# Derivative Extrapolation Using Least Squares

Nick Butler  Ian Faber  Boris Shapoval  Armen Davis  Peter Borrell  Jake
Mcgrath

## Abstract

Here, we present three methods for differentiating discrete sets from
streaming processes, e.g. WIFI. One approach is based on optimization of the
well-known Savitzky-Golay algorithm. These methods are tested on synthetic
data sets and will be implemented on subsets of a real university campus WIFI
data set. The applicability of all methods are discussed, where we provide
insights on both some of their benefits and pitfalls. This article ends with
our conclusion on which method is better for our WIFI data.

Time series data is generated in practically every discipline, and it comes in
countless forms. This means that analyzing time series data is important, and
potential new approaches that can be developed and used to extract information
from them can lead to recognizing important new patterns and possibly to lead
to new insights and discoveries. In this article, novel Least Squares
techniques that are "data driven" are presented. The approaches presented
provide a powerful framework that allows polynomial regression, and
differentiation, of virtually any set of data points, including time series
and streaming data. We also present a different point of view on the problem
and propose improvements to previous algorithms. To develop the derivative
approximations we implement a degree finder that allows us to create low error
approximations. Finally, we apply our methods to a real-world WIFI data set
and find that our approach based on SSA is the best result.

Key Words: Least Squares, Derivative Extrapolation, Savitzky-Golay, Singular
Spectrum Analysis (SSA), WIFI data, data-driven methods

Faculty Sponsors University of Colorado Boulder : Dr. James H. Curry,
Departments of Applied Mathematics and Computer Science and Dr. Daniel Massey,
Department of Computer Science.

##  1 Introduction

Questions of interpolation and differentiation of data are well known.
Initially, polynomial interpolations and divided difference methods were
considered. Interpolated polynomials must go through all points of the data,
and splines, proposed by Schoenberg in 1946, [11] were an example of this
approach. It was found that for real and "dense data," or data having multiple
values given for some points, splines and polynomial fits were messy, hard to
calculate, and provided an incorrect pattern. However, Vaughan further
explored the method in 1982 [14] and found that quintic splines are quite good
for applications when computing power is limited, yet Vaughan’s method was
still wasn’t ideal. Burden and Faires’ numerical analysis textbook [1]
provides an approachable exploration of the concept of splines in detail in
Chapter 3, indicating some of its advantages and pitfalls.

As an alternative to splines, Least Squares proved to be a better method of
approximating sections of generic data sets. Savitzky and Golay [10] first
noticed this possibility in 1964, and their approach led to generating good
approximations by splitting up a data curve into numerous windows and
calculating a Least Squares regression through each window. They also proposed
a method of differentiating data using a table of convoluting integers,
described in Appendix I of [10]. The Least Squares approach of approximation
gained popularity in works such as [4], [7], [2], [9], and [12] and is also
included in popular text books such as Oliver and Shakiban [8] and Strang
[13]. Of those references, the most interesting application of Least Squares
for this article was presented by Mortari [7] in 2017. Mortari’s application
to "unknown differential equations" motivated our thinking about data sets
that don’t have known derivatives. While the method proposed by Savitzky and
Golay in 1964 is very good at reducing noisy data via Least Squares,
computational power and algorithmic strategies have progressed. For example,
because of limited computing power, the Savitzky-Golay approach took all
points into consideration at the same time. Further, it requires massive
tables of integers, which may not be the most intuitive.

The purpose of this article is to describe methods that can determine
derivatives of inherently noisy data. For each of the proposed methods, how
the noise is reduced and how derivatives are extrapolated will be determined
in several different ways and for different orders. This article is structured
as follows. Section 2 will present our first derivative extrapolation
technique, Polynomial Extrapolation (PE), which uses Savitzky-Golay as its
base. Section 3 talks about Reverse Polynomial Extrapolation (RPE), a
combination of simple differentiation techniques and the Savitzky-Golay
technique. Section 4 introduces our third technique of derivative
extrapolation, based on Singular Spectrum Analysis (SSA). Section 5 details
the results of running each method on different data sets, including two real
world WIFI data sets. Finally, Section 6 contains our discussion of the
methods, their benefits and shortcomings, and possible directions for future
research.

We have not seen these methods in previous literature, and believe they are
new. In particular, we believe the degree optimization algorithm we introduce
in Section 2.1 is a new take on Least Squares regression, and our definition
and use of window size throughout the article is unique. Also, our approach of
using Least Squares as opposed to other numerical derivative methods is a new
approach to the problem.

##  2 Polynomial Extrapolation

The most basic method we propose for extrapolating Least Squares derivatives
from data, here referred to as Polynomial Extrapolation (PE), is based on a
variant of the Savitzky-Golay method’s core idea. Savitzky and Golay proposed
analyzing a time series by parts, running a polynomial regression of a
specified degree on each window slice [10]. They identify numerical values for
coefficients of desired polynomials by careful tabulation, which are then used
in the numerical analysis. We have replaced this with a more modern polynomial
differentiation technique. We use a simple formula to find the derivative of a
polynomial and approximate the slope of a point in the data, which reduces
complexity compared to the giant tables developed by Savitzky and Golay. These
polynomial solutions are obtained with a standard Least Squares regression.
The parameters needed for each step are the window size and the polynomial
degree. These parameters in turn give the rows and columns, respectively, of
the matrix used in Least Squares. To describe the window size we use the
variable $n$. This variable represents the number of points to the left or
right of whatever point we are analyzing. For example, an $n$ value equal to
10 will have 10 points to the left and right of point $i$ resulting in a total
window size of 21. The first step of this algorithm is finding the Least
Squares solution of specified window size and degree for point $i$. This
solution will be an array as shown below, where $d$ is the degree of the
polynomial.

$\\{c_{0},c_{1},c_{2},...,c_{d}\\}$

The polynomial function that this describes is

$f(x)=c_{0}+c_{1}x+c_{2}x^{2}+...+c_{d}x^{d}$

From here we know by the power rule that the derivative would take the form

$f^{\prime}(x)=c_{1}+2c_{2}x+...+dc_{d}x^{d-1}$

resulting in an estimate for the slope at point $i$ by finding
$f^{\prime}(i)$. This is done for all points $i$ in the algorithm which
ultimately generates a curve for the derivative. The pseudocode for this is
shown in algorithm 1.

Algorithm 1 Least Squares Derivative Extrapolation (X,Y,n,d)

0: $X$ is an array of domain data, $Y$ is an array of data on that domain, $n$
is an integer number relating to window size, $d$ is degree for polynomial
fits.

for $i$ $1$ to $size(X)-2n$ do

$coef\leftarrow LeastSquares(X[i:i+2n+1],Y[i:i+2n+1],d)$

$derivativeValue\leftarrow 0$

for $c$ $1$ to $size(coef)-1$ do

$derivativeValue\leftarrow derivativeValue+c*coef[c+1]^{c-1}$

end for

$dY[i]\leftarrow derivativeValue$

end for

return $dY$

While the PE method works with a single specified degree across the entire
data set, the "appropriate" degree for each window may differ. For example, a
data set composed of curved and linear sections will be better approximated
with a mix of degrees, namely linear for the linear sections and higher degree
regressions for the curved sections. To find these sets of "ideal" degrees for
each window, we developed a degree finder algorithm. Note that for all errors
discussed the equation below was used, where $"n"$ is the number of data
points and $"f"$ is a predicted polynomial function.

$e=\sqrt{\sum_{i=1}^{n}\frac{(f(x_{i})-y_{i})^{2}}{n-1}}$

###  2.1 Polynomial Extrapolation Degree Optimization

We used Least Squares to find the ideal polynomial degree for each window,
based on relative error of one degree to the next. We created this relative
error algorithm with two underlying assumptions. The first is that with
increasing degrees, the error would always decrease. The second is that the
proper degree would be found due to fast convergence of the error versus
degree function. We picked the degree, $d$, using algorithm 2.

