^N (2n-1+M-N)\min(v_n,u_N)\right)^+=r} \sum_{n=1}^N(2n-1+M-N)(v_n+u_n-\alpha)\\
&=d_{\mathcal{O}}(r).
\end{split}
\end{equation}

Therefore, the overall error probability can be written as
\begin{equation}
\begin{split}
\mathcal{P}_e(\rho)&\leq \mathcal{P}_{\mathcal{O}}+\mathcal{P}(\text{error},\mathcal{{O}}^c)\\
&\doteq \rho^{-d_{\mathcal{O}}(r)}+\mathcal{P}(\text{error},\mathcal{{O}}^c)\\
& \buildrel \textstyle .\over \leq \rho^{-d_{\mathcal{O}}(r)}+\rho^{-d_G(r)} \doteq
\rho^{-d_{\mathcal{O}}(r)}
\end{split}
\end{equation}

Since the MIMO channel with the proposed power adaptation scheme
leads to an error probability lower than or equal to
$\rho^{-d_{\mathcal{O}}(r)}$, we can say that the MIMO channel is
able to achieve the diversity gain of $d_{\mathcal{O}}(r)$. Theorem
1 is thus obtained.

\section{Discussions}

In this section, we discuss the additional diversity gain $\Delta_{
d}(r)$ brought by the imperfect CSIT through power adaptation.

Case A) $N=1$ (MISO/SIMO): According to (\ref{eq14}), the imperfect
CSIT provides an additional diversity gain of
$\Delta_{d}(r)=M^2\alpha $ at any spatial multiplexing gain in the
considered MISO/SIMO channel. Most remarkably, when $\alpha = 1/M$,
one can achieve both full diversity gain
 (i.e., $M$) and full spatial multiplexing gain (i.e., $1$) at the same time,
while $\alpha$ has to be equal to or greater than $1$ to achieve the
same performance in \cite{IEEErelay:OFT}. Note that the case of
$\alpha<1$ is much more practical than the case of $\alpha\geq1$ as
one usually allocates much less power to the reverse (feedback
pilot) channel than the forward transmission channel.

Case B) $\alpha \geq \frac{1}{M-1},\  N>1$: For such MIMO channel,
according to (\ref{eq14}), the additional diversity gain is $\Delta
_{d}(r)=(M^2N^2\alpha+r-r^2)$, for $r=0,1,...,N$. Specifically,
$\Delta _{d}(0)=M^2N^2\alpha$ and $\Delta _{d}(N)=\alpha
M^2N^2+N-N^2> MN^2+N$. If $0<r<N$, the additional diversity gain is
between the two extreme values $\Delta_{d}(0)$ and $\Delta_{d}(N)$.

Case C) $\alpha < \frac{1}{M-1},\  N>1$: When $r=N$,
$\Delta_{d}(N)=d(N)\geq d_1(N)=\alpha N(M-N+1)^2$. When $r<N$, for
the convenience of comparison with \cite{IEEErelay:DMT}, we consider
integer spatial multiplexing gains, i.e., $r=N-k,\ k=1,2,...,N$.
Since $r=N-k\leq (N-k){\tau}(k)$,  from Theorem 1, the achievable
diversity gain is $d(r)\geq k(M-N+k){\tau}(k)=
(M-r)(N-r)\left(1+\alpha (M-r)(N-r)\right)$. Recall that the optimal
diversity gain without CSIT
 is $d^*(r)=(M-r)(N-r)$. Therefore, the
additional achievable diversity gain with our scheme is
$\Delta_{d}(r)\geq \alpha (M-r)^2(N-r)^2=\alpha
\left(d^*(r)\right)^2$. It indicates that even a very small $\alpha$
leads to a significant diversity gain improvement.

We use numerical results to show the additional diversity gain
achieved with imperfect CSIT. We compare the following two
scenarios: 1) No CSIT \cite{IEEErelay:DMT};
 and 2)
Imperfect CSIT with power adaptation. Figs. 2 and 3 plot the DMT
curves for $3\times 3$ and $4\times 2$ MIMO fading channels,
respectively. It is obvious that imperfect CSIT provides significant
additional diversity gain improvement and offers non-zero diversity
gain at any possible spatial multiplexing gain. Fig.~2 also shows
the impact of $\alpha$ value. When
$\alpha\geq\frac{1}{M-1}=\frac{1}{2}$, we only have $d_N(r)<\infty$
and thus $\mathcal{B}=\{3\}$. Therefore, the DMT curve is a single
line segment. However, when $\alpha=\frac{1}{3}<\frac{1}{M-1}$,
$\mathcal{B}=\{1,2,3\}$. Therefore, the DMT curve is made up of
three discontinuous line segments. Fig.~3 shows how
$d_{\mathcal{O}}(r)$ depends on $d_1(r)$ and $d_2(r)$ in a $4\times
2$ MIMO channel with $\alpha=0.1$. We observe that $d_2(r)\geq
d_1(r)$ and there is only one corner point on $d_1(r)$ (or $d_2(r)$)
over spatial multiplexing gain region $r\in \tilde{\Omega}_1$ (or
$r\in \tilde{\Omega}_2$).

Next we illustrate the impact of $\alpha$ on DMT. Fig.~4
 plots the relationship between
the achievable diversity gain and the channel quality $\alpha$ in a
MISO/SIMO channel. It clearly shows that power adaptation makes
better use of the imperfect CSIT than rate adaptation. In other
words, to achieve the same performance our scheme saves a great
amount of pilot power and thus is more applicable. Specifically, the
diversity gain improvements over \cite{IEEErelay:DMT} and
\cite{IEEErelay:OFT} are $M^2\alpha$ and $(M-1)M\alpha$,
respectively, at any spatial multiplexing gain.
It is no doubt that the achievable DMT increases with CSIT quality
$\alpha$. Fig.~5 plots how the achievable diversity gain with power
adaptation improves with the channel quality $\alpha$ in a $5\times
3$ MIMO channel at the full multiplexing gain. We observe that there
are fast increases of diversity gain at $\alpha=0.25$ and
$\alpha=0.1667$. These two values of $\alpha$ are actually
thresholds for $d_k(r)<\infty, k=1,2,3$. When $\alpha\geq
\frac{1}{M-1}=0.25$, $\mathcal{B}=\{3\}$. Therefore, we have
$d_{\mathcal{O}}(N)=d_3(N)$. When $0.1667 \leq \alpha<0.25$, we have
$\mathcal{B}=\{2,3\}$ and $d_{\mathcal{O}}(N)=d_2(N)$. When
$\alpha<0.1667$, we have $\mathcal{B}=\{1,2,3\}$ and
$d_{\mathcal{O}}(r)=d_1(N)$. Combining with the fact that
$d_1(r)<d_2(r)<d_3(r)$ for any fixed $\alpha$, it is not difficult
to understand the cliffs on this curve.

