text:
\section{Introduction}

Much success in gaining high spectrum and energy efficiency has been demonstrated by massive multiple-input multiple-output (MIMO) transceiver systems in
5G and future generations of
wireless systems.
Benefits of massive MIMO require
accurate downlink (DL) channel state information (CSI) at the gNB (i.e., gNodeB). However, in frequency-division duplexing (FDD) systems,
gNB often relies on user equipment (UE) feedback
to estimate DL CSI. Since the feedback overhead grows proportionally with the increasing array size at the gNB,  CSI feedback reduction is vital to the widespread deployment of FDD MIMO systems.

To improve feedback efficiency, several notable works in \cite{CsiNet, CsiNet+, CsiNetVar3}
proposed a deep autoencoder framework by deploying
encoder and decoder at UEs and base stations, respectively,
for CSI compression and recovery. They have
demonstrated significant performance improvement over
traditional compressive sensing approaches.
Other recent works have revealed the importance of exploiting
correlated channel information from
UL CSI \cite{DualNet, CQNET, DualNet-MP}, past CSI \cite{MarkovNet}, and CSI adjacent UEs \cite{CoCsiNet} to assist DL CSI recovery at base stations.
For example, important physical insights regarding limited changes in propagation
environment even under vehicular speed
underscore the strong temporal correlation among
CSI in delay-angle (DA) domain.
Since
side information from correlated CSI lowers the conditional entropy of the
DL CSI for recovery,
effective utilization of historical CSI
can reduce encoded feedback payload
required from UEs \cite{MarkovNet}.

Importantly, the estimation
accuracy of DL CSI at UEs
depends on several factors such as
channel fading properties and reference signal (RS)  placement.
However, the required resource overhead of RS
(i.e. pilot) allocation for CSI estimation
grows proportionally with the antenna array
size. Too much resource allocated to CSI-RS
would degrade spectrum efficiency
Although sparser RS placement can mitigate the problem, it also can lead to larger CSI
distortion due to higher
interpolation error, especially in scenarios of
large multipath delay spread. Yet, to the best of our knowledge, the deep learning frameworks
that take into account RS placement optimization
to address the tradeoff of CSI accuracy versus spectrum
efficiency has
not been previously investigated for massive MIMO
downlink.

In this work, we consider a practical RS placement constraint \cite{3GPP} and develop a deep learning (DL) based partial CSI feedback framework which can conserve RS resource overhead while reducing the interpolation loss for high-quality DL CSI
recovery. Addressing the overall performance of DL CSI recovery, our contributions are as follows:
\begin{itemize}
    \item The work develops an efficient deep learning feedback framework of partial CSI
   by taking RS placement into practical consideration

\item We exploit CSI temporal correlation in deep learning network design to achieve improved
CSI recovery performance in terms of accuracy, computation complexity, and memory use.

\item We incorporate into the proposed framework
an inverse discrete Fourier transform (IDFT) reformulation for sparser partial CSI representation
and improve the efficiency of
subsequent partial CSI compression.

\end{itemize}

\section{System Model}
\subsection{CSI Feedback Framework in FDD system}
Without loss of generality, we
consider a single-cell MIMO FDD link in which
a gNB with $N_b$ antennas communicates with a single
antenna UE.
The OFDM signal spans $N_f$ DL subcarriers.
The DL received signal of the $k$th subcarrier is
\begin{equation}
\setlength{\abovedisplayskip}{4pt}
\setlength{\belowdisplayskip}{4pt}
y^{(k)}= \mathbf{h}^{(k)H} \mathbf{w}_\text{T}^{(k)}x^{(k)} + n^{(k)}\label{DL signal},
\end{equation}
where $(\cdot)^H$ denotes  conjugate transpose.
Here for the $k-$th subcarrier, $\mathbf{h}^{(k)}\in \mathbb{C}^{N_b \times 1}$ denotes the
CSI vector and $\mathbf{w}_\text{T}^{(k)}\in \mathbb{C}^{N_b \times 1}$ denotes the corresponding precoding vector\footnote{gNB calculates precoding vectors at subcarriers with DL CSI matrix.} whereas
$x^{(k)}\in \mathbb{C}$ and $n^{(k)}\in \mathbb{C}$ denote the DL source signal and additive
noise, respectively.

We rewrite the DL channel vectors as a frequency-spatial CSI (FS-CSI) matrix ${\mathbf{H}}^\text{FS} = [\mathbf{h}^{(1)},...,\mathbf{h}^{(N_f)}]^H \in \mathbb{C}^{N_f \times N_b}$.
Typically in FDD systems, DL CSI  ${\mathbf{H}}^\text{FS}$ is estimated by UE and feedback to gNB. However, the
number ($N_f\times N_b$) of unknowns in  ${\mathbf{H}}^\text{FS}$ occupies
substantial feedback spectrum in large or massive MIMO systems. To exploit CSI sparsity to reduce feedback overhead,
we apply IDFT
$\mathbf{F}_{D}\in \mathbb{C}^{N_f \times N_f}$ and DFT $\mathbf{F}_{A}\in \mathbb{C}^{N_b \times N_b}$ on
$\mathbf{H}^{\text{FS}}$ to generate
DA domain CSI matrix
\begin{equation}
\setlength{\abovedisplayskip}{4pt}
\setlength{\belowdisplayskip}{4pt}
\mathbf{H}^{\text{DA}} =\mathbf{H}^{\text{DS}}\mathbf{F}_{A}= \mathbf{F}_{D}\mathbf{H}^{\text{FS}}\mathbf{F}_{A},\label{DL CSI matrix in angle-delay domain}
\end{equation}
which demonstrates sparsity. Owing to limited multipath
delay spread and limited number of scatters,
most elements in $\mathbf{H}^{\text{DA}}$
are found to be near insignificant,
except for the first $Q_f$ and the last $Q_l$ rows.
Therefore, we shorten the CSI matrix $\mathbf{H}^{\text{DA}}$ in DA domain
to $Q_t = Q_f + Q_l$ rows that contain
sizable non-zero values and
utilize $\mathbf{H}$ denote the truncated matrices of
${\mathbf{H}}^\text{DA}$.

Subsequently, to further reduce the feedback overhead, the DL CSI matrix $\mathbf{H}$ is encoded
at the UE and recovered by the gNB. The recovered DL CSI matrix can be expressed as
\begin{equation}
\setlength{\abovedisplayskip}{3pt}
\setlength{\belowdisplayskip}{3pt}
 \widehat{\mathbf{H}} = f_{\text{de}}(f_{\text{en}}(\mathbf{H})),\label{Recovered DL CSI matrix}
\end{equation}
where $f_{\text{en}}(\cdot)$ and $f_{\text{de}}(\cdot)$ denote encoding/decoding operations.

\subsection{RS placement issue and interpolation loss}
In FDD wireless system, we assume that UEs estimate CSIs based on RSs, termed as pilot CSIs for simplicity, every $T$ time slots which are denoted as \textit{super slots}. Then, UEs interpolate the corresponding DL CSIs of payloads, termed as payload CSIs, according to pilot CSIs for the subsequent data decoding and CSI feedback. In scenarios with CSI changing smoothly along with frequency domain, the interpolation distortion usually can be neglected. However, typically, the number of RS resources need to be proportional to the number of antennas and thus cause fewer resources for data transmission in large scale MIMO system. To avoid this, a simple way is to reduce the RS placement density for each antenna. Yet, an overly sparse RS placement would cause a frequency-selective fading and hence induce a non-negligible interpolation loss.