Algorithm 2 Degree Finder(x,y,check)

0: $x$ is an array of domain data, $y$ is an array of data on that domain,
$check$ is an integer number that limits the maximum possible degree.

$error\leftarrow$ error of linear polynomial fit

for $d$ from $2$ to $check$ do

$newError\leftarrow$ error of d-degree polynomial fit

if $\frac{error}{newError}-1<\epsilon$ then

return $d$-1

end if

$error\leftarrow newError$

end for

return $1$

For our numerical experiments, $\epsilon$ was chosen to be $1\%$, meaning that
the relative error from the previous degree to the next degree was small
enough, namely only a $1\%$ change, that the lower degree was sufficient to
describe the data. Figure 1 shows a comparison between PE with and without the
degree finder algorithm, and it can be clearly seen that the degree finder
results in a better approximation of the actual derivative curve. However, the
degree finder is not as smooth, and may be more susceptible to noise. In terms
of the actual degrees picked, we can see that higher degrees perform better
when approximating values at the local extrema of the actual derivative. The
quadratic PE consistently underestimates the magnitude of the actual
derivative at those points, whereas the degree optimized PE better
approximates those extrema. However, they seem to do equally well when
approximating linear sections of the derivative. The degree finder is not
limited to just PE, it can also be applied to the Savitzky-Golay algorithm.
This means that we can generate better approximations for both derivatives and
data sets themselves.

Figure 1: Generated data from a function that shows derivative extrapolation
using PE without a degree finder and with a degree finder. The bottom graph
shows the degrees chosen when the degree finder was used.

Our initial assumption that increasing degrees led to decreasing error was
found not to always be true. In fact, the error became "chaotic" as higher
degrees were chosen. This resulted in no clear trend from degree to degree.
This was the strangest result especially when considering the Least Squares
application to our problem. Theoretically, when choosing $n+1$ distinct points
for an $n$ degree polynomial fit, the error should equal zero. This appeared
to rarely be the case in our experiments when $n$ exceeded around 15 or more.
However, this potential numerical artifact did not pose a problem for PE, as
the degrees chosen were generally smaller than window size.

The second assumption broke down with varying amounts of noise in the data.
The noise in the data was determined from a normal distribution to the
original curve. When the standard deviation of the data was low, the error
versus degree function behaved as expected, where the error converged quickly
to zero. On the other hand, when the data had a high standard deviation, the
error first decreased slowly, leading to a linear fit most of the time. Though
we did not plan for the poor convergence on data with high variance, PE still
proved viable as it would not try to over fit these data occurrences with high
degree regressions.

##  3 Reverse Polynomial Extrapolation

Our Reverse Polynomial Extrapolation (RPE) method is based on reversing the
order of PE. In RPE, we first take a simple numerical derivative, then we
employ the Savitzky-Golay noise reduction technique. Taking the derivative and
removing the noise are two non-commutative operations, making the results of
PE and RPE different. The Savitzky-Golay method will remove some random noise
that was in the initial data, resulting in a "better final curve." The
Savitzky-Golay method can also be used iteratively if further reductions of
noise is desired.

###  3.1 Reverse Polynomial Extrapolation Mathematics

The numerical derivative is taken by a simple symmetric quotient

$f^{\prime}(x_{i})\approx\frac{y_{i+1}-y_{i-1}}{x_{i+1}-x_{i-1}}$

We do not need to know an exact derivative value at every point. Those points
are subject to random noise, this makes an exact derivative value far off from
the actual function’s derivative value. A major concern is to have derivative
values be accurate with a "similar error," and the symmetric quotient rule
satisfies that requirement.

We expect that derivative data will be inaccurate due to the noise in the
original data. However, that chaotic behaviour will be removed with our "best
variation" of the Savitzky-Golay algorithm discussed above, i.e. the algorithm
with the degree finder. It will remove the noise and in the end we will have
an accurate derivative trend.

###  3.2 Number of noise reductions

When taking the derivative of noisy data, the derivative will have more noise
than the data set itself, and that is exactly what RPE does. To fix this, we
introduced more iterations of Savitzky-Golay method to make sure that our
result is actually smooth and uninfluenced by noise from differentiation.
Choosing the correct number of extra iterations isn’t trivial, because after
some iteration reducing the noise will only lock the curve on a fake trend.

Since PE removes noise before differentiating, there is no extra noise
introduced once the derivative is actually taken. However, since RPE
differentiates first, more noise is introduced and it will always be noisier
than PE. To fix this and get similar behaviour from RPE, we applied the
Savitzky-Golay method twice after differentiating. The first iteration removes
the extra noise that came from differentiation, and the second iteration
ensures that RPE and PE are based on similarly noisy data.

##  4 Derivative Extrapolation Using Singular Spectrum Analysis

Singular Spectrum Analysis (SSA) is helpful for time series data, as it can
split that data into components. To split the data into components, SSA
utilizes Singular Value Decomposition (SVD). For a much more in-depth dive
into all things SSA, see [3]. We thought to use this method in derivative
extrapolation because of its ability to reduce Gaussian noise from data. The
first step of SSA is to put time series data into a Hankel data matrix, which
is then the input of an SVD. For our application, the number of columns of
this Hankel matrix represents the window size. Below shows how a time series
array, $X$, is converted to the Hankel data matrix, $H$.

$X=[x_{1},x_{2},...,x_{end}]\to H_{n\times
m}=\begin{bmatrix}x_{1}&x_{2}&\ldots&x_{m}\\\ x_{2}&x_{3}&\ldots&x_{m+1}\\\
x_{3}&x_{4}&\ldots&x_{m+2}\\\ \vdots&\vdots&\ddots&\vdots\\\
x_{n}&x_{n}+1&\ldots&x_{end}\\\ \end{bmatrix}$

The next step in our process is removing components that contribute mostly
Gaussian noise. Each component has an eigenvalue associated with it. The
larger the eigenvalue, the more the component explains the data. The smaller
the eigenvalue, the more it contributes to noise. If all components are used,
we would say that 100% of the variance is explained. To help remove noise, we
only use the components that contribute to between 90% and 99% of the
variance. The results in this article commonly used a "variance explained"
value of between $0.95$ or $0.975$.

Once the standard steps of SSA have been performed and most of the Gaussian
noise is removed, we can find the derivative. From SSA we have a constant
number of components, where each row in a component represents a window
surrounding the point where we want to find a slope. Typically at this point
in the process of SSA, the components are converted back to a time series by
averaging diagonal cells of the Hankel matrices. By averaging these cells,
there is a loss of information. Our derivative extrapolation method attempts
to preserve this information by skipping the process of averaging the
diagonals. Instead, our algorithm will loop over each component, extract a
row, perform a Least Squares linear regression to find a slope, and sum these
slopes for each component. For example, if we desire to estimate the
derivative at point $i$, we perform a linear regression on the $i$th row of
each component and sum the results.

Algorithm 3 SSA derivative(X,Y,n,var=0.95)

0: $X$ and $Y$ are arrays holding the data, $n$ is an integer number relating
to window size, $var$ is a floating point number between 0 and 1 giving
variance explained.

$window\leftarrow 2n+1$

$H\leftarrow$ hankel matrix using array $Y$ with number of columns equal to
$window$

$U,E,V\leftarrow$ SVD on H

$numEigenvalues\leftarrow$ number required for $var$ variance to be explained

$Components\leftarrow$ array of matrices of length $numEigenvalues$ where a
matrix is equal to $E[idx]*(U_{:,idx}\times V_{idx,:})$

for $i$ $1$ to $numEigenvalues$ do

for $j$ $n$ to $length(X)-n$ do

$slope\leftarrow LeastSquaresLinearFit(X[j-n][j+n],Components[i][j])$

$dY[j]+=slope$

end for

end for

$dY\leftarrow dY$ shifted due to the hankel matrix

return $dY$

##  5 Results

Figure 2: Top: A graph showing the original function, which consists of
multiple components, that we want to find the derivative for. Bottom: A graph
showing the derivative extrapolation of the test function with the three
proposed methods. The noise in the top graph is based on a standard deviation
of 0.1.