Note that the additional diversity gain comes at the price of
reverse channel pilot power to obtain the CSIT. As long as the
reverse channel SNR does not scale with $\rho$, i.e., $\alpha=0$,
even with some partial CSIT at the transmitter, there will be no
improvement on the fundamental DMT. However,
 when the reverse channel SNR relative to $\rho$ becomes asymptotically zero, i.e., $\alpha<1$,
 there will be a significant improvement of the diversity gain.
   When the reverse channel SNR as compared to the forward SNR is asymptotically unbounded,
   i.e., $\alpha>1$, one can achieve the full spatial multiplexing gain while enjoying a
   even more remarkable diversity.

\section{Conclusion}

In this paper, we investigated the impact of CSIT on the tradeoff of
diversity and spatial multiplexing in MIMO fading channels. For
MISO/SIMO channels, we showed that using power adaptation, one can
achieve a diversity gain of $d(r)=K(1-r+K\alpha)$, where $K$ is the
number of transmit antennas in the MISO case or the number of
receive antennas in the SIMO case. This is not only higher but also
more efficient than the available results in literature. For general
MIMO channels  with $M>1$ transmit and $N>1$ receive antennas, when
$\alpha$ is above some certain threshold, one can achieve a
diversity gain of $d(r)=MN(1+MN\alpha)-(M+N-1)r$; otherwise, the
achievable DMT is a collection of discontinuous line segments
depending on $M$, $N$, $r$ and $\alpha$. The presented DMT shows
that exploiting imperfect CSIT through power adaptation
significantly increases the achievable diversity gain in MIMO
channels.

\appendices
\section{}
Letting $q_n\triangleq-\log(b_n)/\log (\rho)$ for all $n$ and
$\mathbf{q}\triangleq[q_1,...,q_N]$, we have
\begin{equation}
\begin{split}
&E\{P(\hat{\textbf{H}})\} =\int_{\textbf{b}\succeq
0}\frac{\kappa\bar{P} }{\left(\prod_{n=1}^N b_n^{2n-1+M-N}\right)^t}
\hat{\xi}^{-1}\prod_{n=1}^N b_n^{M-N} \prod_{n<j}^N
(b_n-b_j)^2\exp\left(-\frac{1}{1+\sigma_e^2}\sum_{n=1}^N b_n\right)
d \textbf{b}\\
&=\int_{\textbf{q}\succeq 0} \frac{\kappa\bar{P} \hat{\xi}^{-1}(\log
\rho)^N}{\left(\prod_{n=1}^N \rho^{-(2n-1+M-N)q_n}\right)^t}
 \prod_{n=1}^N \rho^{-(M-N+1)q_n} \prod_{n<j}^N (\rho^{-q_n}-\rho^{-q_j})^2\exp\left(-\frac{1}{1+\sigma_e^2}\sum_{n=1}^N \rho^{-q_n}\right)
d \textbf{q}.
\end{split}
\label{eq13}
\end{equation}

At high SNRs, it is easy to show that
\begin{equation}
E\{P(\hat{\textbf{H}})\}= \lim_{\rho\rightarrow\infty}
\int_{\textbf{q}\succeq 0}\kappa  \bar{P}  \hat{\xi}^{-1}(\log
\rho)^N \left(\prod_{n=1}^N \rho^{-(2n-1+M-N)q_n}\right)^{(1-t)} d
\textbf{q}=\bar{P}.
\end{equation}

\section{}
Let $v_{1,k_1},...,v_{k_1,k_1}$ denote the solutions of
$v_1,...,v_{k_1}$ that minimize $d_{k_1}(r)$, and let
$v_{1,k_2},...,v_{k_2,k_2}$ denote the solutions of
$v_1,...,v_{k_2}$ that minimize $d_{k_2}(r)$. Without loss of
generality, we assume
\begin{eqnarray}
&&v_{1,k_1}=...=v_{i-1,k_1}=\tau(k_1),\tau(k_1)>v_{i,k_1}\geq \alpha, v_{i+1,k_1}=...=v_{k_1,k_1}=\alpha\\
&&v_{1,k_2}=...=v_{j-1,k_2}=\tau(k_2),\tau(k_2)>v_{j,k_2}\geq \alpha, v_{j+1,k_2}=...=v_{k_2,k_2}= \alpha.
\end{eqnarray}

It follows that the corresponding spatial multiplexing gain $r$
satisfies
\begin{eqnarray}
 &&r=(N-i+1)\tau(k_1)-(k_1-i)\alpha-v_{i,k_1}\\ &&r=(N-j+1)\tau(k_2)-(k_2-j)\alpha-v_{j,k_2}
 \end{eqnarray}which leads to
\begin{equation}
\label{eqnv2v1}
\left\{(N-j+1)\tau(k_2)-(k_2-j)\alpha-v_{j,k_2}\right\}
-\left\{(N-i+1)\tau(k_1)-(k_1-i)\alpha-v_{i,k_1}\right\}=0.
\end{equation}

We consider the following three cases.\\
Case 1) $j<i$: Letting $B$ denote the LHS of (\ref{eqnv2v1}), we
have
\begin{equation}
\begin{split}
B>&
(N-j)\tau(k_2)-(k_2-j)\alpha  -(N-i+1)\tau(k_1)-(k_1-i+1)\alpha\\
\geq &(N-i+1)\tau(k_2)-(k_2-i+1)\alpha  -(N-i+1)\tau(k_1)-(k_1-i+1)\alpha\\
\geq &\alpha(k_2-k_1)\left((N-i+1)(M-N+k_2+k_1)-1\right)>0.
\end{split}
\end{equation}
This contradicts with $B=0$. Therefore, $j<i$ is not possible.

Case 2) $j>i$: It is easy to observe that
\begin{eqnarray}
&&v_{1,k_2}-v_{1,k_1}=...=v_{i-1,k_2}-v_{i-1,k_1}
=k_2\alpha(M-N+k_2)-k_1\alpha(M-N+k_1)>0\\
&&v_{i,k_2}-v_{i,k_1}>k_2\alpha(M-N+k_2)-k_1\alpha(M-N+k_1)>0\\
&&v_{i+1,k_2}-v_{i+1,k_1},...,v_{k_1,k_2}-v_{k_1,k_1}\geq \alpha-\alpha= 0\\
&&v_{k_1+1,k_2},...,v_{k_2,k_2}\geq \alpha.
\end{eqnarray}

Then, it follows that
\begin{equation}
d_{k_2}(r)-d_{k_1}(r)=\sum_{i=1}^{k_2}v_{i,k_2}-\sum_{i=1}^{k_1}v_{i,k_1}>0.
\end{equation}

Case 3) $j=i$: Similarly, we have
\begin{eqnarray}
\label{eqn_65}
&&v_{1,k_2}-v_{1,k_1}=...=v_{i-1,k_2}-v_{i-1,k_1}=k_2\alpha(M-N+k_2)-k_1\alpha(M-N+k_1)>0\\
\label{eqn_66}
&&v_{i+1,k_2}=...=v_{k_2,k_2}=v_{i+1,k_1}=...=v_{k-1,k_1}=\alpha.
\end{eqnarray}

From (\ref{eqnv2v1}), we get
\begin{equation}
\label{eqn_67}
v_{i,k_2}-v_{i,k_1}=\alpha(k_2-k_1)\left((N-i+1)(M-N+k_2+k_1)-1\right)>0.
\end{equation}
Combining (\ref{eqn_65}), (\ref{eqn_66}) and (\ref{eqn_67}), we get
$d_{k_2}(r)>d_{k_1}(r)$. The proof of Lemma 2 is complete.