Assuming that RSs for each antenna are placed at $N_p$ ($N_p \ll N_f$) different subcarriers and the pilot CSIs can be perfectly estimated, we define the $(k,m)$-th element of the raw CSI matrix is given by
\begin{equation}
    (\mathbf{H}^\text{SF, raw})_{\{k,m\}} = \left\{
    \begin{array}{lr}
    (\mathbf{H}^\text{SF})_{\{k,m\}}, &k \in \Omega_m\\
    0, &\text{else}.
    \end{array}
    \right.
\end{equation}
where $(\mathbf{A})_{\{k,m\}}$ denotes the $(k,m)$-th element of a matrix and $\Omega_m$ denotes the subcarrier index set of the $m$-th antenna for RS placement.
The interpolation loss can be expressed as follows:
\begin{equation}
\text{Loss}_\text{itp} = \norm{{\mathbf{H}^\text{DA}_\text{itp}} - {\mathbf{H}^\text{DA}}}^2_\text{F} = \norm{{\mathbf{F}_{D}\widehat{\mathbf{H}}_\text{itp}}\mathbf{F}_{A} - {\mathbf{H}^\text{DA}}}^2_\text{F},
\end{equation}
where $\widehat{\mathbf{H}}_\text{itp} = \text{ITP}(\mathbf{H}^\text{SF, raw})$ is the full CSI after interpolation and $\text{ITP}(\cdot)$ denotes the interpolation operator. As illustrated in Fig. \ref{interpolation examples}, even if we could obtain accurate pilot CSIs, the interpolation loss would be non-negligible when RS placement density is not high enough in some scenarios.

\begin{figure}
    \setlength{\abovecaptionskip}{0.cm}
    \setlength{\belowcaptionskip}{-1cm}
\centering
\resizebox{3.4in}{!}{
\includegraphics*{interpolation_examples.eps}}
\caption{Comparison of (a) perfect CSI and (b) CSI after interpolation according to pilot CSI. (In this example, The simulated channel follows the 3GPP TS38.901 UMa line-of-sight (LOS) channel model. The finest grids are resource elements. Following the specification \cite{3GPP}, the bold black frame covers the region within a resource block (RB) which is assigned to place RSs. Assume that the array size is 32, RSs for each antenna can only be placed every two RBs, causing non-negligible interpolation distortion.)\label{interpolation examples}}
\end{figure}

\section{Partial CSI feedback Framework with Spatio-Temporal Division Network (STNet)}
High temporal correlation exists in consecutive time slots and is proved to be used to effectively enhance the CSI recovery performance in previous work \cite{MarkovNet}. However, the RS placement issue and the subsequent interpolation loss are still not tackled. To deal with the interpolation loss, instead of reducing the RS placement density, we propose a learning-based partial CSI feedback framework to estimate and feedback partial CSIs so that the required RS placement density for each antenna could be satisfied and thus a nearly-zero interpolation loss could be achieved.

Fig. \ref{basic architecture} shows the general architecture of the proposed framework. Firstly, we separate a whole array into $\kappa$, called \textit{division factor}, non-overlapped and interleaved subarrays as shown in Fig. \ref{array examples} and let UEs to estimate pilot CSIs of the subarrays and do interpolation for payload CSI acquisition. We term the pilot and payload CSI as \textit{partial CSI} collectively. Secondly, an IDFT reformulation pre-processing is applied to partial CSIs for representations with higher sparsity and the combination at the gNB. Then, UEs encode them in every super slots and feedback to the gNB for partial CSI recovery. Subsequently, with the aids of high temporal correlation, a combining network is designed to merge the $\kappa$ partial CSIs received in the most recent $\kappa$ super slots for full CSI recovery. In this section, the above are described in details as follows:
\begin{figure}
    \setlength{\abovecaptionskip}{0.cm}
    \setlength{\belowcaptionskip}{-1cm}
\centering
\resizebox{3.4in}{!}{
\includegraphics*{basic_architecture.eps}}
\caption{The general architecture of the proposed partial CSI feedback framework. (To estimate the full DL CSI in the $n$-th super slot, the framework requires the current and the previous $\kappa - 1$ partial CSIs. Subsequently, the framework acts like as a sliding window to estimate CSIs of the following super slots. Namely, the required computations related to the previous $\kappa - 1$ feedbacks can be exempted.)\label{basic architecture}}
\end{figure}

\begin{figure}
    \setlength{\abovecaptionskip}{0.cm}
    \setlength{\belowcaptionskip}{-1cm}
\centering
\resizebox{3.4in}{!}{
\includegraphics*{array_examples.eps}}
\caption{Example of interleaved down-sampled subarray and the corresponding RS placement. (In this example, we consider a MIMO FDD link with the division factor $\kappa = 4$ where the gNB with a uniform planar array (UPA) with $32$ elements attempt to place RSs. To do so, there are two RSs per RB, which can significantly reduce the interpolation loss while being risky in losing some degrees of channel temporal correlation.)\label{array examples}}
\end{figure}
\subsection{IDFT reformulation pre-processing}

To maintain the efficiency to encode CSIs, most of the state-of-the-art works \cite{CsiNet, DualNet,CoCsiNet} opt to compress DA domain CSIs at UE side since they are with sparser representations. By reformulating the full CSI, we can decompose the DA domain full CSI as the summation of the $\kappa$ independent partial DA domain CSIs $\mathbf{H}^\text{DA}_\text{0,zp}$,...,$\mathbf{H}^\text{DA}_{\kappa-1\text{,zp}}$ as follows:
\begin{equation}
    \mathbf{H}^\text{DA}_\text{itp}=\mathbf{F}_{D}\widehat{\mathbf{H}}_\text{itp}\mathbf{F}_\text{A}=\mathbf{H}_\text{itp}^\text{DS}\mathbf{F}_\text{A}=\sum_{k=0}^{\kappa-1}{\mathbf{H}^\text{DS}_{k\text{,zp}}\mathbf{F}_\text{A}}
    =\sum_{k=0}^{\kappa-1}{\mathbf{H}^\text{DA}_{k\text{,zp}}},
\end{equation}
\begin{equation}
    (\mathbf{H}^\text{DS}_{k\text{,zp}})_{\{:,m\}} = \left\{
    \begin{array}{lr}
    (\mathbf{H}^\text{DS}_\text{itp})_{\{:,m\}}, &m = k, k+\kappa,...\\
    \mathbf{0}, &\text{else}
    \end{array},
    \right.
\end{equation}
where $\mathbf{H}^\text{DS}$ denotes the CSI in delay-spatial (DS) domain and we can find that the partial DA domain CSIs are periodic with a constant phase difference and a period of $N_b/\kappa$ elements along with the angle axis\footnote{The details of the derivation is described in Appendix.} as shown as follows:

\begin{equation}
    (\mathbf{H}^\text{DA}_{k\text{,zp}})_{\{:,m\}} = (\mathbf{H}^\text{DA}_{k\text{,zp}})_{\{:,m+N_b/\kappa\}}e^{-j2\pi/\kappa}.\label{eq:periodic}
\end{equation}
$(\mathbf{A})_{\{:,m\}}$ denotes the $m$-th column of a matrix $\mathbf{A}$. We denote the truncated matrices of partial CSIs $\mathbf{H}^\text{DA}_\text{0,zp}$,...,$\mathbf{H}^\text{DA}_{\kappa-1\text{,zp}}$ as $\mathbf{H}_\text{0,zp}$,...,$\mathbf{H}_{\kappa-1\text{,zp}}$ in this paper for brevity. In Eq. \ref{eq:periodic}, given the characteristic of the spatially down-sampled subarrays, we can find that only the first $N_b/\kappa$ columns of the truncated matrices $\mathbf{H}_\text{0,zp}$,...,$\mathbf{H}_{\kappa-1\text{,zp}}$ are aperiodic and the remaining are simply their copies with constant phase rotations. Hence, UEs only need to encode the non-periodic portion of the matrices, $\mathbf{H}_\text{0,p}$,...,$\mathbf{H}_{\kappa-1\text{,p}}$, with a size of $Q_t \times N_b/\kappa$, whose size is reduced by a factor of $\kappa$ as compared to the full CSI.