In Figure 2, we use test data with 3 main components which are in the form of
sine or cosine functions, namely, $sin(2x)$, $cos(\frac{x}{2})$, and
$2sin(x)$. PE and RPE seem to straddle the actual derivative equally above and
below, showing no apparent systematic error. For SSA, the bottom graph shows
an almost perfect fit of the line with minimal amounts of noise. We can also
see the effect of window size in figure 2 in the form of a "delay" at each end
of the derivative graph. Since the window size we’ve chosen is 15 points, we
can see a corresponding delay of 7 points on the left and right sides of the
generated derivative curve. This means that in order to capture derivative
information at the extremes of a data set, either a smaller window size can be
chosen or the domain of the original data curve can be increased. Regardless,
there will always be a delay with these methods.

The trends we see in this case may not agree with real life, due to the random
nature of the error in this case and more systematic issues in real life.
Figure 2 only gives us a general feeling of the performance of the methods. In
real life we would also expect longer linear parts and quicker falls and
rises, which our test case doesn’t have. No matter what we do, a fake data set
will never prepare us for real world features. Nevertheless, we will look upon
another fake data set to get a feeling of how well different methods estimate
linear trends. To see if small oscillations are inherent to the sinusoidal
curve or the noise in any data, we performed these methods on a simple linear
line shown in Figure 3.

Figure 3: Top: Two graphs showing a linear function we want to find the
derivative for. Bottom: Two graphs showing the derivative extrapolation of the
test function with the three proposed methods. The left and right graphs show
different levels of noise.

In Figure 3, we see that there are oscillations in the data from all explored
methods. This means that small oscillations in the derivative extrapolation
must be attributed to the noise in the data. For larger amounts of noise in
the data, we see that there appears to be increased amounts of oscillations
above and below the actual solution curve. This is expected, as the methods
are following less clear data trends when the data curve is noisy. We can also
see that in the case of the curve with more noise (larger standard deviation),
PE does much better than RPE, while PE and SSA seem to follow similar trends.
We can also see that the magnitude of oscillations increases as the ratio of
standard deviations increases. In this case, the ratio of standard deviations
is 5, and we see a corresponding increase in magnitude by about the same
ratio. When comparing the three methods here, SSA shows the greatest reduction
in noise. This makes sense, as the main goal of SSA is to take out Gaussian
noise from time series data. The PE method does fairly well and "matches" SSA
in many places; however, it tends to have large jumps away from the true
solution since it does not pass over the noise in the data well.

After verifying our methods with the test data sets and noting their
advantages and disadvantages, we moved onto our "real" data set of Wi-Fi usage
at the CU Boulder campus. The campus has three different networks: CU
Wireless, CU Wireless Guest, and Eduroam. CU Wireless is the most used
network, and we focused on it exclusively in our analysis. The data was
collected via routers distributed over the campus territory and buildings. A
number of connected users is measured at times with no particular periodicity
and is summed up over all routers to acquire a total number of users across
the campus, or in a particular building. We analyzed both the full network and
an average dorm, Smith Dorm [6], during a full week in October of 2019. The
real world data used had personal identification characteristics removed prior
to processing the data. The information used has been stripped of any
information other than what is required for counting active users, a general
datum of where the count was taken, and the time when the value was obtained.
It is not possible to identify a movement of any of the real data recorded
since there is equal likelihood of them staying, or moving to another location
measured. This data set has no known derivative, and we will use our methods
to determine mathematically reasonable approximations. The full network data
set is shown in the top half of Figure 4, and the Smith Dorm data set is shown
in the top half of Figure 5.

Figure 4: Top: Data of the total Wi-Fi user count on the CU Boulder wireless
network. Bottom: Derivative extrapolation using three methods on a real data
set with a small amount of noise.

Figure 4 shows a smoother curve and Figure 5 shows a more "jittery" and noisy
curve. However, the curves show similar trends based on the day of the week.
We can quickly see that in both cases, RPE is the most noisy derivative
extrapolation method. The RPE curve tends to mimic the PE approximation the
most; however, RPE is better at showing peaks in the derivative. On the whole,
SSA seems to be much smoother than both PE and RPE, but it differs
significantly from both in multiple places.

Figure 5: Top: Data of user count on CU wireless network in Smith Dorm.
Bottom: Derivative extrapolation using three methods on a real data set with a
large amount of noise.

In the case of overall network trends from Figure 4, we can see that our
methods create trends that match what we’d expect for a typical week at a
university, namely, more rapid changes in network traffic during the week and
significantly less on the weekends. We can see a clear increase in the number
of users per second after the weekend, which can be explained by students
coming back to campus after taking the weekend off. More students on campus
equates to more devices connecting to the network, which our methods correctly
show as a higher magnitude of users per second. Likewise, when students leave
campus for the day the number of devices connecting to the network per second
becomes negative, which we’d expect with so many devices disconnecting from
the network. Our methods also correctly show critical points where we’d
expect, namely the "humps" of each day.

In terms of network trends in the dorm from Figure 5, despite the messiness of
the curves we can still see patterns that we would expect for a typical dorm,
i.e. more heavy network use in the evenings and early morning hours than
during class times. On the weekends, particularly Fridays and Saturdays, the
oscillations settle to small values, meaning that not too many people are
leaving the dorms if they’ve decided to stay in them over the weekend.
Understandably, many students choose Sunday to catch up on work and/or get
ahead for the week, which is accordingly reflected by higher network traffic
and users per second. When students leave for class, we can correctly see a
negative spike in users per second, which means devices are disconnecting from
Smith’s section of the network. Likewise, when they come back after class we
can see corresponding spikes in positive users per second.

##  6 Discussion

###  6.1 Comparison of the Three Methods

In carrying out our experiments, we found that the best of our methods for
differentiating a curve via Least Squares was SSA. In general, the PE and SSA
methods are most closely related to each other, as for many parts of both
curves they are nearly identical. Where they differ is when the data becomes
messy. In Figure 4, the messiest parts of the data are when there are positive
slopes and local maxima. Though PE does well to approximate these sections, it
does not show a uniform and smooth derivative. This is easily seen on the
sections that the SSA method is larger than PE. PE flattens out here whereas
SSA shows clear sinusoidal behavior. Figures 2 and 3 also show the
effectiveness of SSA in approximating a well-known derivative. Whereas PE and
RPE oscillate wildly around the known derivative, SSA matches the derivative
incredibly closely in context of both large and small noise standard
deviations. Similar to other diagrams, in Figure 5, there is a clear
distinction between SSA and PE on noisy parts of the data. We see that on
sharp, "almost" non-differentiable parts of the data, PE tends to show rounded
off parts whereas SSA appears to accurately show the proper peaks and troughs
of the cyclical data set. RPE has the most amount of noise and overestimates
the derivative’s peaks, which is an indication that this method is the worse
one.

We believe that the SSA-based strategy is the best method because it exhibits
better long-term behavior, continuity, and noise reduction than RPE or PE.
Long-term behavior in this case refers to the algorithm’s ability to correctly
calculate the derivative in context of points outside its window size. This
inherently makes sense when looking at how each method works. For RPE, it only
uses one point to either side and relies on Savitzky-Golay to take into
account a large window size. PE is slightly better than RPE since it initially
looks at a larger window size when approximating the derivative, yet it is
still limited to that window. Lastly, SSA does best since its uses the data as
a whole and can best recognize long-term behavior. The most significant
problem with RPE is that it struggles to reduce noise and it therefore tends
to over-fit the data. The main problem with PE is it lowers magnitudes at
peaks and troughs. PE does not find large slopes as well as SSA and tends to
dull parts of the curve as a result.