\section{}
We compare the spatial multiplexing gain $r$ of the corner point $k'$ ($k'=1,...,k-1$) on the DMT curve $d_k(r)$, i.e., $r=(N-k')\tau(k)-(k-k')\alpha$, with the lower boundary of
$\Omega_{k-1}$, i.e., $(N-k+1)\tau(k-1)$, and get
\begin{equation}
(N-k')\tau(k)-(k-k')\alpha - (N-k+1)\tau(k-1) \geq
\left((N-k+1)(M-N+2k-1)-1\right)\alpha > 0.
\end{equation}

If $(N-k')\tau(k)-(k-k')\alpha<N$, it suffices to have
$(N-k')\tau(k)-(k-k')\alpha\in {\Omega}_{k-1}$. Otherwise, we get
$(N-k')\tau(k)-(k-k')\alpha \notin \Omega_k$. Since
${\Omega}_{k-1}\bigcap \tilde{\Omega}_{k}=\emptyset$ and
$\tilde{\Omega}_{k}\subseteq \Omega_k$, both cases lead to
$r\notin\tilde{\Omega}_k$. This completes the proof of Lemma 3.

redpajama_set_name: RedPajamaArXiv


text:
Cursing our mothers
By: Ma. Ceres P. Doyo - @inquirerdotnet
Philippine Daily Inquirer / 12:16 AM October 13, 2016
The current joke now is that the Philippines should also be known as the "Republic of P.I." Not for Philippine Islands, as our country was called during the American colonial era, but for "p***** ina," the favorite cuss words of President Duterte who cannot go without them in his rambling speeches. Translated into English, the phrase means "child of a whore" or "son of a b****." If you add the word "mo," it means you are one, but in English you don't really add "You are a" to SOB. So with or without mo, your mother is insulted just the same.
I don't know how it is said in other Philippine languages and dialects but I know that in Iloilo, it is said in Spanish—that is, "hijo de p***" or "yudep***." It has been further contracted or sanitized as "deputa" or "depuga," the last one used as an expression of awe or amazement, as in "Depuga gid." Another variation is "yude"-to praise or compliment. With this, the original meaning has been completely erased because it is not even a cuss word.
But to inflict pain or insult, there is nothing like the complete expletive in Spanish, uttered harshly and deliberately to insult the other person and his or her mother.
I have never heard my parents utter cuss words when I was growing up, but walls are not impermeable especially in the province, so I got to hear "bad words" used on some people. I got to know the Ilonggo (Hiligaynon) words for whore. Like most towns, ours had a menagerie of peculiar characters, their names appended with their particular disabilities or dishonorable preoccupations. For example: "Manuel Buang," "Amin Kurog" or Estrella Padót.
Taal Volcano in 1881
But why does cursing have to dishonor mothers? In Ilocano the equivalent of "P.I." refers to the mother's birth canal, to say it rather clinically. Not about what she is but about the offspring that passed through it. The ultimate insult.
It is the opposite of what a woman said to Jesus as recounted in the Bible: "Blessed is the womb that bore you and the paps that gave you suck." The ultimate compliment.
Another variation of the mother-son insult is the "M.F." cuss words which are of American origin. This time it is directed to the good-for-nothing son, but the mother is still in the picture. And both of them are being called sexual perverts.
Speaking of "M.F.," there is an old joke about a Filipino family in America having a good time in a park. When the toddler began running, the concerned parents yelled, "Madapa ka (You might stumble)! Immediately, dagger looks were thrown their way.
Seriously now, the "P.I." cuss has become so commonplace, popularized by no less than the President whose vocabulary is littered with it. Some of his defenders argue that it is just his manner of speaking, a verbal expression. One can even say that eventually, it will lose its original meaning and that it will just be a set of nonsense syllables that can add color to one's limited vocabulary. I don't think so. I shudder when I think that an insult to mothers will soon be as commonplace as "OMG" or "LOL."
Some time ago someone posted on Facebook a cartoon which showed kids exclaiming "P.I." enclosed in so many dialogue balloons.
Last Sunday the Catholic Church in the Philippines celebrated Indigenous Peoples (IP) Sunday. I could not help thinking whether in their pristine state in the forest primeval our IP communities had an equivalent of "P.I." Did they deliver insults by referring to their enemies' mothers? Did it get into their vocabulary?
The Old Testament has lots of stories about fornication and people committing sexual taboos, but later, in the new dispensation, didn't Jesus save the woman caught in adultery from being stoned to death? (Emphasis on caught.) As the story goes, the woman was caught in flagrante delicto. She was not merely being falsely accused.
Last year while he was on the plane to (or from?) the Philippines, Pope Francis was asked about violence. He began by saying: "Curse my mother and expect a punch." During the presidential campaign, Mr. Duterte did throw a "P.I" at the Pope for the traffic his visit had caused.
Send feedback to [email protected] or www.ceresdoyo.com
An unconventional growth agenda
Nonito Donaire vs Naoya Inoue is BWAA 2019 Fight of the Year
OSG plea to revoke ABS-CBN franchise 'a duplicitous move' – Lacson
Joe Devance leadership helps Ginebra in another title run
Sea turtle trapped in net freed in Legazpi City
TAGS: cursing, expletives, Language, profanity, Rodrigo Duterte

redpajama_set_name: RedPajamaCommonCrawl


Slow down the virus outbreak, solve the murder, complete your final test as a trainee secret agent… Ladies, for the ultimate test of wits, nerve and teamwork, look no further than the Breakout rooms!
This thrilling hen weekend activity is taking Manchester by storm. At a secret location, a series of themed rooms are waiting to give up their secrets - but only if you're quick enough to solve the clues! With 60 minutes to escape, you'll have to find the evidence, break the codes, crack the clues and master the tech. Will you prove to be Charlie's Angels, or the hen weekend version of Maxwell Smart?
If you're looking for something totally different for your hen weekend, then escape rooms are for you. It combines adrenaline, brilliant stories, hands-on detective work and clue-solving with cool technology and believable sets. It's like starring in your very own thriller!