\subsection{STNet}

We now present a new DLN called STNet. For recovering the CSI of the $n$-th super slot, gNB decodes $\kappa$ codewords received in the current and the previous $\kappa-1$ super slots as $\kappa$ estimated partial CSIs, and combine them as follows:

\begin{equation}
    \widehat{\mathbf{H}}_n = f_\text{C}(\widehat{\mathbf{H}}_{n,\text{ini}}),\label{final_estimate}
\end{equation}
\begin{equation}
    \begin{aligned}
        \widehat{\mathbf{H}}_{n,\text{ini}} = \sum_{k=n-\kappa+1}^{n}\underbrace{\left[
        \begin{matrix}
            \widehat{\mathbf{H}}^T_{k\text{,p}}\\
            \widehat{\mathbf{H}}^T_{k\text{,p}}e^{j2\pi\text{mod}(k,\kappa)/\kappa}\\
            \vdots\\
            \widehat{\mathbf{H}}^T_{k\text{,p}}e^{j2\pi(\kappa-1)\text{mod}(k,\kappa)/\kappa}
        \end{matrix}
        \right]^T}_{\kappa\text{ copies}}
        \label{IDFT combination}
    \end{aligned}
\end{equation}
\begin{equation}
    \widehat{\mathbf{H}}_{k\text{,p}} = f_\text{de}(f_\text{en}(\mathbf{H}_{k\text{,p}}))
\end{equation}
where $f_\text{en}(\cdot)$, $f_\text{de}(\cdot)$ and $f_\text{C}(\cdot)$ denote encoding, decoding, and combining networks, respectively. $\mathbf{H}_{k,p}$ is the non-periodic portion of the partial DL CSI transmitted by the UE in the $k$-th super slot. $\text{mod}(n,k)$ denotes the remainder of a division of $n$ by $k$. Before forwarding to the combining network, due to the periodic features of the partial CSIs, by following Eq. \ref{IDFT combination}, rotation and concatenation operations are applied to the recovered partial CSIs $\widehat{\mathbf{H}}_{k\text{,p}}\text{,} k = m - \kappa +1,...,n$, for initial estimation of the full CSI. Subsequently, it is forwarded to the combining network for the full CSI refinement and estimation.

As for the encoder network, similar to \cite{CQNET}, we forward the real and imaginary parts of CSI to the encoder network, including four $7 \times 7$ circular convolutional layers with 16, 8, 4, and 2 channels and activation functions. Given the circular characteristic of CSI matrices, we introduce circular convolutional layers to replace the traditional linear ones. Subsequently, a fully connected (FC) layer with $\left\lceil{Q_t(N_b/\kappa)/\text{CR}}\right\rceil$ elements is included for dimension reduction after reshaping. $\text{CR}$ denotes the compression ratio. The output of the FC layer is then fed into the quantization module, called the sum-of-sigmoid (SSQ) \cite{CQNET} to generate codewords for feedback.

As for the decoder networks, similar to the encoder, we forward the received codewords to a FC layer with $\left\lceil{Q_t(N_b/\kappa)/\text{CR}}\right\rceil$ elements. Then, four $7 \times 7$ circular convolutional layers with 16, 8, 4, and 2 channels and activation functions are included for partial CSI recovering. Then, the gNB forwards the current recovered partial CSI and the previous estimated $\kappa-1$ partial CSIs to the combining network for final estimation. The combining network adopts the same design of the circular convolutional layers and activation functions as the decoder.

The STNet is optimized by updating the network parameters $\Theta_\text{en}$, $\Theta_\text{de}$ and $\Theta_\text{C}$
\begin{equation}
   \mathop{\arg\min}_{\Theta_\text{en}, \Theta_\text{de}, \Theta_\text{C}}
   \left\{\norm{\widehat{\mathbf{H}}_{n}-\mathbf{H}_{n}}^2_\text{F}
   +
   \sum_{k=n-\kappa+1}^{n}\norm{\widehat{\mathbf{H}}_{k\text{,p}}-\mathbf{H}_{k\text{,p}}}^2_\text{F}/\kappa
   \right\} \\ \label{loss_magnitude}
\end{equation}
where $\mathbf{H}_n$ is the true DL CSI of the $n$-th super slot.

Owing to the framework design, the required storage and computational complexity can be reduced significantly. In details, given the similar features of partial CSIs, only one encoder network needs to be trained and deployed at UEs. Plus, owing to the small input size for partial CSI compression, with the same compression ratio (CR)\footnote{$\text{CR} = \frac{\text{Number of real numbers in CSI to be compressed}}{\text{Number of real numbers in codewords}}$}, the model parameters are reduced with a factor of $\kappa$ as compared to the vanilla CsiNet Pro \cite{MarkovNet}.
In addition, for recovery of the $n$-th full CSI, although STNet collects the partial CSIs in the most recent $\kappa$ super slots, with the locally available previous $\kappa-1$ partial CSIs, only an additional process to encode and decode the partial CSI in the current super slot is required.
Thus, the required UE storage and computational complexity can be significantly reduced\footnote{Storage utilization is especially vital for UEs, as compared to gNBs}.
Note that, the selection of the division factor $\kappa$ would significantly affect the recovery performance\footnote{
An excessive $\kappa$ may induce recovery performance degradation since the recovered past partial CSIs could be uncorrelated to the current CSI.}, which will be demonstrated in Section IV.

\section{Experimental Evaluations}
{
\subsection{Experiment Setup}
In our experiments, we let the UL and DL bandwidths be 20 MHz and the subcarrier number be $N_f$ = 1024. We assume that the FDD system would place CSI-RS every $T = 20$ time slots (i.e., $10$ ms).
We consider both indoor and outdoor cases.
We place the gNB with a height of 20 m at the center of
a circular cell coverage
with a radius of 20 m for indoor and 200 m for outdoor.
We consider a gNB with a $N_b = 32$-element uniform linear array (ULA) communicates with UE with a single antenna. A half-wavelength inter-antenna spacing is considered.
For each trained model, the number of epochs and batch size were set to 1,000 and 200, respectively. We generate several indoor and outdoor datasets, each containing 100,000 random channels.
60,000 and 20,000 random channels are for training and validation.
The remaining 20,000 random channels are test data for performance evaluation.

For indoor data generation, we used the COST 2100 \cite{COST2100} simulator and select the scenario \textit{IndoorHall at 5GHz} to generate indoor channels at 5.1-GHz UL and 5.3-GHz DL with LOS paths. The antenna and band types are set as \textit{MIMO VLA omni} and \textit{wideband}, respectively. As for the outdoor dataset, we utilized QuaDRiGa simulator \cite{QuaDriGa} with the scenario features of \textit{3GPP 38.901 UMa}.
We considered the UMa LOS and NLOS scenarios at 300 and 330 MHz of UL and DL bands, respectively, with different UE velocities (considering 1, 2 and 4 m/s). The antenna type is set to \textit{omni}.