###  6.2 Other Methods

There are some other strategies that we consider valuable, but did not look at
in this article. One is an improvement of the degree finder in the way that it
will favor higher degrees by adding some type of weights to the system. The
weights would ideally avoid most of the small perturbations that caused the
oscillations seen in Figure 3 and approximate long linear parts better.
Another way to remove extra zeros calculated from noise, and hence reduce
oscillations, is to implement a minimum - maximum - saddle point finder and
make the derivative zero at those points. Then, we will only have one unknown
coefficient to build the derivative as a polynomial from its zeros. That last
coefficient can be found, again, with linear regression techniques by solving
$y_{i}=b*(x_{i}-r_{1})...(x_{i}-r_{r})=b\bar{x}_{i}$ for $b$, given $r_{j}$ to
be the roots and $y_{i}$ random derivative samples measured with a symmetric
quotient rule. We believe that both of these methods may be valuable
alternatives to PE and RPE methods in the long term behaviour, but their
behaviour in context of quick changes is yet to be discovered and would be a
beneficial area of future investigation. We also thought about a potential
method that combines SSA and PE. Currently, we only employ a linear regression
on each component of SSA decomposition, but it may be beneficial to optimize
that degree of fit using PE’s degree finder.

When we used the SSA method to find derivatives, we compared it to using Non-
Negative Matrix Factorization (NMF)[5]. Not surprisingly, these two methods
were very similar to each other. The reason we used SSA instead of NMF is for
two reasons. First, NMF requires many iterations to converge to a solution;
this makes the computation time of NMF much longer than SSA. Second, by
reducing noise similar to our SSA method, NMF will consistently underestimate
the real derivative due to its requirement of only non-negative values.
Hpwever, further investigation may be beneficial.

##  7 Conclusion

In this article, we developed three new methods for calculating derivatives of
data sets: Polynomial Extrapolation, Reverse Polynomial Extrapolation, and
Derivative Extrapolation using Singular Spectrum Analysis. All methods
incorporate the technique of Least Squares applied to streaming data. The PE
method first uses Savitzky-Golay to reduce the noise of data, then finds the
derivative using a Least Squares solution of linear degree polynomial or
higher. In developing PE, we also found a way to optimize the degree of fit
for the Least Squares problem by comparing relative error from one fit to the
next. We have not seen this degree-based approach in previous literature, as
well as applying a sliding window to the differentiation process. We are
confident that both approaches are new. RPE first finds the "symmetric
derivative," then uses the Savitzky-Golay method twice to reduce noise.
Lastly, SSA was used to take into account the whole data set and find linear
fits for each component of the data. After developing these methods, we
applied them to a real-world Wi-Fi data set and found trends in network
activity that correspond to real-world activity. In addition, the methods
provided some insights into the structure of the CU Boulder campus’ inner
life. We concluded that the SSA derivative method was best since it reduced
the largest amount of Gaussian noise and showed better long-term behavior.

##  8 Acknowledgement

The research reported here was supported in part by a contract from Sandia
National Laboratory to the University of Colorado Boulder, Departments of
Applied Mathematics and Computer Science. Special thanks to our colleagues in
the University of Colorado Office of Information Technology, Orrie Gartner and
Glenn Rodrigues, who made the anonmyized data presented in figures 4 and 5
available and helped with many discussion and guidance on data policies and
the broader research effort of which this is a part. Special thanks to Maxim
Moghadam for making his undergraduate Computer Science thesis material
available to the research team.

## References

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# 6G Communication Technology: A Vision on Intelligent Healthcare

Sabuzima Nayak and Ripon Patgiri Sabuzima Nayak and Ripon Patgiri, Department
of Computer Science & Engineering, National Institute of Technology Silchar,
Cachar-788010, Assam, IndiaEmail<EMAIL_ADDRESS>and
<EMAIL_ADDRESS>(URL: http://cs.nits.ac.in/rp/)Corresponding author:
Ripon PatgiriManuscript received Month 00, 20XX; revised Month 00, 20XX.

###### Abstract

6G is a promising communication technology that will dominate the entire
health market from 2030 onward. It will dominate not only health sector but
also diverse sectors. It is expected that 6G will revolutionize many sectors
including healthcare. Healthcare will be fully AI-driven and dependent on 6G
communication technology, which will change our perception of lifestyle.
Currently, time and space are the key barriers to health care and 6G will be
able to overcome these barriers. Also, 6G will be proven as a game changing
technology for healthcare. Therefore, in this perspective, we envision
healthcare system for the era of 6G communication technology. Also, various
new methodologies have to be introduced to enhance our lifestyle, which is
addressed in this perspective, including Quality of Life (QoL), Intelligent
Wearable Devices (IWD), Intelligent Internet of Medical Things (IIoMT),
Hospital-to-Home (H2H) services, and new business model. In addition, we
expose the role of 6G communication technology in telesurgery, Epidemic and
Pandemic.

###### Index Terms:

6G, 6G communications, Smart Healtcare, Intelligent Healthcare, Quality of
Services, Quality of Experience, Quality of Life, Intelligent Internet of
Medical Things, Intelligent Wearable Devices, Hospital-to-Home Service,
Telesurgery, Edge Computing, Artificial Intelligence.

##  I Introduction

6G communication technology is attracting many researchers due to its
prominent features and its promises. It will revolutionize diverse fields and
we will evidence the revolution from 2030 onward. Many features of 6G have
already been discussed in premier forum and continuously gathering various
requirements of 6G communication technology [1, 2, 3, 4]. Also, Nayak and
Patgiri [5] exposes issues and challenges of 6G communication technology. Many
countries have already started 6G communication technology for timely
deployment. Firstly, Finland initiated 6G project in 2018[6]. Secondly, United
State, South Korea and China have started 6G project in 2019 [7]. Recently,
Japan has also initiated 6G research project in 2020 [8]. In addition, many
algorithms have been developed for 6G [9, 10]. Now, it is essential to
initiate 6G project to not be left behind by other countries. On the contrary,
5G communication technology is yet to deploy in full scale over worldwide and
B5G yet to be developed. 5G and B5G will have various drawbacks for
revolutionize modern lifestyle, society and business. For instance, unable to
support holographic communication due to lower data rate. Therefore, it is the
peak time to envision future possibilities of 6G communication technology.
Also, it is necessary to envision the future healthcare for well-being of
peoples of the society.

The current healthcare system is providing basic facilities and the key
barrier of the current healthcare system is time and space. This is
unavoidable in the current scenario, however, it will not be a barrier in the
near future. Moreover, ambulance service is just a transporter of patients
with oxygen facility and road traffic priority which can be served by a normal
car too. Besides, the elderly service is very unsatisfactory in current
scenarios. The elderly service requires intensive care from medical staffs.
However, it is unavailable till date. Most of patient dies in ambulance while
travelling from home to hospital or before ambulance reaching the spot. Also,
the accident detection system is unavailable in current healthcare systems.
The accident detection system requires real-time detection to provide medical
services on time and on the spot. Furthermore, Epidemic and Pandemic
outbreaks, for instance, COVID-19, cannot be controlled due to lack of
advanced infrastructure. A similar kind of virus will again arise in future.
Thus, it is utmost important to develop the intelligent healthcare system.

Figure 1: A landscape of intelligent healthcare systems. This figure includes
Intelligent Internet of Medical Things (Blood Sample Reader (BSR) sensor,
Intelligent Wearable Devices (IWD), Online Prescription, MRI, CT Scan),
Hospital-to-Home (H2H) Services implements mobile hospital, Pathology, Local
Doctors, Remote Doctors, and Data Scientist.

The requirements of 6G communication technology for future healthcare are high
data rate ($\geq 1~{}Tbps$), high operating frequency ($\geq 1~{}THz$), low
end-to-end delay ($\leq 1~{}ms$), high reliability ($10^{-9}$), high mobility
($\geq 1000~{}km/h$) and wavelength of $\leq 300\mu m$ [4]. In particular,
telesurgery requires real-time communications. Also, holographic communication
and augmented/virtual reality will boost up the intelligent healthcare
systems. However, 5G and B5G will be unable to support intelligent healthcare.
In the 5G communication era, intelligent healthcare will be implemented
partially which will push forward a step ahead. However, the rural
connectivity is still a challenge for 5G communication technology [11] as well
as healthcare. Communication technology boost up the performance of health
service and a landscape of intelligent health service is depicted in Figure 1.