The Pattaya News reported that Thai and foreign tourists ran for cover as a group of 50 young Thai people fought and threw things in the Soi 7 and 8 Beer Bar areas.
In a video people could be heard shouting that the police were coming and there were further cries of "chuay duay" (Help!).
The tourists were worried about being hit by stray objects.
The media said this all occurred at about 6 pm on Monday.
The police made a few arrests but most of the melee miscreants melted into the crowds.
Pattaya celebrates Songkran longer than everywhere else - the water wars are expected to continue until Friday.
Looks like a good time, said who?
I remember on another post yesterday, one poster R==M--- defending Songkran in Pattaya, saying it was a great bit of Thai culture, real fun, and less boring than the western 'New Year' fireworks displays !
I'll stick with the pyrotechnics thanks Rob.
Just a few skinny young teenagers. Boys will be boys.
Credit to the cops who were there and had the situation under control in less than minutes keeping everyone happy and safe.
good guys out, bad guys out, all guys out.
New Year celebrations in most countries that use alcohol usually involve a bit of violence. Songkran Pattaya brings drunks from around the world night after night and the violence per liter of alcohol consumed would be very low.
The Thais who work in these areas have a very high tolerance for drunken idiots and credit to them.
500,000 people celebrating and the only incident is with a group of 15 year old boys.
Nothing much in this at all except for a squeaking bar girl.
i was down there last night and everyone was happily enjoying the festivities. It reminded me of the Summer of Love.
It'll be worst on the 19th..normally the real guns (not water pistols) come out to play on that day.
Boys will be boys, until someone gets killed. Just young hooligans taking advantage of the 'celebrations', such as they are in that dump of a place.
At 2:30 is that music or someone's car alarm going off?
Shhhh you can't say nasty things about Pattaya....its just clean family fun!
The problem with the pyrotechnic on NYE is a lot of the strays dogs freak out and dash onto the road into oncoming vehicles, some just ran for their lives and lost their way back to their usual hunts. I much rather have some water wars at least then if humans wanna fight and kill each other let them.


text:
Major Changes to Rules Governing the MDEQ
Home/Environmental Law/Major Changes to Rules Governing the MDEQ
By Brian Considine.
The New Gatekeepers at the MDEQ
On June 28, 2018, Governor Snyder signed into law a package of bills intended to reign in the Michigan Department of Environmental Quality ("DEQ") which some in the regulated community feel has an "agenda." This article is the second in a three part series and summarizes Senate Bill 652 which became Public Act 267 of 2018.
Public Act 267 (the "Act"), which has an effective date of June 29, 2018, amended the Administrative Procedures Act (MCL §24.201 et seq.) and created what is commonly referred to as the "environmental rules review committee" (the "ERRC"). The purpose of the ERRC is to review any new regulations proposed by the DEQ.
As soon as Senators Casperson (R-38 Dist) and Robertson (R- 14 Dist) proposed SB 652 (along with SBs 653 and 654) battle lines were drawn. Senator Casperson asserted that that the bills were necessary because of DEQ staff who are too often arbitrary and unreasonable in their decisions: "It's not rules and laws they are following; it's an agenda…they are going to save the planet, no matter what."[1] Lisa Wozniak of the Michigan League of Conservation Voters saw it differently: "Instead of relying on science to guide decisions that impact our land, air and water, this legislation gives polluters undue influence over the state agency charged with protecting our communities and natural resources." [2] Despite the rhetoric on both sides, in the end, the Governor signed the legislation into law.
Section 65(1) of the Act, created the ERRC as an independent body in the Office of Performance and Transformation which itself was created within the State Budget Office in 2016 by Executive Order 2016-4.[3] From the get-go, many stakeholders were troubled by the composition of the ERRC which is composed of a majority of industry leaning members.
Composition of the ERRC
The ERRC is composed of four non-voting members and twelve voting members. The non-voting members include the directors of the Departments of Environmental Quality, Health and Human Services ("DHHS"), Agriculture and Rural Development and Natural Resources. The voting members, who are appointed by the Governor with the advice and consent of the Senate, consist of one representative from each of the following six industries: solid waste management, manufacturing, small businesses, public electrical utility, oil and gas, and agriculture. The other members include representatives of: an environmental organization, local government, land conservancy, and public health. The ERRC is rounded off with two members of the general public. Act §65(2).
Qualifications of ERRC Voting Members
To ensure the ERRC is competently staffed to handle complex scientific issues related to public health and the environment, each voting member must "possess knowledge, experience, or education that qualifies him or her to represent" their respective constituency. Act §65(3). In addition, the directors of the DEQ and the DHHS must each select a science advisor to provide expert advice to the ERRC members on relevant science-based issues and those advisors must possess the requisite credentials to act in such capacity. Act §65(13). ERRC members may also select their own administrative, technical and legal consultants to assist the ERRC to carry out its duties. Act §65(18).
Conflict/Bias Provisions
Because ERRC members are selected by the Governor (who has his or her own political affiliations), the Act has several mechanisms to reduce bias and prevent conflicts of interest. Members are appointed with the advice and consent of the senate, member terms are staggered (Act §65(7)), and no more than six of the voting members can be members of the same political party (Act §65(6)). In addition, Section 65(4) prevents someone from being a voting member of the ERRC if they: are currently employed by any State agency or has been at any time within the preceding three years or the person (or their employer) has had a contract with the DEQ in the preceding three years that generated more than 5% of the member's annual gross income or member's employer's annual gross revenue. In addition, Section 65(9) gives the Governor the right to remove a voting member for cause. This, however, is a double edged sword because a Governor could not only use this right to remove a member with conflicts of interest but could also remove legitimate member for political reasons.
ERRC Review Process
As explained in Section 65(19), "the purpose of the [ERRC] is to oversee all rule-making of the [DEQ]." Rules that are not processed in compliance with section 66 are invalid. Act §43(1). The only exception is when an emergency necessitates quicker action. Act §§48(1) and (2).
As a result of the changes made to the APA, the actual rule-making process that the DEQ must now follow much more complex. As before, if the DEQ is contemplating any changes to its rules, it must file a request for rule-making with the Office of Regulatory Reinvention. MCL 24.239(1). However, the DEQ must also transmit the request for rule-making to the ERRC and the DEQ is encouraged, but is not obligated to form a stakeholder review. Act §66(1). If the chair and vice chair of the ERRC determine that no review is needed, the ERRC does not review the proposed rules. However, this decision can be overruled by a vote of seven or more members.
If the ERRC decides to review the rules, they must decide if the rules satisfy all of the following criteria:
They do not exceed the rule-making delegation in the relevant authorizing statute;
They reasonably implement and apply the statute and are otherwise consistent with other law;
They are necessary and suitable to achieve their purposes in relation to the burdens placed on business;
They are clear and unambiguous considering the subject matter and businesses that will have to comply with the rules;
They are based on sound and objective scientific reasoning. Act §66(4).
Under Section 66(5), the ERRC has 35 days to review the above and then decide one of the following:
By a vote of 9 members, to allow the rule-making to proceed forward normally under the APA;
By a majority vote, that the 5 criteria have not been met or that more information is needed and notifies the DEQ, in which case the DEQ must address the ERRC's concerns. If the ERRC has not made a decision (within 90 days after notifying the DEQ of the deficiencies) that the proposed draft rules or revised draft rules satisfy the 5 criteria, then the DEQ is to proceed with a public hearing under APA §§41 and 42.
By a majority vote, that the 5 criteria have been satisfied and that the DEQ is to proceed with a public hearing under APA §§41 and 42.
If the ERRC fails to make the Section 66(5) determination in 35 days, the DEQ may proceed with a public hearing under APA §§41 and 42.
After holding a public hearing the DEQ has 120 days to prepare a report and synopsis of comments and suggested changes for the ERRC to review. If that deadline is not met, the DEQ must withdraw the rules request. If the report is timely submitted to the ERRC, the ERRC has 120 days to review the DEQ's report and either approve the proposed draft rules, approve them with modifications or reject them. Act §66(9).
If the ERRC approves the proposed draft rules (or does not act within 120 days), the ORR has 1 year from the last public hearing to transmit the rules, comments, any revisions and certificate of approval from the legislative services bureau and ORR to JCAR (Joint Committee on Administrative Rules). If the ERRC modifies the draft rules or rejects them, it must submit a notice of objection an explanation to the DEQ and the Governor. If the ERRC and DEQ resolve the issues, the rules are submitted to JCAR. If they cannot resolve the ERRC's issues within 11 months from the last public hearing, the DEQ must submit a report to the Governor and if the Governor concurs with the DEQ, the rules are forward to JCAR, otherwise, the rules are withdrawn. Act §§66(10)-(12).
While it is true that no law is perfect, this Act does have some deficiencies that could produce problems down the road. A few of these concerns are outlined below.
Composition of the voting members is seemingly skewed toward business interests. The ERRC will have 6 voting members representing the business sector. While there are 6 non business related voting members, the 6 business members will tend to favor business interests that may not align with environmental or public health protection. The composition could result in more frequent appointment of a chairperson and vice chairperson with business friendly interests. Also, it could result in deadlocked voting (in which case after 35 days the DEQ could hold public hearings under APA §§ 41 and 42), or, more likely than not, one of the non-business interest members (local government or general public) will align with the business sector votes to force the rules modification process, and possible review by the Governor. This risk is especially since one of the 5 criteria the ERRC must consider involves a balancing of the necessity of the rules in relation to the burdens placed on business. If the Governor sides with the business related voting members, there could be situations where rules to protect public health or the environment are either not promulgated or are less protective.[4]
Act §65(9) gives the Governor the ability to remove a member for cause, however, cause is not defined and this power is not subject to review. Could the Governor remove a member for extreme views on a subject or always voting a certain way? Because there is no review mechanism, this would likely end up being scrutinized in the court of common opinion.
The political affiliation limitation also presents unique issues. The Act prevents more than 6 members being from one political party. The first question is how will party affiliation policed? Voting rolls cannot be reviewed because those types of records are not kept so it would be based solely on a member's word. However, what prevents a person from switching parties? Is an independent more likely to be business friendly or not? Will there be periodic reviews of party affiliation? Will ERRC members have to police this and call out any members who seem to be voting contrary to their self-declared party affiliation?
In addition to the foregoing, the ERRC is prohibited from conducting business if there is a vacancy in one of the voting member positions. If the Governor and/or Senate do not take action to fill that vacancy, the ERRC cannot consider any proposed rules. This arrangement could be abused to slow down and/or halt the rule promulgation process. There is a question as to whether section 66(7)(d) would apply (failure of the ERRC to make a determination within 35 days) so that the rules promulgation process could proceed forward unhindered.
The new environmental rules review committee was created with the intent to oversee an agency that was perceived by some as having a pro-environment/public health agenda. The question is whether there was an issue in the first place and, if so, does the new ERRC fix that or simply create another level of bureaucracy? Will this put an end to labeling DEQ rules as being "agenda" driven? Is the ERRC an overreaction that will end up turning rules making into a pitched partisan battle with one side asserting that the rules are too economically burdensome even though there is a public health threat or threat to the environmental that should be addressed? And if people are injured as a result of a rule not being promulgated due to economics, how is that really any different than what happened in Flint? These are questions that will end up being answered very soon as the DEQ attempts to move regulations relating to indoor air and polyfluoroakyl substances ("PFAS") through the new environmental rules review committee.
[1] "Can Michigan's polluters be trusted to self-regulate?" Detroit Free Press, December 19, 2017, accessed on August 30, 2018 at https://www.freep.com/story/news/local/michigan/2017/12/18/legislation-michigan-industries-rules-pollution/956636001/
[2] "Michigan LCV blasts lawmakers for passing 'Fox Guarding the Henhouse Bills'", accessed on August 30, 2018 at https://michiganlcv.org/news/michigan-lcv-blasts-lawmakers-for-passing-fox-guarding-the-henhouse-bills/
[3] The goal of the OPT is to work "with all state departments to establish a more effective system of customer service, performance measurement and regulatory and business practices." Press Release "Gov. Rick Snyder issues executive order creating Office of Performance and Transformation", February 2, 2016, accessed on August 30, 2018 at https://www.michigan.gov/snyder/0,4668,7-277-57577_57657-375344–,00.html
[4] In this instance, given what transpired with the Flint water crisis, there is a question as to whether the ERRC members or Governor could be held to account for ignoring evidence of the need to protect public health because of the cost to business.
By admin@dawdamann|2022-01-11T09:59:24-05:00September 19, 2018|Categories: Environmental Law|Comments Off on Major Changes to Rules Governing the MDEQ