The performance metric is the normalized MSE
\begin{equation}
\text{NMSE} =  \frac{1}{D}\sum^{D}_{d=1}\norm{\widehat{\mathbf{H}}_{d}^\text{SF} - {\mathbf{H}}_{d}^\text{SF}}^2_\text{F} /\norm{{\mathbf{H}}_{d}^\text{SF}}^2_\text{F},\label{NMSE1}
\end{equation}
where the number $D$ and subscript $d$ denote the total number and index of channel realizations, respectively. Instead of evaluating the estimated DL CSI matrix $\widehat{\mathbf{H}}$, we evaluate the estimated SF-CSI matrix $\widehat{\mathbf{H}}^\text{SF}$ that can be obtained by reversing the Fourier processing and padding zero matrix.
Note that this NMSE includes both the
errors caused by truncation at the encoder
and the overall recovery error. Thus, it
is practically more meaningful.

In the following section, we evaluate the performance
of CSI recovery by adopting the proposed partial CSI feedback framework. To show the efficacy of the framework, we compare the STNet with CsiNet Pro used in \cite{MarkovNet} which shares the same core layer design of the encoder/decoder networks. Namely, the CsiNet Pro can be regarded as the STNet without multiple super-slot branches and the combing network. As shown in Fig. \ref{layer architecture comparison}, the only difference between STNet and CsiNet Pro is the IDFT reformulation pre-processing and the additional combining network.

As mentioned in Section III, STNet can obtain the current full CSI by obtaining the current partial CSI. Thus, in each super slot, as compared to CsiNet Pro, the codeword size to be transmitted at the same CR can be reduced by a factor of $\kappa$. Herein we define a new term called effective compression ratio ($\text{CR}_\text{eff} = \kappa\text{CR}$).

\begin{figure}
    \setlength{\abovecaptionskip}{0.cm}
    \setlength{\belowcaptionskip}{-1cm}
\centering
\resizebox{3.4in}{!}{
\includegraphics*{layer_architecture_comparison.eps}}
\caption{Architecture of (a) CsiNet Pro and (b) STNet.\label{layer architecture comparison}}
\end{figure}

\subsection{Different Division Factor $\kappa$}

To demonstrate the superiority of the proposed framework, we first applied different division factors $\kappa$ in both indoor and outdoor scenarios with low UE mobility ($v = 1$m/s) for different effective compression ratios $\text{CR}_\text{eff}$. Fig. \ref{sim1} (a), (b) and (c) show the NMSE performance of the proposed framework STNet and vanilla CsiNet Pro under indoor and outdoor scenarios, respectively, at different compression ratios. By adopting the proposed framework, with the aids of the high CSI temporal correlation, STNet performs much better than CsiNet Pro and has the best performance when using a larger division factor $\kappa$.
However, for higher recovery accuracy, we still cannot just choose a large division factor $\kappa$ in all scenarios, especially in outdoor scenarios since STNet highly depends on the CSI temporal correlation. The reason will be shown in the following section.

\begin{figure}
\centering
\resizebox{3.4in}{!}{
\includegraphics*{sim1.eps}}
\caption{NMSE performance for different division factor $\kappa$ in (a) indoor, (b) outdoor UMa LoS and (c) outdoor UMa NLoS scenarios.\label{sim1}}
\end{figure}

\subsection{Different UE mobility}
To comprehensively assess the robustness of the proposed framework, we tested the same alternatives in outdoor scenarios with different UE mobility (= 1, 2 , 4 m/s\footnote{These velocities roughly corresponds to the UE velocities of walking, jogging, and biking, respectively.}). Fig. \ref{sim2} shows the NMSE performance of STNet and CsiNet Pro in the outdoor scenarios with different average UE velocity and at different compression ratios. We can find that STNet performance degrades as the increasing UE velocity and even perform worse than CsiNet Pro when division factor $\kappa = 4$. Namely, the higher UE mobility would induce a lower CSI temporal correlation, causing the performance degradation of STNet. According to the numerical simulations, to strike a trade-off, an intermediate division factor $\kappa = 2$ seems to be a plausible solution in outdoor scenarios.

\begin{figure}
\centering
\resizebox{3.4in}{!}{
\includegraphics*{sim2.eps}}
\caption{NMSE performance for different UE velocities in the outdoor UMa LoS scenario.\label{sim2}}
\end{figure}
\subsection{Assessment of FLOPs and parameter numbers}

\begin{table}
\centering
\caption{FLOP and parameter numbers of STNet and CsiNet Pro.\label{Complexity_Diff_Encoding}}
\begin{tabular}{|c|c|c|c|c|}
\hline
      & \multicolumn{2}{c|}{FLOPs} & \multicolumn{2}{c|}{Parameters} \\ \hline
Method & $\text{CR}_\text{eff}=8$            & $\text{CR}_\text{eff}=16$         & $\text{CR}_\text{eff}=8$            & $\text{CR}_\text{eff}=16$              \\ \hline
STNet, $K=2$  & 1.1M        & 583K       & 555K           & 292K           \\ \hline
STNet, $K=4$  & 583K        & 321K       & 292K           & 160K           \\ \hline
CsiNet Pro  & 2.13M        & 1.08M       & 1.07M          & 0.54M          \\ \hline
\end{tabular}
\end{table}
Due to the limited storage and computation power of UEs, it is crucial to design a light-weighted and easy-to-implement neural network. Table \ref{Complexity_Diff_Encoding} shows that, besides the superiority in terms of the NMSE performance, the required computation power and storage for model parameters can also significantly reduced. To explain, with smaller input and output sizes of STNet's encoder and decoder networks, the required FLOPs and parameters are significantly lower than CsiNet Pro. In addition, since STNet can act in a sliding window fashion, the encoder and decoder networks are conducted only once instead of $\kappa$ times. Thus, even considering the implementation of the combing network, the STNet's FLOPs and parameters are still obviously less than the ones of CsiNet Pro.}
\section{Conclusions}
This work presents a new deep learning framework
for large scale CSI estimation
that utilizes partial CSI feedback compression
and leverages CSI temporal correlation in FDD systems.
To control time-frequency resources needed for CSI-RS in the proposed IDFT reformulation, our
proposed STNet allows UE to transmit
partial CSI feedbacks associated with interleaved non-overlapped subarrays in $\kappa$ super slots.
Subsequently, the gNB estimates the full CSI based on aggregated partial feedbacks by utilizing
CSI temporal correlation. Our test results
demonstrate significant improvement
of recovery performance at
reduced computation complexity and storage
usage in comparison with the existing
benchmark model of CsiNet Pro.
\section*{Appendix}
\setcounter{equation}{0}
\setcounter{subsection}{0}
\renewcommand{\theequation}{A.\arabic{equation}}
\renewcommand{\thesubsection}{A.\arabic{subsection}}
\subsection*{Proof of Eq. (\ref{eq:periodic}):}
Since the array is divided into non-overlapped and interleaved subarrays, the CSI matrix in DS and DA domains for the $k$-th subarray are expressed respectively as follows:
\begin{equation}
    (\mathbf{H}^\text{DS}_{k\text{,zp}})_{\{:,m\}} = \left\{
    \begin{array}{lr}
    (\mathbf{H}^\text{DS}_\text{itp})_{\{:,m\}}, &m = k, k+\kappa,...\\
    \mathbf{0}, &\text{else}.
    \end{array}
    \right.
\end{equation}