It is expected that 6G communication technology will revolutionize the
healthcare completely and the healthcare will fully depend on communication
technology. We will evidence the paradigm shift in healthcare due to the
advent of communication technology. Current state-of-the-art healthcare system
is unable to provide telesurgery due to communication issues. Moreover,
ambulance service is to be replaced. Wearable devices need to be redefined.
The hospital is required to restructure. The health services should be
provided in real-time. Health monitoring and elderly services need to be
redefined. Therefore, in this perspective, we envision the future healthcare
using 6G communication technology. We brief the required parameters of 6G
communication technology and its prime technologies. Also, we focus on Quality
of Services (QoS), Quality of Experiences (QoE) and Quality of Life (QoL).
Moreover, we envision the requirement of Hospital-to-Home (H2H) services,
Blood Sample Reader (BSR) sensor, Intelligent Wearable Devices (IWD), and
Health Insurance at Hospital (HIH) business model. Moreover, the role of
Artificial Intelligence (AI) and Edge technology in healthcare is exposed.
Thus, Section II surveys detail parameters of 6G communication technology to
establish the understanding of the article. In addition, Section III reviews
the enabling technology for 6G to meet intelligent healthcare in near future.
Sections IV, V and VI expose the role of holographic communication, augmented
and virtual reality, and tactile Internet in intelligent healthcare. Moreover,
the parameters of intelligent healthcare are envisioned in Sections VII, VIII
and IX. This article also exposes the role of communication in handling
Epidemic and Pandemic in Section X. Furthermore, A new business model also
discussed in Section XII. Most importantly, intelligent healthcare requires
security, secrecy and privacy which are addressed in Section XIII. Finally,
this article is concluded in Section XIV.

##  II 6G Technology

6G will be using the terahertz (THz) signal for transmission [2]. THz signal
increases bandwidth and data rate. Moreover, it will provide bandwidth three
times higher than 5G signal, i.e., mmWave [12]. 6G will have a data rate of 1
TBPS or more. 5G and B5G follow 2-dimensional communication structure, whereas
the 6G will follow 3-dimensional, i.e, time, space and frequency. 6G will
provide the 3D services with the support of emerging technology such as edge
technology, AI, cloud computing and blockchain. The 6G communication network
will be ubiquitous and integrated [13]. 6G will provide deeper and broader
coverage through device to device, terrestrial and satellite communication. 6G
aims to merge computation, navigation and sensing to the communication
network. In the area of security, 6G will cover security, secrecy and privacy
of the Big data generated by billions of smart devices. However, there will be
a transition from smart device to intelligent device.

###  II-A Requirements

The requirements of 6G communication are gathered and discussed by various
researchers [14, 15, 16, 17, 18, 19, 20, 21]. The key requirements of 6G
communication technology are 1 THz operating frequency, 1 Tbps data rate, 300
$\mu m$ wavelength, and 1000 kmh mobility range [1, 5]. The 6G architecture is
3D with consideration of time, space and frequency. The end-to-end delay,
radio delay and processing requirements are $\leq$ 1 ms, $\leq$ 10 ns and
$\leq$ 10 ns respectively to provide real-time communication [2, 22].
Moreover, 6G will be truly AI-driven communication technology [5]. It is
expected that 6G will be fully backed by satellite. The NR-Lite will be
replaced by Intelligent Radio (IR) [23]. Also, the core network the Internet
of Things (IoT) will be replaced by the Internet of Everything (IoE). It is
expected that 6G will enable and revolutionize many technologies in coming
future. We will evidence the transitions of IoT to IoE, Smart Devices to
Intelligent Devices, and other numerous possibilities.

###  II-B Terahertz Communication

6G will use terahertz radiation (THz) also called submillimeter radiation. It
is electromagnetic waves with wavelengths in between 1mm to 0.1 mm, hence
called submillimeter radiation. THz has many advantages making it suitable for
6G communication such as high bandwidth, high data rate (upto several Gbps),
high capacity and high throughput [4]. Efficiency of THz signals is possible
to increase by spectrum reuse and sharing. Some techniques already exist for
spectrum reuse such as cognitive radio (CR). It helps many wireless systems to
access the same spectrum through spectrum sensing and interference management
mechanisms [4]. In case of spectrum sharing, temporally underutilized or
unlicensed spectrum is utilized to maintain availability and reliability.
Symbiotic radio (SR) is a new technique to support intelligent, heterogeneous
wireless networks. It will help in efficient spectrum sharing. However,
deploying these techniques in the 6G wireless network are still big
challenges. Moreover, continuous THz signal generation is strenuous due to
requirement constraints regarding size. Designing an antenna/transmitter is
also complex. In addition, the signal gets attenuated to zero after short
distance transmission. It occurs due to energy loss, i.e., molecular
absorption and spreading loss [24].

###  II-C Transition from Smart to Intelligent

6G is expected to be truly AI-driven communication technology and hence, it
will be able to introduce intelligent era [5]. Therefore, all smart devices
will be converted to intelligent devices in the era of 6G [25]. The advent of
AI along with mobile communication, we will evidence many transitions from
smart things to intelligent things. From 2030 and onward, the IoT will be
intelligent and will be replaced by IoE. The smart phone will be replaced by
intelligent phones. Intelligent devices will be AI-driven devices that are
able to connect to the Internet. Thus, the intelligent device (may be tiny
device) will be able to predict, make a decision and share their experience
with other intelligent devices. Therefore, there is a paradigm shift from
smart to intelligent era using 6G communication technology.

###  II-D Quality of Services

The Quality of Services (QoS) parameters of 6G technology are higher than 5G
and B5G. For instance, QoS includes high data rates, extremely reliable and
low latency communication (ERLLC), further-enhanced mobile broadband (FeMBB),
ultra-massive machine-type communications (umMTC), long-distance and high-
mobility communications (LDHMC) and extremely low-power communications (ELPC)
[18]. Also, QoS includes mobile broad bandwidth and low latency (MBBLL),
massive broad bandwidth machine type (mBBMT), massive low latency machine type
(mLLMT) [2]. This QoS service parameters enables diverse applications to
revolutionize. Thus, the 6G technology will be proven as a revolutionary
technology in many fields along with healthcare.

###  II-E Quality of Experiences

The Quality of Experiences (QoE) defines a high QoS and user-centric
communications. QoE will be achieved by holographic communications, augmented
reality, virtual reality, and tactile Internet which requires high data rate
with extremely low latency. Moreover, QoE is expected to be revolutionary in
intelligent cars, intelligent devices, intelligent healthcare, intelligent
drones and many more. A high QoE can be achieved only when all desired
parameters are implemented by 6G technology. 6G technology will be truly AI-
driven communication technology [5], and thus, we will evidence many changes
in our lifestyles, societies and businesses. Also, 6G promises to provide five
sense communication to provide rich QoE. Thus, 6G communication will be a
major milestone for healthcare. Healthcare requires high QoE for critical
operations, intelligent hospitals and intelligent healthcare.

###  II-F Quality of Life

The Quality of Life (QoL) is defined as enhanced lifestyle with QoS and QoE in
healthcare. 6G technology will enable high QoL using communication technology.
The QoL is not a core parameters of 6G communication technology, however, it
will be core parameters of the intelligent healthcare systems. 6G will be able
to provide high QoE along with desired parameters of QoL. The key parameters
of QoL are remote health monitoring of patients, including elderly persons,
connection to intelligent wearable devices (IWD), intelligent accident
detection, telesurgery, precision medicine, and many parameters will be
included in future. Also, another prominent feature of QoL is Hospital-to-Home
(H2H) services. H2H service will be implemented using mobile hospital in an
intelligent vehicle. The mobile hospital will have minimum requirements to be
a hospital including medical staffs. This service is essential in QoL to
improve the modern lifestyle and emergency services. In addition, Health
Insurance at Hospital (HIH) will emerge to replace the current health
insurance policy. HIH will increase faith on hospital services and it is also
included in QoL. The Hospitals will be ranked based on QoL parameters in near
future.