text:
Saturday 28 January 2023 \
What is Islam
Prophet Muhammad
Sciences of Quran
Sciences of Hadith
Family & Health
Islam for Children
Personalities in Islam
Islamic spirituality
Back in Islam
Du`a/Supplication
Mufti Talgat Tajuddin: "We need to bring order to Europe"
Putin emphasized high level of relations between Russia and Islamic countries
Tatarstan Muslims help poor families to prepare children for school
Muslims of Penza helped needy families to get children ready for school
Photo exhibition "Lead us on the straight path" opened in St. Petersburg
"Muz-TV" Ex-CEO to make a mosque from his house
Sport contest among mosques was held in Kuzbass
Lack of halal food in prisons discussed in Russia
Nutritionist: Halal foods are good for everyone
Grand Mawlid from Suleiman Kerimov held in Dagestan
Europe's Muslim population expected to rise by third by 2030
muslims in Europe
If current trends continue 79 countries will have a million or more Muslim inhabitants in 2030, up from 72 countries in 2011.
Source : Agencies / 07 Mar 2014
According to the Pew Islam is growing about 2.9% per year. This is faster than the total world population which increases about 2.3% annually. The world's Muslim population is expected to increase by about 35% in the next 20 years. In mid 2010 the Pew forum estimated that there were 1.57 billion Muslims in the world. This represents 22% of the world's population.
Islam is the second largest religion in the world, beaten only by Christianity which represents 33% of the world's population with a little over 2 billion adherents.
The Pew Forum on Religion & Public Life stated that Islam is the fastest-growing religion in Europe. Driven by immigration and high birth rates, the number of Muslims on the continent has tripled in the last 30 years. Most demographers forecast a similar or even higher rate of growth in the coming decades.
In 2011 statistics tell us that 74.1% of the world's Muslims live in the 49 countries in which Muslims make up a majority of the population. More than a fifth of all Muslims (23.3%) live in non-Muslim-majority countries in the developing world. These minority Muslim populations are often quite large.
In Europe as a whole, the Muslim share of the population is expected to grow by nearly one-third over the next 20 years, rising from 6% of the region's inhabitants in 2010 to 8% in 2030.
In absolute numbers, Europe's Muslim population is projected to grow from 44.1 million in 2010 to 58.2 million in 2030. Nearly three-in-ten people living in the Asia-Pacific region in 2030 (27.3%) will be Muslim, up from about a quarter in 2010 (24.8%) and roughly a fifth in 1990 (21.6%). Muslims make up only about 2% of the population in China, but because the country is so populous, its Muslim population is expected to be the 19th largest in the world in 2030.
In Germany, the estimated 4,000 converts each year, can be compared with an annual average of 300 in the late 1990s, still, less than 1 percent of Germany's 3.3 million Muslims are converts.
A report by France's domestic intelligence agency, published by Le Figaro, estimated that there were 30,000 to 50,000 converts in France. The bulk of French Muslims are French citizens, and Islam is France's second highest ranked religion.
Muslims are a minority in the United Kingdom, making up 2.7 per cent of the country's total population of some 60 million people. The number of converts to Islam is, as expected very difficult to either predict or find hard data about. One British newspaper however, the Independent, reports that the number of Britons converting to Islam has nearly doubled in the past decade, despite the fact that the UK has witnessed a rise in Islamophobia. This is according to a comprehensive study by inter-faith think tank Faith Matters.
Previous estimates have placed the number of Muslim converts in the UK at between 14,000 and 25,000, but this study suggests that the real figure could be as high as 100,000, with as many as 5,000 new conversions each year. By using data from the Scottish 2001 census - the only survey to ask respondents what their religion was at birth as well as at the time of the survey - researchers broke down what proportion of Muslim converts there were and then extrapolated the figures for Britain as a whole.
Europeans live longer but obesity threatens life quality
Over 430,000 people murdered worldwide, says new study
Europe: Christian Continent or Not?
Study ranks UAE number one in social progress
43 million people lack food in Europe: Red Cross
Western hoteliers targeting Muslim travelers
Record 33.3 mln people worldwide displaced by conflict
The Great Shamil, Imam of Daghestan and Chechnya, Shaykh of Naqshbandi tariqah.
Russia and Turkey ditched US currency for S-400 missile system deal
Almost 1 in 5 Germans is 'at risk of poverty' despite record employment – study
Philippine Congress moves a step closer to expanding Islamic banking
'Cryptocurrency can be used among Islamic countries'
Muslim Doctor Develops Method to Help Coronavirus Patients
Muslim Scientist's New Tool Can 'Listen to Bacterial Communicate' to Curb Infections
Benefits of reciting Salawat
Dawah is Easy - Street dawah in UK
Allah Companions Culture economy hadith health islam Muslims Muslim women Prophet Muhammad Quran Sunnah
MuslimsToday
Islam, Muslims, Sufism
MuslimsToday.info © Copyright 2011 All Rights Reserved