\begin{equation}
\begin{aligned}
(\mathbf{H}^\text{DA}_{k\text{,zp}})_{\{:,m\}} & =
(\mathbf{H}^\text{DS}_{k\text{,zp}}\mathbf{F}_\text{A})_{\{:,m\}} = \mathbf{H}^\text{DS}_{k\text{,zp}}(\mathbf{F}_\text{A})_{\{:,m\}}\\
&= \sum_{m'=k,k+\kappa,...}(\mathbf{H}^\text{DS}_\text{itp})_{\{:,m'\}}w^{(m'-1)},
\end{aligned}
\end{equation}
By substituting the column index $m$ by $m^*=m+N_b/\kappa$, we can find that the CSI matrix in DA domain is periodic with a constant phase difference and a period of $N_b/\kappa$ elements along with the angle axis as follows:
\begin{equation}
\begin{aligned}
(\mathbf{H}^\text{DA}_{k\text{,zp}})_{\{:,m^*=m+N_b/{\kappa}\}} & =
(\mathbf{H}^\text{DS}_{k\text{,zp}}\mathbf{F}_\text{A})_{\{:,,m^*\}} \\ &= \mathbf{H}^\text{DS}_{k\text{,zp}}(\mathbf{F}_\text{A})_{\{:,,m^*\}}\\
& = \sum_{m=k,k+\kappa,...}(\mathbf{H}^\text{DS}_\text{itp})_{\{:,m\}}w^{(m+N_b/\kappa-1)}\\
& = (\mathbf{H}^\text{DA}_{k\text{,zp}})_{\{:,m\}}e^{-j2\pi/\kappa}
\end{aligned}
\end{equation}
where

\begin{equation}
    (\mathbf{F}_\text{A})_{\{:,m\}} = [1,w^{(m-1)},...,w^{(N_b-1)(m-1)}]^T,\label{eq:IDFT}
\end{equation}
\begin{equation}
    w = e^{-j2\pi/N_b}.\label{eq:IDFT factor}
\end{equation}

redpajama_set_name: RedPajamaArXiv


text:
Brexit News, Member News
Arendt | Brexit: new status, new residence permits for UK nationals residing in Luxembourg
Under the transition period as foreseen by the Withdrawal Agreement, UK nationals may continue to reside in the EU without additional measures until 31 December 2020.
With the end of the transition period fast approaching and as announced by the Luxembourg government, UK nationals residing in Luxembourg have begun to receive letters from the Immigration Directorate inviting them to prepare an application for a residence permit in Luxembourg.
Key points on these new residence permits:
Invitations are issued automatically to UK nationals registered as residing in Luxembourg;
Residence permits are available for UK nationals and their family members residing in Luxembourg before 1 January 2021;
Applications must be introduced before 30 June 2021;
Residence permits will be valid as of 1 January 2021;
The residency permits will be valid for 5 or 10 years (depending on current residence in Luxembourg);
The residence permits will be renewable upon request, provided that the residence conditions continue to be fulfilled.
Our employment and immigration team remains at your entire disposal for more information. Our team remains also available to assist you in the introduction of residence permit applications in Luxembourg as UK nationals.
Philippe Schmit, Partner
Louisa Silcox, Counsel
Compliments of Arendt & Medernach SA – a member of the EACCNY.

redpajama_set_name: RedPajamaCommonCrawl


text:
Mata Panas
Photo essay – Sunday afternoon in the village of Suli, Ambon Island. A mother with her child visiting a healer. This is a ritual healing of an infant who has been attacked by a so called suangi. A suangi is said to be a witch.
People believe that a suangi drinks the blood or eats the internal organs of their victims and fill their victims bodies with leaves and grass. In the village community, it's said that infants are easy targets for a suangi. Eventually, it is believed that they devour an infant's soul. This social phenomenon is also known as mata panas, literally it means hot eyes. In the social context of the village, it refers to the evil eye of a male or a female witch who is seeking for an infant to feed him or herself. If an infant has a swollen abdomen and hot eyes it seems to be attacked by a suangi.
The child in this photo essay was mysteriously ill and considered to have been attacked. The man, 'uncle' Paul, is healing the child with a certain cleansing ritual. He is performing it through Christian prayers and using betel nut* in a traditional way. The betel mixture in his mouth he spits on the buttocks of the child. This particular healing ritual takes place according to certain acts that are derived from Christianity and customary law, the adat. Typical expressions of religious syncretism which are complementary to such matters, concerning religion and the invisible ancestral world. [July 2014]
*The specific ingredients to chew betel. The betel nut [pinang], lime spatulas [kapur sirih] and betel leaves [daun pinang]. This stimulant is a mixture of areca palm nuts and leaves from the betel, a climbing plant. All these ingredients together are wrapped in betel leaves and chewed into a fine substance. The betel quid is used during ceremonies, for ritual purposes or in situations to make a connection with the ancestral world. Sometimes people use slightly different ingredients that go along with chewing betel nut.
Side note: During conversations in the village I noticed that it is still taboo to talk about 'mata panas'. Most people don't talk about these cases of spirit possession. If it occurs people accuse 'someone' [often an elderly] to be a Suangi. Also important to know is that 'Mata Panas' has different nuances, it depends from which perspective is spoken. In this case, it is a form of spirit possession among children.


text:
May 5, 2019 / 3:06 PM / 2 months ago
Premier League: Chelsea grab top-four spot as rivals self-destruct again
Martyn Herman
LONDON (Reuters) - While the Premier League title race has been contested by two thoroughbreds the battle to finish third and fourth has descended into a demolition derby in which Chelsea emerged from the wreckage to seal a top-four finish on Sunday.
Soccer Football - Premier League - Chelsea v Watford - Stamford Bridge, London, Britain - May 5, 2019 Chelsea's Olivier Giroud shoots at goal as Watford's Craig Cathcart attempts to block Action Images via Reuters/Matthew Childs
Maurizio Sarri's team beat Watford 3-0 at Stamford Bridge in their penultimate game to ensure they will return to the Champions League next season but Manchester United will definitely not be joining them.
United's prospects were already slim but a woeful 1-1 draw away to bottom club Huddersfield Town ensured Ole Gunnar Solskjaer's side can finish no higher than fifth.
Arsenal then handed their London rivals Chelsea and Tottenham Hotspur a welcome gift by only drawing 1-1 at home to a Brighton & Hove Albion side whose top-flight survival had been sealed 24 hours earlier.
That meant Chelsea were guaranteed a top-four finish while Tottenham Hotspur, whose domestic form has collapsed culminating in a nine-man defeat at Bournemouth on Saturday, are all but assured of a Champions League spot due to their superior goal difference.
While Arsenal could still match their north London rivals' total of 70 points should they win at Burnley on the final day of the season and Spurs lose at home to Everton, they must also achieve a highly unlikely eight-goal swing.
"We knew it is going to be difficult but our focus is now the Europa League," Arsenal manager Unai Emery, whose side lead 3-1 going into the second leg of their semi-final at Valencia next week, said with an air of resignation.
"We have the opportunity in the Europa League to do something important and we will try and do that."
Arsenal had taken an ninth-minute lead through Pierre-Emerick Aubameyang's early penalty but Glenn Murray's spot kick dragged Brighton level, meaning Arsenal have earned a miserly one point from the past 12 on offer.
Chelsea have not been a great deal better in an increasingly inept scrap for the top-four, picking up only two from nine points in their previous three games, and they were booed off at halftime against Watford with the score 0-0.
Quickfire headers from Ruben Loftus-Cheek and David Luiz early in the second half, both from Eden Hazard assists, put them in control and Argentine marksman Gonzalo Higuain added a third in the 75th minute.
"In the first half we were in trouble because we were tired, physically and mentally," Sarri said.
"We were lucky of course because we scored after two minutes and after the first goal, probably we improved mentally."
Sarri gave a brief substitute appearance to title-winning defender Gary Cahill for what is almost certainly his last Chelsea appearance in the league at Stamford Bridge.
Manchester United, for whom Solskjaer's impressive start after taking over from sacked former Chelsea boss Jose Mourinho in December is now a fading memory, failed to even rouse themselves for a trip to Huddersfield, who until Sunday had managed 14 points.
Looking for a first win in five matches in all competitions, United made a fast start with Scott McTominay putting them ahead.
But they deteriorated and an error by Luke Skaw allowed Isaac Mbenza to race on to a goal kick and score his first ever Premier League goal after the break.
"We've talked about next season as in we need to start to rebuild and of course next season will be one without Champions League football," Solskjaer said.
"We haven't deserved to be top four, we've chased the pack and been given chances, the league is so tight. When we got the opportunities we didn't take them."
Chelsea are 21 points behind second-placed Manchester City, who could go top with a home win over Leicester City on Monday.
Tottenham, considered title contenders as recently as January, have lost seven of their last 11 league games, evidence of just how far the chasing pack have fallen.
One fan neatly summed it up on a BBC chatroom: "As a Chelsea fan it just doesn't feel justified. We've been the best of a bad bunch," he said.
Reporting by Martyn Herman, editing by Pritha Sarkar