##  III Enabling Technology for 6G

6G communication technology requires supporting technologies to fulfill the
promises. 6G is truly AI-driven communication technology [5], and thus, it
requires AI to integrate its communication technology. Moreover, 6G will
enable Internet of Everything (IoE), and it will boost up many fields. Also,
edge technology is necessary for 6G technology for bringing the Cloud features
closer to intelligent devices. Thus, 6G communication technology comprises of
many technologies.

###  III-A Internet of Everything (IoE)

6G follow 6C’s for communication [2]. 6C’s are capture, communicate, cache,
cognition, compute, and control. High level sensing is capturing. It is
essential for holographic communication in healthcare. The captured data are
converted to digital data, stored in a local cache and transmitted to remote
locations in real-time. In some cases, digital data are further converted to
signals and transmitted to other devices for processing. But before computing,
cognition helps in formulating feasible determinations based on input digital
data. These are intelligent determinations which helps in making the computing
easy. The computed data are transmitted to smart devices to help in
controlling the action taken by smart devices for healthcare [2]. For example,
raising an alarm on Epidemic and Pandemic. It will use the core services of
combined and enhanced eMBB and mMTC. It will require high data rates to
support touch experiences in the intelligent devices for healthcare. IoE will
be required by 6G to have a huge capacity to connect millions of intelligent
devices, collect tactile sensations and convert to digital data [2]. Huge
capacity to connect the sensors and actuators in healthcare communication.
And, low latency to maintain seamless integration among them [2]. When 6G will
be commercial, it will not be the era of Big data but rather Big data 2.0. Big
data 2.0 require a supercomputer to compute and analyze massive scale of
small-sized data produced by healthcare devices [25].

###  III-B Edge Intelligence

6G will rely on Cloud computing for storage, computing and analysis of Big
data [5]. Data produced by the intelligent devices are transferred to Cloud
for storage, however, it consumes communication resources and bandwidth.
Nowadays, the technologies are brought closer to the data source due to the
exponential growth of data. This technology is Edge technology. 6G is claiming
to have a high capacity to provide smooth services to billions of intelligent
devices [26]. 6G will rely on Edge technology to provide the smooth and high
speed Internet services to the intelligent devices which is vital for
healthcare. Edge technology collects, computes and analyses the health data in
real time in its Edge nodes [10]. These nodes are located closer to the
intelligent medical devices. The data generated by the user are transmitted to
the Edge nodes. Also, the Edge nodes compute the health data. Then, Edge nodes
analyze the data to decide the appropriate action. For example, Edge node will
receive user health data transmitted from the intelligent medical devices and
determines whether the user is suffering from any deficiency. The health data
are constantly transmitted to Edge nodes. The Edge node monitors the health
related data. Edge node also filters the health related data and transmits the
important information to the Cloud for storage. Edge technology reduces cost
of communication and computation [27]. Some other advantages of Edge
technology are low latency, reliability, privacy, scalability and
adaptability. The massive number of intelligent devices will connect to 6G
Internet, hence, all the advantages of Edge technology will greatly help 6G to
meet its requirements to provide high QoS in healthcare.

“The marriage of edge computing and AI gives the birth of Edge intelligence
[28].” Edge intelligence is implemented using AI algorithms for analysis in
Edge nodes called Edge analytics. Edge nodes receive a huge volume of health
related data and AI is used to find patterns or compute them for analysis.
With the help of AI, Edge nodes are capable of developing image, data and
video Edge analytics. GigaSight [29] is a video Edge analytics with a
decentralized hybrid cloud architecture. Xie et al. [30] proposed a video
analytics that has lightweight virtualization by implementing container
technology. For filtering of data in Edge nodes, Nikolaou et al. [31] proposed
a predictive Edge analytics. Similarly, Cao et al. [32] proposed a descriptive
analytics for mobile Edge nodes. However, AI algorithms are computationally
intensive. Currently, AI algorithms execution requires high computational
resources, and power consumption, which is limited in the Edge nodes. Hence,
they depend on the Cloud for execution. However, Edge nodes will be one of the
network nodes in 6G. All 6G network nodes will be AI-enabled for providing
intelligence services to the healthcare systems. Moreover, 6G will have real-
time intelligent Edge which will dramatically boost up the healthcare system.
It will perform computing and analysis on live data [33]. Therefore, it is
very important to execute the AI algorithms in Edge nodes instead of Cloud to
reduce latency in providing the services [13].

###  III-C Artificial Intelligence

6G will be a truly AI-driven communication network[5, 34]. 6G will make every
aspect of network communication intelligent to make the system self-aware,
self-compute and self-decide on a situation. The goal of 6G is to provide
global coverage, including space-air-water. This is achievable only by making
the different aspects of communication “intelligent”. Implementation of AI
algorithms is generating high accuracy and performance in communication
networks. Truly AI-driven communication can offer real-time communication
which is very important for modern healthcare.

AI-driven healthcare improves clinical diagnosis and decision making [35]. The
healthcare requires AI to perform tasks in real-time. Deep learning (DL) does
not require data preprocessing. It takes original health data and performs the
computation, thus, real-time data can be given as input. Moreover, it shows
high accuracy while computing a large number of network parameters[36].
Similarly, another AI algorithm that is currently explored on health data is
Deep Reinforcement Learning (DRL). In reinforcement learning, the system first
develops a few decisions, then observes the results. Based on the observation
the decision is again computed to obtain an optimal decision. DRL combines
both reinforcement learning and deep neural networks algorithms and combines
the advantages of both [37]. Thus, DRL gives high performance within small
computation time. In addition, federated AI will share their knowledge among
the intelligent devices which will booster healthcare. AI algorithms have
shown high performance. AI algorithms require expensive infrastructure. The AI
is also preferred for proactive caching. For Big Data, parallelism in training
should be explored. All AI algorithms perform high computation task. The high
computation task takes a long time and consumes more power. Whereas, 6G is
unable to provide such relaxation. The AI algorithms that will be implemented
in 6G will have their own issues. For example, large numbers of layers in
Neural Network. However, research is performed to improved AI algorithms with
less computation time and less energy consumption to improve the performance
of 6G which leads to increase in efficiency in healthcare.

##  IV Holographic Communication

“Hologram is a physical recording of an interference pattern that uses
diffraction to generate a 3D light field [38]”. The image generated has
parallax, depth and other properties of the original object. Holographic
communication uses cameras from different angles to create a hologram of the
object. It will use the core service of combined and enhanced eMBB and URLLC.
It will require high data rates to provide good quality of service and
streaming high definition videos. Moreover, very low latency is required for
real-time voices and immediate control responses [2]. Holographic
communication will be a major breakthrough for healthcare. And, 6G is capable
of providing this service. 6G Holographic communication will help connect
people. In case of emergence, in some cases the doctors have to wait for the
expert doctor(s) for a diagnosis. However, using holographic communication the
expert doctor(s) can diagnose the patient while travelling. And, can supervise
the doctor for an early medical treatment. Many times the patient has to
travel to many doctors for a correct diagnosis or the treatment is unavailable
in that hospital. The patient may have to travel to different states or to
different countries. In such cases, it becomes an economical and physical
burden for the patient. Also, travelling in bad health is very stressful for
the patient. However, using holographic communication the doctors can diagnose
remotely. The patient can only visit the hospital for treatment. Holographic
communication will also help the expert doctors provide services in rural
areas while staying in cities or towns. Similar to 6G global coverage, the 6G
holographic communication will help in global connectivity of healthcare. Upon
request the expert doctor can instantly provide services without having to
adjust their schedule and travel. Moreover, it will be possible to connect
different doctors around the world to discuss/supervise in complex medical
cases.