Gibbon in an application stack that provides module-based functionality related to school systems.
While try to install it on a Macbook Air, I bumped into a roadblock: the installation screen was blank. Turns out, Gibbon requires a PHP extension gettext which is not installed on Mac OSx by default.
Download the library from gettext website.
Confirm using a php-info file that the extension has been successfully installed and enabled.
© 2019 Technology as I experience it…. All rights reserved.


This picturesque property was the first winery on Greer Road (near Hillier), now one of the County's main wine streets. The 63-acre vineyard was planted through the early part of the last decade to grow Pinot Gris, Chardonnay, Riesling, Pinot Noir and Cabernet Franc. Winemaker Paul Battilana took the helm, finishing the 2008s and making the 2009s, which included the addition of sparkling wine to the lineup. The Cucina Italiana is open for casual lunches and dinners during the summer, doubling as a wedding and event space. The wine shop often features local artwork.


That became especially evident to Tori Ward '13 and Sophie Burke '13 while conducting research on climate change this past July in Sweden. During their month at the Abisko Scientific Research Station some 200 kilometers north of the Arctic Circle, they lived and worked alongside scientists from around the world, including Canada, Germany, Bangladesh and Sweden.
"It was great to be in another country and to realize how international science is, especially the earth sciences," says Ward, who is studying hydrology.
Ward and Burke received Summer Undergraduate Research Fellowships from the Hamel Center that enabled them to participate in the inaugural summer of Northern Ecosystems Research for Undergraduates (NERU), a UNH summer program directed by research associate professor of biogeochemistry Ruth Varner and sponsored by the National Science Foundation. The nine students in NERU—representing seven different colleges and universities—designed individual projects related to climate change. After a month at UNH doing preliminary work, the group headed to Sweden to collect data.
Ward's research examined the effect of precipitation on the release of soil hydrogen, an area that has received little attention from researchers. "In order to understand global warming, we need to know more about this process," says Ward.
It's expected that increased precipitation and thawing of the permafrost (frozen ground) will lead to wetter soils, causing more hydrogen to be released, Ward explains. Increased hydrogen levels may contribute to warming by trapping greenhouse gasses such as carbon dioxide and methane in the atmosphere.
Sophie Burke '13 takes methane gas measurements in local peatland.
Burke focused on the impact of warming on the amount of greenhouse gases released into the atmosphere by peatlands. "We're finding that peatlands, when they work properly, can be huge sinks of carbon," Burke says. Now, with global climate change, peatlands are "turning from sinks into sources of carbon." That shift is occurring because the warming of the atmosphere is thawing the permafrost and causing a release of trapped carbon.
One of her findings was that the July 2012 samples from thaw ponds contained a higher percentage of methane than those from peat, possibly because of characteristics of the thaw ponds such as their vegetation and moisture content.
Ward and Burke will use their data from Sweden as a basis for their senior theses and expect to present their results at the American Geophysical Union Fall Meeting in San Francisco this December. They both plan to attend graduate school and credit Varner with helping them develop as researchers.
Editor's Note: To read more Ward's and Burke's projects, visit the NERU blog.
Each year in October, the Hamel Center for Undergraduate Research marks the academic homecoming of IROP students with the IROP SYMPOSIUM, brief illustrated research presentations crafted for a general audience of faculty, students, administrators, supporters, families, and invited guests. The special anniversary edition of the International Research Symposium will be held during Homecoming on Friday, October 12, from 2-5 p.m. in MUB Theatres 1 and 2.
Written by Sonia Scherr '13MFA. Photos courtesy Northern Ecosystems Research for Undergraduates blog.