As the visitor starts on the tour of the Ohio Statehouse, they receive a voting card that can be used at the Vote Today exhibit. The visitor uses their magnetic card at one of the three voting booths in the Elections Gallery. They insert the card into the card reader, and the issue of the month appears on a customized touchscreen. The visitor selects their vote, and the current results show up momentarily on the touchscreen. After the voting period is over, the final results are shown on the Ohio Statehouse's website. This AMX-based voting system allows the museum director to change the issue, keep a tally on the current results, and even display custom messages on the Vote Today LED displays.


text:
es un exfutbolista japonés que se desempeñaba como delantero y entrenador.

Clubes

Como futbolista

Como entrenador

Referencias

Personas de la prefectura de Aichi
Futbolistas de Japón
Futbolistas del Yokohama F. Marinos
Entrenadores de fútbol de Japón
Entrenadores del Yokohama F. Marinos
Entrenadores de la selección de fútbol de Laos

redpajama_set_name: RedPajamaWikipedia


Amy Caine Fitness: Oofos Recovery Shoes Review & Giveaway!
Would love to try these. My feet need some assistance after my 20 milers.
I'd like to try them because I have been having a great deal of trouble finding shoes that do not cause my ankle to hurt outside of running shoes. Thank you for the giveaway!
Oh I so wish I could enter! I've been looking for a pair of shoes/flip flops to wear post run because my flats are awful!
I know that my flip flops aren't great, so I would totally love to see how these make my legs feel!
I need a good recovery shoe!
Recovery shoes would be great!!! ;) Maybe help me with my arch issues.
My feet always hurt after long runs, these look like a great way to help with that!
Well those are certainly interested. I've never heard of them before. Sounds pretty cool.
These sound lovely and it's wonderful they're attractive! I am always looking to ditch my race shoes as soon as I cross the finish line! What a fabulous giveaway too!
I would like to try them because they look comfy. Who doesn't love a great pair of flip flops?!?!
I usually slip on flip flops after a run and the Oofos look a lot more comfortable!
I would love to try Oofos because they look so comfy for post-run tired feet. Enhance recovery. Yes please!
I need something well-cushioned to wear around the house and out on errands.
Everyday recovery is so important and nobody understands that more than runners! Hope you get some rejOOv time Jill! Thanks for entering the contest!
The feeling of slipping into the OOfoam post race is an experience all on its own! You've got to try it Zaneta!
They are designed to help rejOOv your body after physical activity like running, or even running errands! Its the technology and the feeling behind the shoe that makes them a workout must have! We know you'll get it once you try them on Michelle!
Easy to slip on. The flip flop itself is a relaxing shoe, OOFOS take it to another level we like to call rejOOv! Hope you get to check them out!
There is nothing like the feeling of taking your sneakers off after you've run your heart out - oh well except for the feel the OO experience of OOFOS! Hope you can slip into a pair post race soon Emily!
We are located in over 600 retail stores nationwide! On our website you can find local retailers if you'd liek to experience what they are like first hand Courtney!
Sounds like you could definitely use some rejOOv Tracey!
They are Natalie! Once you try them on we know you'll be saying "OO"
We've got you covered. Check out OOFOS online for the full collection of styles. Amanda!
What are you wearing now RunToTheFinish?
Check us out on facebook and twitter for more giveaways Kierston!
LeeAnn! Send us an email at info@oofos.com, we are always interested in injuries and love to help anyway we can!
Training for anything Debbie, or just love the long run?
YES, training for the BOA Chicago Marathon in 3 weeks!!!!
Right now post long run I'm just in my compression socks, no sandals at all!