##  V Augmented Reality and Virtual Reality

Augmented reality (AR) helps to include virtuality to real objects. Moreover,
it is combined with multiple sensory abilities such as audio, visual,
somatosensory, haptic etc. AR also provides real-time interaction, and
presents 3D images of virtual and real objects accurately. Virtual reality
(VR) refers to presenting an imaginative or virtual world where nothing is
real. AR and VR will use the core service of combined and enhanced eMBB and
URLLC. It will require high data rates to provide good quality of service.
Moreover, to stream high definition videos. Moreover, very low latency is
required for real-time voices and immediate control responses [2]. AR and VR
require a peak data rate of 1 Tbps and user experience of $>$10 Gbps with
$>$0.1 ms latency which can be provided by MBBLL[2]. Currently, both AR and VR
are developing. However, 6G will open new windows for their usage in the field
of healthcare. AR will help to view the inside of the body of a patient
without any incision. Moreover, doctors can adjust the depth of the specific
location in the body [39]. The specific body area can also be enlarged for
better visibility. 6G will help the doctors to view a patient remotely. The AR
and holographic communication can be combined for better diagnosis. Using VR
the doctors can practice medical procedures without any patient. It will be
very helpful in case of practicing complex procedures/surgery having high
risk. All these devices will be intelligent devices and connected to 6G
Internet. As discussed above using 6G a smooth and high resolution
presentation can be created for remote medical learning or diagnosis.

##  VI Tactile/Haptic Internet

Haptic technology creates a virtual touch using force, motion or vibration on
the user. Tactile Internet is used to transfer the virtual touch to another
user, maybe human or a robot. Tactile Internet requires high speed of
communication and ERLLC to grab the tactile in real-time. This technology will
be used for remote surgery, i.e., telesurgery. It will also help doctors for
diagnosis using touch without being physically present. Haptic human-computer
interaction (HCI) is classified into three types, namely, desktop, surface,
and wearable [40]. In desktop HCI, the remote doctor will be able to use a
virtual tool for surgery or diagnosis. In surface HCI, the movement is not 3D,
but 2D. The device to give command has a flat screen such as a mobile or
tablet. As moving the hand on the screen the robot can be given a command to
interact with the patient. In wearable HCI, for instance a haptic glove, is
used by the remote doctor. Tactile/haptic technology will also help in
providing healthcare during disaster time. For example, the COVID-19 when all
countries are under lockdown and interaction with outside of the state and
country is closed or natural disasters. During such situations, tactile/haptic
technology will help in healthcare. Expert doctors can perform complex surgery
remotely using robots. In addition, during epidemics and pandemics, the
medical personnel are at great risk. A little carelessness may expose them to
the deadly/contagious disease. Using tactile/haptic technology robots can be
used to interact or care for the patient while medical personnel will be
present remotely. All this is achievable by using 6G high speed and low
latency Internet.

##  VII Intelligent Internet of Medical Things

In 6G communication paradigm, Intelligent Internet of Medical Things (IIoMT)
will evolve and serve many purposes for well-being of humankind. IIoMT are
intelligent devices that are AI-driven that makes its own decision using
communication technology. IoE will also emerge along with IIoMT, and thus,
medical things can connect to the Internet. For instance, MRI and CT scan. The
scanner will scan the devices and send the data to remote locations through 6G
technology as depicted in Figure 1. These data can be analyzed by a
pathologist in real-time. Almost all medical things will be able to connect to
the Internet and instant decision can be taken. Therefore, IIoMT will be able
to overcome the barrier of time, space and money. Another example, cancer
patients can easily be treated by remote doctors. Currently, it takes time to
detect whether the cancer patients having benign or malignant. However, cancer
can be detected in real time in the near future using 6G communication
technology. Also, the doctors and patients do not have to visit specialist
hospitals. It takes time and money. Therefore, remote doctors will treat the
cancer patients in collaboration with local doctors. Early detection of cancer
patients can reduce the mortality rate to nearly zero. However, such sensors
need to be invented. This scenario not only applies to cancer, but also
applies to many diseases. For instance, cardiovascular treatments.

###  VII-A Blood Sample Reader

Blood is vital for the human body and most of the diseases can be detected
from blood. Conventional blood sampling requires needles to inject to sample
the blood from the human body. However, numerous research is being conducted
for needle-free blood sampling devices. For instance, Lipani et. al. devices
new needle-free method for glucose monitoring for diabetic patients [41].
Blood Sample Reader (BSR) sensors will be needle-free intelligent wearable
device. The BSR sensors will revolutionize the health industry. BSR will
correctly read every parameters of blood, for instance, WBC, RBC, etc. This
BSR sensor will remain connected to the 6G Internet. A blood sample will be
transmitted to a testing center for test results periodically, automatically
or with permission from the patient. Hence, no manual intervention will be
required for testing Blood sample. This device will play vital role in
intensive care on elderly service and monitoring. Moreover, COVID-19 outbreak
could be easily stopped using BSR sensors. With the number of cases crossing
millions, countries are running out of medical gears. Taking the blood sample
using needle exposes the medical staff to the disease. This BSR sensor can
easily track the spread of COVID-19 virus in real-time. Thus, it will be a
huge help during Epidemic and Pandemic. Therefore, BSR sensor will be the most
demanded medical devices in the future.

###  VII-B Intelligent Wearable Devices

Intelligent Wearable Devices (IWD) are connected to the Internet and transmit
psychological and physical data to test centers and monitoring centers. This
devices will monitor heartbeat, blood pressure, blood tests, health
conditions, body weight and nutrition. The test result will be received
quickly. Also, IWD learn from the personal body history and advise the person
for the next action, for instance, advising for walk or running. IWD will
maintain a personal history of health, nutrition, and habits. Thus, IWD can
advise what to eat in case of any deficiency. Detection of minor body issues
such as deficiency will reduce the frequency of hospital visit. So, it will
reduce hospital bill and hospital can focus on more complex diseases. In
addition, IWD will read blood sample and the blood sample will be transmitted
to pathological results. Thus, early detection of cancer can be possible using
IWD. Therefore, IWD can improve health conditions and increase human life
span. Also, it is vital in elderly services because elderly service requires
intensive cares. Future IWD will combine multiple features in a single device.
All features will be packed into a single device. The initial release of such
devices will be expensive, however, over a time period cost will decrease and
the common people can afford.

##  VIII Hospital-to-Home Services

Currently, the ambulance services are just a transporter of patients with
oxygen and road traffic priority. It does not serve the purpose of emergency
service due to absence of intelligence. Therefore, the ambulance services are
not impacting on our lives. Any normal car can also solve the same purposes if
we keep oxygen and emergency signal. Therefore, a new kind of ambulance
service is required to improve lifestyle.

To replace ambulance services, the Hospital-to-Home (H2H) services will be
emerging. Due to the advent of communication technology, hospital can reach to
home on demand and in an emergency situation. The future vehicles will be
fully AI-driven to make intelligent vehicles [42]. Therefore, H2H will be
implemented upon mobile hospital on an intelligent vehicle platform that will
have a minimum dependence on hospitals including doctors and nurses. This
mobile hospital will replace ambulance services. For instance, mobile hospital
detects an accidents in real-time and reaches the spot. Then, the mobile
hospital will start treating the patients before reaching the hospitals.
Moreover, mobile hospital can detect any emergency situation in real-time and
reach the spot to save lives. It will also enhance modern lifestyles.
Specially, it is immensely necessary in elderly services. Thus, 6G
communication revolutionizes modern lifestyle through the H2H services.

##  IX Telesurgery

The telesurgery is emerging and it is a concept for the future. It is defined
as remote surgery by the doctor(s) [43]. Telesurgery requires robots, nurses
and mediator of remote doctors. Communication plays a key role in telesurgery.
Also, it requires a very high data rate and URLLC. 5G and B5G are unable to
provide these requirements. Hence, telesurgery requires the support of 6G
technology. Moreover, the success of telesurgery requires real-time
communication. For telesurgery, the doctor can provide guidance through
verbal, telestration or tele-assist [44]. Due to 6G, more interactive verbal
guidance can be provided using holographic communication. In holographic
communication, the doctor can be present in the surgery for guidance and also
can also move to have a better visual of the surgery area. Telestration is
showing the surgery procedure remotely, for instance using video. In
intelligent healthcare, AR and VR can be used for telestration. In addition,
the doctor(s) can tele-assist the surgery using tactile/haptic technology. The
requirements of telesurgery can be fulfilled by 6G communication technology
and 6G will prove that surgery can be perform beyond boundaries.