The Hattadare Indian Village Park in Bunnlevel is one of the homes of the Lumbee Indian Nation, or what's left of it.
The Park was built beginning in 1968 by a TV repairman and part-time preacher named James Lowery. He had a little Indian blood (although not Lumbee) and called himself Chief Little Beaver. Lowery envisioned his village as a place where members of all tribes could meet and just hang out. To whatever degree that actually happened, it ended in 1990, when the Chief died.
The Park has continued its slow decay ever since. When we last visited, a sign out front read "Indian Snack Bar," but the trailer that housed it had been abandoned and filled with garbage and rotting mattresses. Other trailers sheltered barking dogs, screaming children, and adults, but the Lumbees wouldn't show themselves.
Big letters dangle off of the fence that surrounds Hattadare: "Indians Are People Too," they read. Humming, overhead high-tension power lines run down the center of the Park; their clear-cut creates a nice, sunny path from which you can admire the scary, overgrown shrines and statues on either side. Venture into the trees only if you dare; you'll find statues of cacti and polar bears(???), as well as garden shop concrete Indians wearing headdresses, something that the swamp-dwelling Lumbees never even considered.
The highlight of Hattadare is the World's Largest Arrowhead, an uneven concrete pillar with little rocks stuck into it. In the center of the arrowhead is a framed photo of an Indian -- Chief Little Beaver. It doesn't look much like an arrowhead, but perhaps the mysterious Lumbee knew a thing or two about aerodynamics that modern science has yet to learn.
Lowery's widow, Letha, lived in a trailer at the Park of many year's after the Chief's death. It was reported that she constantly encouraged the Chief's son to fix the place up, but he was disinterested.
Hwy. 401, 12 mi. N of Fayetteville. Look for the cement horsey and the lichen-encrusted teepee.
Inventor of the Power Chord, Dunn, NC - 10 mi.
Marvin Johnson's Gourd Collection, Angier, NC - 14 mi.
Ben Harris Sculptures, Fuquay Varina, NC - 18 mi.
Muffler Man, Raleigh, NC - 41 mi.


We are a resource for you if you encounter any problems, would like to file a grievance, and/or need assistance. We can facilitate contact and communication with your health care providers and the many service departments in the Health System. We'll help you with questions about patients' rights and Health Care Proxy forms. We can serve as your liaison to the Ethics Committee.
Following is a list of some of the most commonly asked questions about patient representatives. We provide the highest quality of care to all our patients in a safe environment that respects dignity, cultural, spiritual and personal needs. With your active participation in the treatment process, we can assist you in your medical progress and guide you toward a speedy recovery and discharge.
Our goal is to provide the best health care and medical service possible. We hope to exceed your expectations. Sometimes, however, you may feel that we could have done better. The Patient Representative Office welcomes your comments, whether you wish to tell us that your stay was wonderful or to ask for help to resolve a problem. We want to hear from you. Sometimes patients or their loved ones hesitate to contact us about difficulties they may have encountered. We promise to try to resolve your problem quickly, and you will have the satisfaction of knowing that you have given us a chance to learn how to improve services at Mount Sinai Beth Israel. The information that we collect is shared with our leadership and used to develop service improvements. We value what you have to say and we welcome your call. You can expect a comprehensive investigation and detailed response to your concerns.
Can I file a grievance without giving my name?
We cannot effectively investigate anonymous grievances, but we promise to be discreet and try to honor your requests for confidentiality. If what you tell us reveals a dangerous or illegal situation, we do have an obligation to make sure that it is corrected.
Are patient representatives employed by the hospital?
Yes, patient representatives are employees who are specifically empowered to act as a neutral party by serving as a link between you and the hospital. Our goal is to facilitate a good hospital experience. We are not lawyers and do not provide legal advice.
What kind of issues does the Patient Representative Office handle?
Patient representatives can help you communicate with other staff members and can advocate on your behalf when appropriate. They also can help you understand hospital policies and procedures and can answer any questions you may have about your rights and about advance directives. Your patient representative can tell you about a Health Care Proxy and help you complete the form if you require assistance. Additionally, patient representatives serve as liaisons to the Mount Sinai Beth Israel's Ethics Committee, and can assist you in resolving dilemmas about care, treatment, and services. The Patient Representative Office can assist you if you have not been able to obtain a satisfactory resolution to a problem with your hospital stay. You have the right to safely voice your concerns. A patient representative will investigate any issues you raise and respond to you in a nonjudgmental and timely manner.
Who can call a patient representative?
Anyone can call us—you, a family member, or friend. Hospital staff members often call the Patient Representative Office on behalf of a patient when they feel we can help.


As you should probably be aware by now, we have a new artist in the Wah Wah family.
Lea Lea (formerly Lea Lea Jones) came to our attention in 2012 with her immense AK-47 release on First Word records. A massive sound and forceful production that even then cannot eclipse the strength of Lea Lea's own commanding delivery – we were hooked.
On hearing a complete album of songs full of the same energy, beautifully crafted and produced with her songwriting team Jack Baker and Kim Garrett, we knew that Lea Lea and Wah Wah 45s were a perfect fit.
So here we are in the lead up to her debut single for us Black Or White. Resounding brass issuing a clarion call for her arrival, this single is epic enough in itself. But add to that a stunning video created by AK-47 collaborators Art War Entertainment (www.aweltd.com) and you have something pretty special.
So join us in welcoming Lea Lea to Wah Wah 45s. Do it by watching the video, by pre-ordering the single which features incredible remixes from Goth Trad, Other Echoes and DJ iZem, by sharing this video with your friends and by saying hello to her on the Lea Lea facebook page.
This entry was posted in All news, Lea Lea, News. Bookmark the permalink.


text:
import * as Yargs from "yargs";

/** Parse cli arguments. */
export const parse = (): Yargs.Arguments => {
    const argv: Yargs.Arguments = Yargs
        .usage("Usage: peer-review <item-number> [options]\n"
            + "Opens and populates default mail client with peer review email. "
            + "Copies generated email body to clipboard.")
        .help("h")
        .alias("h", "help")
        .version()
        .env("PEER_REVIEW")
        .alias("proj", "project")
        .describe("proj", `Project name to your Visual Studio Team Services project `
            + `(https://<project>.visualstudio.com).`)
        .alias("u", "user")
        .describe("u", "Username for Visual Studio Team Services project.")
        .alias("p", "password")
        .describe("p", "Password for Visual Studio Team Services project.")
        .alias("t", "template")
        .describe("t", "Email markdown template to use. Interpolated values: ${ID}, ${TITLE}. ")
        .describe("to", "Recipient of peer review email.")
        .demandCommand(1) // require the work item number
        .demandOption(["template", "project", "user", "password"])
        .example("peer-review 135", "Generates email for work item 135, assuming "
            + "all other options are defined by environment variables.")
        .epilog(`All options can be defined via environment variables prefixed `
            + `with "PEER_REVIEW" (e.g, PEER_REVIEW_PASSWORD).`)
        .argv;
    return argv;
};

redpajama_set_name: RedPajamaGithub


The grill restaurant Ionia in Nea Smirni is located in the small square of Iroon Polytechniou, offering greek cuisine. It is famous for its roast meat, kebabs and many traditional greek grilled delicacies. In a cozy and traditional place, you will enjoy the best greek "kokoretsi", spicy kebabs, juicy burgers, traditional "kontosouvli" (from lamb or pork meat), crispy pork souvlaki "gyros" meat and delicious daily specials along with a wide variety of appetizers and fine wine. The restaurant Ionia is the meeting point in Nea Smirni for many meat lovers. Make a discount reservation via e-table and enjoy the best offers in greek restaurants.