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text:
Drawings by the Princess
Clementine d'Orleans, princess (1817-1907), daughter of Louis Philippe, King of the French; married to Prince August of Saxe-Coburg, mother to King Ferdinand of Bulgaria. Sketchbook/scrapbook containing drawings by the Princess and other artists, including sketches by William Daniell.
[France and England], 1827-1851.
13 watercolours and pencil and ink drawings mounted on 60 leaves of white and brown-toned paper. Splendid red morocco binding by Alphonse Giroux of Paris with covers and spine gilt and inlaid (wanting the fore-edge lock). Small oblong folio (340 x 245 mm). Red moirée silk endpapers. All edges gilt.
A magificently bound, early album containing sketches by the artistically gifted princess as well as by other artists. It was not until the year of her birth that her father Louis Philippe, the Duke of Orleans (1773-1850), who had had to leave Europe after the French Revolution and spent several years in America, returned to France, where in 1830 he accepted the crown, following the deposition of Charles X. Until the February Revolution of 1848 and his emigration to England he reigned as "King of the French".
The present album contains three unsigned portrait studies in pencil attributable to the princess, probably based on details from an old master painting (possibly a Crucifixion or Lamentation of Christ). In her youth, Clementine is known frequently to have copied details from Dürer, Michelangelo, Leonardo da Vinci, Holbein, and Titian. Two of the present studies are dated "1831", when she was but fourteen years old: among the earliest of her known works, they show off her remarkably developed talent.
Among the other drawings in the album is a watercolour still life with fowl, signed "D. Pedro 1850" and inscribed, "Offert À Son Altesse Royale Madame La Duchesse de Saxe Cobourg Gotha le 3 Juin 1851", while a similar still life is signed "D. Suid [?] fecit / 20 Set. 1850". Other drawings include four pencil sketches by the English painter and engraver William Daniell (1769-1837), who had accompanied his uncle Thomas Daniell to India in 1784 and subsequently produced a wealth of highly regarded landscapes and scenes of Indian life (including work for the famous "Oriental Scenery" volume), many of which are in the Royal collections (cf. Thieme/Becker VIII, 361f.). His signed contributions are two boating scenes (1827, one entitled "Patience in a Punt"), an Indian riverside scene (1827) entitled "The Plantane tree, Bengal", and an "Indian Bull" (1830, inked and watercoloured). Another particularly finely executed watercolour shows a beach scene at Ingouville (in Normandy), dated August 1839 and signed "L. Laurent". In addition, there are three skilled but unsigned pen-and-ink sketches, apparently also by a trained artist, showing a watchman with a shouldered musket, the Falls of Clyde in Scotland ("Chute de la Clyde / Lanarke 11 Juillet 51"), and the profile study of a lady (all but the latter washed in ink). A few torn stubs show the album to have formerly comprised several additional leaves, while the faint nature-printed impressions left by plants between two leaves prove that the album was once also used to preserve botanical mementos.
The princess grew up in the Palais Royale in Paris. In 1843 she was married to Prince August of Saxe-Coburg; in 1861 she would give birth to Prince Ferdinand of Saxe-Coburg, who in 1887 accepted the crown of Bulgaria, against the wishes of the European Powers and indeed those of the house of Coburg. Having long lived under the same roof with the similarly aged Victoria of Kent, later Queen Victoria (1819-1901), Clementine maintained a lifelong correspondence with the Queen of England, and her more than 600 letters are now in the Royal Archive in Windsor. Also the Hoover Institution at Stanford University keeps material from the estate of Princess Clementine within the so-called "Czar Ferdinand I of Bulgaria papers". Her artistic productions have remained enduringly popular: in 1990, one of her pencil drawings ("Etude des chiens") sold for 20,000 Francs (Paris, Tajan, 5 Dec. 1990, lot 23).
Stock Code: BN#46104 Tags: Art, Arts and Crafts, Drawings, History
Sabbagh, Michel. Kitab Musabaqat al-barq wa-al-ghamam fi su'at al-hamam. La colombe, messagère …Paris, an XIV = 1805.
Slatin-Pascha, Rudolf von, administrator in the Sudan, politician, and adventurer (1857-1932). Archive of first-hand contemporary documents concerning the escape of Slatin …Various places, ca. 1895.
Chaussonet, Pierre-François. Noms Surnoms, Qualités, Conditions et Armoiries blasonnées de Messieurs …Lyon, 1749-1755.
You're viewing: Clementine d'Orleans, princess (1817-1907), daughter of Louis Philippe, King of the French; married to Prince August of Saxe-Coburg, mother to King Ferdinand of Bulgaria. Sketchbook/scrapbook containing drawings by the Princess and other artists, …France and England, 1827-1851. € 4,500.00


Emmons Black Album Reissue . . . ?
Topic: Emmons Black Album Reissue . . . ?
Let's re-release Buddy's Emmons Guitar, Inc. (Black Album) digitally before the masters disappear.
Maybe a forum member knows a music business person who will make it happen . . . or the Steel Guitar Hall of Fame can get behind it?
Also, Picks The Famous Sho-Bud Guitars would be a good artifact to salvage before the tapes wind up in a dumpster.
wasn't it released on CD at some point?
every household in the world should have a copy.
I would like a copy, digital or LP.
It was already re-released on CD. Not sure where you can get copies but it definitely is out there in digital format.
As for the SG Hall of Fame getting behind a project, well, you must not get out much... They are defunct.
Who retains ownership? Presumably the Lashley's? If so, don't hold your breath.
Posted 25 Jan 2018 2:03 pm Rip it . . .
I've never seen it sold on CD anywhere, just vinyl, but a CD edition shows up on Discogs . . . so . . . ?
If it will never be released again, I wish someone would rip the CD and post it for guys who don't own it, and for posterity.
the Emmons company sold CDs of it for a while. They even wholesaled them out, and I had them in The Forum's online store. Then they stopped responding to my purchase orders and they were all gone.
It's one of the best albums ever, in my opinion. It was like the Sgt Peppers of steel guitar music.
Ron Lashley should still own the publishing rights and masters. Ron Sr had Steve Palusek remaster in the 90's and had CD's produced. Around 05' I attempted to negotiate a buyout which was not going to include publishing. Steve's master did not have the extreme panning of the original.
Sundazed records do some steel guitar reissues, including Pete Drake, Mooney, Leon Mcauliffe and Speedy West. Until recently they had Steel Guitar Jazz by Buddy/Buddie. They might be interested if it was available.
I've digitized all my vinyl albums, that way they never wear out.
It's heartening to see so much interest in the reissue idea.
I'm pretty sure 16,000 forum members would snag one . . . I'd like to own it.
True, but the devices that play digital music go obsolete every few years.
If it ever happens, I still have a turntable and the original black album.
I don't think cd players will ever disappear. Too many cds still floating around. They may be harder to find, same as turntables did.
Al I'm interested in the vinyl.
I had a CD, that has disappeared, for whatever reason, but I'm almost sure I got the CD from Scotty. Several years ago I talked with Scotty about this, there seemed to be a lot of interest at the time. It would be great if it could be offered into the mass digital market.
Same for Curly's work, Jimmy Day, Tom Morrell and a host of others.
If anyone has CDs, let me know too, please.
Al, I sent you a PM.
I talked to Ron and Rebecca 10+ years ago about a re-release when they had about 20 CDs left. I remember steering them toward CD Baby and iTunes to explore download options but they felt the revenue wouldn't be enough. Having received "tens of dollars" annually myself from CD Baby/iTunes, I really couldn't blame them.
Thats nonsense, especially if they own all the publishing rights. They could assign it over to someone and authorize only digital downloads. Literally no investment. NO CD's , no plastic cases, no printing.
CDBABY, ITUNES etc , millions of artists have tracks available for download at a very minimal fee , in some cases there is no fee, just a fee is collected when tracks are sold. Like me ! Earning tens of dollars or even a few hundred dollars sure beats earning ZERO dollars.
These days probably every artist can't wait to finish a project and get it up on the net for download. Everyday is an opportunity to earn a few dollars and you don't even have to get out of bed or leave the house.
These days probably every artist can't wait to finish a project and get it up on the net for download. Everyday is an opportunity to earn a few dollars and you don't even have to get out of bed or leave the house.
Back in the Old Country I had this on vinyl. I've long since lost track of that, though.
My memory is hazy but I'm pretty sure I was given a complimentary CD by Jim Aycoth at Emmons with one or other of the two new Emmons LeGrandes I bought from the factory (along with a tee-shirt or two ). Some of my happiest steel guitar memories have been my dealings with Jim and Joanne Aycoth.
I'm happy to say I still have the CD and I play it often.
I registered with this outlet but did not give them any money. Indeed you can get tracks for as little as 17 cents but some of the reviews state that there is CC fraud associated. It's either a Russian or Chinese outlet, or something like that.
I still just think that Jr should register the Black album with I tunes or CD baby at 99 cents a track. It costs nothing to do it.
"Crumbs" is what birds eat to stay alive !
Hey Tony, you could be right about the sales potential of downloads when publishing rights are owned. All I know is that at the time, the Lashleys didn't see a favorable cost/benefit ratio and didn't have a legal eagle to sort the issues out for them. If they had had the $ back then, I'm sure they would have been happy to simply burn more CDs.
It costs very little to burn CDs these days. Check out www.kunaki.com. No minimum order.


text:
Q: how can i check if a field is a textarea I know about the form field method is_checkbox that is used to check if a field of a given django form is a checkbox or not. Is there any method to check if the field is a textarea?
i have tried doing this:
{% if field.is_textarea %}

but this does not seem to work.