##  X Epidemic and Pandemic

Communication technology will play a vital role in epidemic and pandemic.
Mostly, epidemic and pandemic are human to human transmission disease.
Therefore, medical staffs are at high risk and often termed as “suicide
squad”. Recently, COVID-19 has taken thousands of lives, including the medical
staffs. COVID-19 outbreaks could easily be stopped using IIoMT. For instance,
blood sample of each person is transmitted to testing center using BSR sensor
without exposing themselves to the outer worlds and the result will be
received at their own home. A blood sample will be taken by intelligent
wearable technology (BSR sensor) and transmit the sample data to the test
centers. Thus, human chain can easily be stopped and the outbreak can be
tracked in real-time. Now, millions of COVID-19 positives have been detected
and billion of testing has to be conducted. This global tragedy demands
intelligent healthcare systems and IWD.

##  XI Precision medicine

Precision medicine is developing a customized medicine or treatment for
providing better treatment to a patient [45]. For the development of precision
medicine the doctors/researchers conduct research by grouping the people based
on some common parameter. 6G technology can greatly help in the development of
precision medicine. Also, it requires AI to provide personalized healthcare
[46]. Better development of treatment requires health data of the clinical
trial people. For instance, cell therapy research is carried out for critical
disease treatment [47, 48]. The doctors and researchers can collect the data
using IWD. This data will be collected in real-time which helps in providing
accurate health data. Moreover, the research can be conducted globally.
Geographical condition influence a person’s immunity system. Hence, moving the
people under observation to a single location will change their environment.
And, this will influence the research. Therefore, through IIoMT the
doctor/researcher will observe the people under observation across the globe.

##  XII New Business Model

6G will revolutionize businesses, and thus, the old business model of the
hospital need to be redefined. Currently, the treatment expenses are paid
directly to the hospital by the patient or by the health insurance policy. The
health insurance policy is operated by a company. The company forms a network
of hospitals. This hospitals allows cashless treatment and incurred money is
charged from the company. Most of the insurances do not cover many diseases
and elderly health services. This business model defines the hospital and
insurance as a different entity during treatment and payment is to be made to
the hospital. The insurance company will pay the incurred money to the
hospital. Excessive amount needs to be paid by the patients. Therefore, health
insurance and hospital services are very unsatisfactory and they do not insure
our lives. In true sense, neither hospital nor insurance company is
responsible for our treatment from the date of birth to death.

To that end, we envision a new business policy for modern healthcare systems.
It is expected that new business model will remove health insurance companies
and the hospitals will plays the role of the health insurance companies. We
term it as Health Insurance at Hospital (HIH). HIH will form a network of
hospitals, and remove mediator (health insurance company). HIH has to take
care of geographical locations while forming network of hospitals. Yearly or
monthly premium of insurance will be directly paid to the hospital. The
hospital will function using the insurance money. The hospital will take care
of a person’s health from birth to death. A patient can call H2H service to
reach the hospital. The hospital will verify the HIH identification, and then
the patient will be admitted to any partner hospital. The patient will be
treated with priority. After getting discharged from the hospital, the patient
does not have to pay any medical bill. Also, this policy will cover QoL
including IWD connection and monitoring, H2H services, telesurgery, surgery,
pregnancy and delivery, vaccines, ICU services, NICU services, elderly
services, personalization and precision medicines. HIH includes all types of
diseases and accidents, including cancer, flu, cardiovascular, neurological
problems, etc. There will be no bar in number of treatments for a patient.
Also, the policy will cover OPD and all other medical expenses, including
pathological and medicine expenses, that is, no bill, no claim and hassle free
treatment.

##  XIII Security, Secrecy and Privacy

The key focus of 6G technology is security, secrecy and privacy [7].
Therefore, 6G requires secure URLLC (sURLLC) to have an enhanced secure
communication. 6G communication technology promises the highest level of
security. It will defend the attacks using federated AI, Quantum Machine
Learning, Quantum Computing and THz communication. THz communication is
eavesdropping and jamming proof [5]. Healthcare requires a high level of
security for data transmission over the network. Any alteration of health data
can kill a patient. Therefore, it is crucial to protect health data from
attackers. Moreover, 6G communication technology also focuses on secrecy of
the most sensitive data. Sensitive data are protected from anyone excepts
owner of the data. Also, administrators are not permitted to view these
sensitive data. For instance, family history. In addition, 6G also focuses on
privacy which is crucial parameters of healthcare. To increase privacy, 6G
will also rely on Edge technology. The Edge nodes are located closer to smart
devices. The computed data are also analyzed in the same Edge nodes. Edge
nodes have small memory, hence, all data are not concentrated in one location.
Therefore, Edge maintains the privacy of the user. Another important point is
filtering of data by Edge nodes. Edge nodes filter the data and transmit only
important information to the Cloud. It also leads to storage of less
information about the user in the Cloud. Thus, it is easier for Cloud to
provide security for lesser data. In the current scenario, Blockchain provides
a high degree of privacy for health data [49]. It provides a secure
infrastructure for handling the health data [50]. In the future, Blockchain
with more advanced techniques will be very helpful in intelligent halthcare.

##  XIV Conclusion

Intelligent healthcare must enhance QoL. Precisely, intelligent healthcare
comprised of IIoMT, IWD, H2H and HIH. All IIoMT requires high quality mobile
communication, AI integration, and support from Edge computing and Cloud
Computing. A key IIoMT is BSR sensors. BSR sensors are yet to be devised. BSR
will be able to solve many issues in healthcare. Thus, BSR sensor needs
extreme attention from the research community. Also, another prominent IIoMT
is IWD. IWD will be a revolutionary technology for healthcare and it will be
equipped with many sensors including BSR. It will help in diagnosis of many
diseases automatically and improve drastically the health of a person. Also, a
person does not require to visit hospital for regular check up, for instance,
blood test, blood pressure, sugar level, etc. IWD sends the personal health
data periodically to the health monitoring center for detection of any kind of
abnormality. Also, an elderly person can be monitored without intervention of
medical staffs. Elderly service requires intensive care, and the integration
of IWD with the healthcare system will automatically take care of the person
without intervention of medical staffs. In addition, IWD will learn personal
medical history, food habit, body structure, environmental pollution level,
and any other abnormality.

Current ambulance service is just a transporter of patients with limited
medical kits. This service should be replaced by H2H services. H2H service
will be able to save billion of lives, and thus, it requires immediate
implementation on intelligent vehicle. In addition, the mortality rate of
accident can be reduced using H2H service. Moreover, intelligent healthcare
requires a new business policy for the hospital. Currently, health insurance
and direct payment are the business model of hospitals. The health insurance
covers only selective diseases which excludes many diseases such as COVID-19,
Ebola virus, pregnancy and delivery. The HIH business model will be truly
hassle-free treatment without any expenses. But, an intensive research is
required for the success of the HIH business model. However, the premium may
rise for HIH due to the coverage of every expense related to a person’s
treatment.

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|  Sabuzima Nayak<EMAIL_ADDRESS>is a research scholar in the
Department of Computer Science & Engineering, National Institute of Technology
Silchar, Assam-788010, India. Her research interest is Bioinformatics, Bloom
Filter, Communication and Networking, and Big Data. She has published numerous
papers in reputed journal, conferences and books.
---|---
|  Ripon Patgiri<EMAIL_ADDRESS><EMAIL_ADDRESS>is currently working
as Assistant Professor in the Department of Computer Science & Engineering,
National Institute of Technology Silchar, Assam-788010, India. His research
interests are Bloom Filter, Communication and Networks, Big Data, and File
System. He has published numerous papers in reputed journal, conferences and
books. He is a senior member of IEEE and member of ACM, EAI, and IETE He has
also chaired many conferences.
---|---