Now Jokes on Women is a Crime, Violence against women ?
London, July 4 Sexist jokes induce an attitude that equates violence against women with a macho image, according to a recent study.
Scientists at the University of Granada in Spain sent questionnaires to a group of 109 students aged between 18 and 26.
They showed them two series of jokes, one of them sexist where women were denigrated, and another one with jokes without any kind of sexist content.
The researchers then proposed to them several scenes with different cases of battering against women, from minor to serious attacks, to ask them how they would react in these kind of situations.
The study showed that those who had listened to sexist jokes were much more tolerant to female battering than those who had not.
However, the researchers warned that those individuals affected by sexist humour showed a previous tendency to tolerate violence against women, said a Granada release.
Some of the perceptions of men's sexist attitudes were: "Deep down, feminists intend women to be more powerful than men", "most of the women do not fully appreciate what men do for them" or "there are many women who make sexual insinuations to men and later they reject their advances just to make fun of them".
These findings are slated for publication in the US Journal of Interpersonal Violence.
Soon new law will come, that women will sue you that you made jokes on her and its upto man to prove that he did`t. thats what FemiNAZIs want.


text:
Book Discussions:
Terrorism and U.S. Foreign Policy
Paul R. Pillar
On the C-SPAN Networks:
Paul R. Pillar is a Nonresident Senior Fellow for the Center for Security Studies in the Georgetown University with 21 videos in the C-SPAN Video Library; the first appearance was a 2000 Forum as a Fellow for Foreign Policy Studies Program in the Brookings Institution. The year with the most videos was 2009 with three videos as a Graduate Studies Director for Security Studies Program in the Georgetown University. The year with the highest average number of views per program was 2014 with an average of 1,539 views per program as a National Intelligence Officer for Near East and South Asia in the National Intelligence Council. Most appearances with Daniel Benjamin (3), Thomas R. Pickering (2), Christopher A. Preble (2). Most common tags: Terrorism, Afghanistan, National Security.
Appearances by Title:c. January 1, 2012 - Present Nonresident Senior Fellow, Center for Security Studies, Georgetown University Videos: 1	March 12, 2013 - Present Senior Fellow, Center for 21st Century Security and Intelligence, Brookings Institution Videos: 2	c. January 1, 2005 - Present Graduate Studies Director, Security Studies Program, Georgetown University Videos: 12
National Intelligence Officer, Near East and South Asia, National Intelligence Council c. January 1, 2000 - c. January 1, 2005 Videos: 2	Coordinator, Iraq Intelligence, Central Intelligence Agency c. January 1, 1990 - c. January 1, 1991 Videos: 1	Intelligence Officer, Near Eastern Affairs, Central Intelligence Agency c. January 1, 1995 - c. January 1, 1997 Videos: 1	Fellow, Foreign Policy Studies Program, Brookings Institution c. January 1, 1999 - c. December 31, 2000 Videos: 2
Iranian Public Opinion
The Atlantic Council held a forum with the pollsters who led a University of Maryland Center for International and Security…
U.S. Policy Toward Syria
Former U.S. Ambassador to Iraq and Afghanistan Zalmay Khalilzad talked about Bashar al-Assad's regime in Syria, as well as the…
Middle East Policy
Former government officials talked about President Obama's foreign policy approach toward the Middle East. They compared the Obama administration's foreign…
U.S. -Israel Relationship
A group of former CIA analysts spoke an event that was critical of the U.S.-Israel relationship. They questioned whether Israel was…
See all appearances
Appearance Stats
Filter By All Event Types Forum - 14 Call-In - 2 House Committee - 2 Joint Meeting - 1 Meeting - 1 Senate Committee - 1
Search Appearances


Mother came within a month. This is very good, despite the holidays in china. The mother did not check, but it is packed very well. The board is clean, there are no blown capacitors. It's probably gonna be okay. The only thing that did not like, i posted in the photo. The seller is sociable. The goods were tracked to the house. We are waiting for zion e5430!
Very good packaging delivered with plate for the case.
The goods came quickly, about two weeks. packed well, the box is not wrinkled. on the motherboard there was not much dust, but the seller returned a little more than half the cost of the goods. i did not check for efficiency. in general, the goods are satisfied.


The foundation of most plant and infrastructure are the automation level consisting of PC, PLC and other automation equipment. The ability to restore any of these components are vital to survival of your company.
what is the difference and why is it vital?
There are many names for it but essentially it comes down to the ability to secure the state of your plant or operation. In many cases you have a place on your file servers where you keep files in some structure that you hope up to date and complete. We will in the next sections try to explain the concepts, the difference between the concepts and when you should use one or the other. It is also vital to understand the fundamental difference between office backup and plant backup. Many let IT handle these challenges and that can be very costly due to their limited knowledge into Automation.
What is the goal of managing your plant configuration? It's not just to restore it when something breaks down, even if that is many times the primary goal. The basic backup/restore is the base function that everybody needs to be able to perform but many aren't! The second level comes in being able to track the different versions you have on each device and the reasons why you changed something. This is vital for example when you're trying to optimize machines or lines. This can also be seen as a matter of ownership of your plant or infrastructure. If you have SIs or consultants that help you it's easy that they forget to give you copies or place the files in the correct spot in the server. With version control you will have full control over these processes. The last and most advanced step is configuration management where you not just look at each file or configuration file, but at the complete plant system or part of process. By doing this you can secure that the combinations used are the right ones, and just like in the regulated industries prove that this is the case.
This is the most basic function for any company, if something breaks you should know how to get back to where you started. Most companies have documented plans for disaster recovery on many levels but once you come down to the plant floor there are a lot of things missing. Many have a CMMS or PAM (Maintenance system) where they can see all the hardware parts that exist, how many spares you have and so forth. A few of these systems handle the software even if that is usually the hardest part to recreate if lost. Therefore many have included the software in the usual filesystem by simply putting the files on the file server with backup. This can work, but leaves room for many mistakes. This can't work if you not have detailed lists of the software that resides in each PLC, PC and other programmable devices.
When you have many people working on your system or you have a lot of different devices, the need for more formal and structured handling of the software is needed. There are many systems that can handle version control and even some free ones that works fine. The important thing is to secure that you have a complete overview of all of the software that affect your plant. It can be as simple as data areas in a PLC that you use for set points which is never part of the backup code since it changes over time but still is vital. So the key thing is to document all your devices, like with the backup case, but remember to add all the none-essential code parts that contain set points and other defining data.
Considering the value that most have invested in the software in their facilities it's strange that most don't have full configuration management of their software. When you come to this level it's about establishing a baseline, a full set of software that you consider your base. To this comes the set of data files or configurations that changes due to changing of the process that can be due to different products or season. This can be done by documenting all the steps and locations for each piece of software, but most would consider that tool ridged and in the end a tool is what takes care of this. The great thing about a tool is also the possibility to handle different users and accessibility options.
The PC have been used in manufacturing and infrastructure since the late 80's. Many IT people see these PC's like any other PC. But they couldn't be more wrong. Automation software are often used much longer than any office application and are therefore in many cases older and never upgraded in the same structured way. You can easily have different versions of the same software of different PCs which makes backup harder. Also the automation software like SCADA/HMI are relatively unknown by IT which does their job harder, without automation knowledge this will fail! We consider the backup of automation software node needs a documented plan per node and if you want to be sure of the restore possibilities you should have a full baseline report on all the nodes. One thing that many forget it that IT many times only support certain operating systems and with automation equipment this is far from sufficient.