A: EDIT: Explanation - the filter takes the field object and returns name of the widget used by Django which can be used in comparison to string.
Use define template filter in templatetags.py:
from django import template
register = template.Library()

@register.filter('input_type')
def input_type(input):
return input.field.widget.__class__.__name__

And use it in template for example like this:
{% if field|input_type == 'Textarea' %}

{{ field }}

{% else %}

{{ field }}

{% endif %}

A: You should do something like:
{% if field.widget...... %}

The widget is responsible for the rendering, not the field it self.
Example to check it in the shell:
from django import forms
from django.forms import widgets

class ContactForm(forms.Form):
    text = forms.CharField(max_length=100, widget=widgets.Textarea)

f = ContactForm()
f.fields['text'].widget

<django.forms.widgets.Textarea object at 0x218ccd0>

A: I had the same intention the only solution is to work with if condition on your views.py.
I mean first you give a name to your text area in the html code then move to views.py.
grab the name like this  assume your text area name is "text"
in views.py write this code text = request.GET ['text'] then create the if statement like
if text == '':
    return render(request, 'html page you want render')
else:
    return render(request, ' the exact page you want render if the textarea is filled ')

redpajama_set_name: RedPajamaStackExchange


Can a cell phone signal booster be homemade?
Though for some people an idea to create their own cell phone signal booster at home may seem really crazy, some other may be fond of doing different interesting devices on their own. And it is quite okay: we all are different. But if you feel that you belong to the second group and can't wait to start work, then this article is definitely for you!
With the right approach, correctly chosen materials, sufficient time investments and careful fulfillment of all the steps of the following instruction, you have very good chances to get an excellent homemade cell phone signal booster. Nevertheless, we would like to warn you that you need to be really confident in your skills and the quality of chosen material before starting. Otherwise, such a DIY session may turn to be really dangerous and risky for you and your properties.
But if you are sure that you want to try, we would be happy to share the following instruction with you. So, let's start.
First of all, we need to create an antenna. Flatten the wire and bend it in a square-like shape: use pliers to bend it in the center at 90 degrees, then at the distance of 9 cm on both sides from the center of your wire, bend it once again at 90 degrees. The both edges should be also bent inwards at 90 degrees. This time you should measure the distance of 8 cm from sides to make the bends.
On the ends of the wire that are bent inwards install the connector block.
Then take a pipe and cut its one side by half. In the center of another side make a hole. The hole needs to be big enough for a bolt to go through. Then put the bolt into this hole, install the antenna on top and use a nut to fix it.
You next task is to connect a coaxial cable. You should separate the inner and outer wires. The inner wire needs to be connected to one side of the small block, while the second wire should be connected to another side of the same block.
The next step is quite important and we ask you to be very careful: put your antenna that you have just made on your TV antenna and place the cable into the house.
Take the another end of the cable and divide the wires inside it just as you have already done. Cut away the external wire. Take a piece of plastic, make a small hole in it and put the inner wire of the cable in it. Now your device is practically ready! To boost your cell signal you just need to place your modem on this piece of plastic or to fasten this plastic to your mobile phone.


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text:
Feminist author Roxane Gay drops book publisher over Milo Yiannopoulos deal
Nick Duffy January 26, 2017
Feminist author Roxane Gay has parted ways with publisher Simon & Schuster – after they signed far-right internet troll Milo Yiannopoulos.
Publisher Simon & Schuster has recently faced calls for a boycott after handing a $250,000 book deal to far-right internet troll Milo Yiannopoulos.
Yiannopoulos, a Donald Trump supporter, has previously claimed he would 'cure' himself of being gay if he could, and describes trans people as "mentally ill gay men dressing up for attention".
He was banned from Twitter last year after allegedly encouraging a wave of racist abuse directed at Ghostbusters star Leslie Jones, while he recently took advantage of a university speech on his 'Dangerous Faggot' lecture tour to single out and bully a transgender student on-stage.
'Bad Feminist' author Roxane Gay announced this week that in response to the Yiannopoulos controversy, she would be parting ways with the publisher, who she had signed with under the TED imprint.
Her upcoming book, How To Be Heard, was set to be published this month.
The bisexual author said:" I was supposed to turn the book in this month and I kept thinking about how egregious it is to give someone like Milo a platform for his blunt, inelegant hate and provocation. I just couldn't bring myself to turn the book in.
"My editor emailed me last week and I kept staring at that email in my inbox and finally over the weekend I asked my agent to pull the book."
She added: "I guess I'm putting my money where my mouth is. And to be clear, this isn't about censorship.
"Milo has every right to say what he wants to say, however distasteful I and many others find it to be. He doesn't have a right to have a book published by a major publisher but he has, in some bizarre twist of fate, been afforded that privilege. So be it.
"I'm not interested in doing business with a publisher willing to grant him that privilege. I am also fortunate enough to be in a position to make this decision. I recognize that other writers aren't and understand that completely."
She added: "I have not placed the book elsewhere. I do hope the book is published someday."
More: Gay, LGBT, milo, Milo Yiannopoulos, Roxane Gay, US
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6 simple ways Saint Dolly Parton made the world a better place for LGBT+ people
Josh Milton - January 19, 2021


Last night, Ariana Grande took the stage at Coachella! Joining her were NSYNC, Nicki Minaj, and more, which sent social media into a frenzy!
Grande's setlist included "Break Up With You. Girlfriend, I'm Bored," "It Makes Me Ill" and "Tearin' Up My Heart" featuring NSYNC, "Bang Bang" and "Side to Side" featuring Nicki Minaj, and more!
Watch @NICKIMINAJ and @ArianaGrande performing "side to side" together at #Coachella ?
Ariana Grande was seen on Broadway in 2008, when she played the role of Charlotte in the musical 13, for which she won a National Youth Theatre Association Award. She played the role of Miriam in the first reading of the forthcoming musical Cuba Libre composed by Desmond Child. Most recently, she appeared as Penny Pingleton in Hairspray Live! on NBC.
Grande released her debut album, Yours Truly, in 2013 and peaked at the top of the US Billboard 200. Grande's second album, My Everything (2014), also topped the US charts and featured four top ten singles on the Billboard Hot 100, the most by any artist in 2014. Her third album, Dangerous Woman (2016), became her first number-one album in the United Kingdom. She most recently released Sweetener (2018) and Thank U, Next (2019), with the former winning a Grammy Award for Best Pop Vocal Album, while the latter had largest streaming week ever for a pop album. With the singles "Thank U, Next" , "7 Rings", and "Break Up with Your Girlfriend, I'm Bored", Grande became the first solo artist to hold the top three spots on the Billboard Hot 100 simultaneously, and the second musical act overall after The Beatles in 1964. Grande is also the first artist to have the lead singles from each of their first five studio albums debut within the top-ten on the US charts.


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Occam's Razor

    <time class="dt-published" datetime="2004-04-18 12:09:00 +0300">18 Apr 2004</time>

This entry was created on my old blog, and has been copied over, simply because I think it is still relevant.

Named for William of Ockham, Occam's Razor is summed up by the following Latin phrase "Pluralitas non est ponenda sine neccsitate"

Literally translated, this means "Plurality should not be assumed without necessity".

More simply ('scuse the pun) it means that when there exists a simple solution, don't search for a more obvious one. Or to quote Einstein - "Everything should be made a simple as possible, but no simpler".

Now this a theme worth living in life - one thats easier said than done!Occam

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