This section is the deliberation of the detailed explanation of proposed mechanism. In this model, M-tier that consists of (Macro cell, Pico cell, and Femto cell) HetNet environment is being formulated in the 3-Dimesional manner for analyzing the dense small cell network deployment scenario. Therefore, for enhancing the energy efficiency, reducing the interference and to enhance the 3D HetNets capacity, the adaptive multi-stream carrier aggregation is being proposed in the 3D HetNets environment. The overall flow of the proposed system is shown below:

*A. System model*

A model of 3-D cellular network is considered which deploys femtocells, Picocells having maximum densities λpc and λfc correspondingly. Regarding a minimum distance (dmin) among two cells respectively, these small cells were distributed as per the density is expressed as follows:

$$\lambda =\frac{1-\text{e}\text{x}\text{p}(-({\lambda }_{pc}+{\lambda }_{fc})\frac{4}{3}\pi {d}_{min}^{3}}{\frac{4}{3}\pi {d}_{min}^{3}}$$

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According to the location of some independent processes of stationary point, the collection of independent mobile user was considered at which the mobile user is taken into consideration at which each mobile user in turn communicates with the neighboring small cells. The model of network must be include Main BS (eNodeB), Each cells Base station like Macro (MBs), pico(PBs), femto(FBs), Mobile users(MU), available users, micro(mBs), and etc.,. The entire cell’s location is independent. This approach is denoted as 4-Tier HetNet network environment as it uses four small cells like Pico, femto, macro, and micro. For ease, both antennas of receiving and transmission are considered as omni directional and targeted mobile user(u) is situated at the coordinate’s origin. The random variable in meters, a distance, among the target cell (co) transmitter and u is signified by means of r. Therefore, depending on the mmWave bands inclusion, the model of general path loss expression is provided by the following expression:

$$\text{P}\text{L}\left(\text{r}\right)=\text{n}\left(10\alpha {log}_{10}\left(\frac{r}{{r}_{0}}\right)\right)+PL\left({r}_{0}\right)+{X}_{\sigma }$$

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At which, α is regarded as the loss exponent path, n is the correction factor of mean slope (unitless) which is attained directly from empirical outcomes, and the free space path loss in dB is denoted by PL(r0) at a close-in reference r0distance.

$$PL\left({r}_{0}\right)=20{log}_{10}\left(\frac{4\pi {r}_{0}}{v}\right)$$

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where, c(= 3 108 m/s) is the light celerity, ν =(c/f) is regarded as the wavelength of carriers in meters, typical lognormal random shadowing variable is denoted by Xσ with mean0 dB, and carrier-frequency is signified by f, and σ is the standard deviation and is (8.2 < σ < 10.6) [dB].

Accordingly, depending on above equations (2–3), the signal attenuation value owing to the path loss could be signified by:

K r− nα (4)

here, coefficient K is specified as

$$k=\frac{{r}_{0}^{n\alpha }}{{10}^{\frac{PL\left({r}_{0}\right)+x\sigma }{10}}}$$

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The relationship among u and co, u, and cell i, i∈ Φ\{co}), in turn involves independent Rayleigh fading by means of the gi∼ CN (0, Ωg), and h ∼ CN (0, Ωh)complex channel fading gains, correspondingly. Therefore, the amplitudes formed of the channel gains entirely sustain the exponential distribution having the unit variances assumptions, for eg., Ωh = Ωg = 1. It is assumed that the additive white Gaussian noise (AWGN) with zero mean and \({ \sigma }_{n}^{2}\)the power spectral density. Typical receiver’s, total interference power (Ir) is the sum of power received that comes from the entire small cells except from their home station, at which the small and macro-BSs are assumed to utilize the similar frequency bands in a simultaneous manner.

Depending on this system model, SINR associated at u is articulated by

$$SINR=\frac{{P}_{t}HK{r}^{-\left(n\alpha \right)}}{{I}_{r}+{\sigma }_{n}^{2}}$$

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here, H =||h||2,

$${I}_{r}=\sum _{i\in \varnothing \backslash \left\{{C}_{0}\right\}}q {p}_{i}{G}_{i}K{l}_{i}^{-\left(n\alpha \right)}$$

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Gi = ||gi||2, li is the distance among transmitter of cell i and the target user u, the transmit power of cell i is denoted by Pi and is with the transmission probability of q. this power could be the power of transmit in Picocells, and is denoted by means of Ppc, or else the femtocells transmit power, that is denoted as Pfc.

In this, all mobile user in turn communicates with the neighbor small cells. The entire femtocells and Picocells are independent. An effective dense small cells deployment was presented in the heterogeneous cellular networks. Depending on the adaptive poisson cluster process the system model is being designed. The Cross-tier interference should be avoided from the femto cells and Co-channel interference from macro base stations.

*B. Deployment of base station*

With respect to the BS’s energy consumption, let us consider that each BS b consists of a set of CCs Sb. From this, the notation CCj,k is utilized for denoting CC ‘K’ of BS ‘j’. The model of energy consumption is considered for the active CCj,k throughout ∆t time interval as:

$$Eˆtotal(CCj,k) = \varDelta t [Pˆon,min(CCj,k) + Pˆon,dyn(CCj,k\left)\right]$$

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Here, Eˆ total (CCj,k) signifies the consumption of total energy of the CCj,k, the power consumed amount is signified by Pˆon,min (CCj,k) irrespective of the handled traffic through CCj,k, and the consumption of dynamic power of CCj,k is represented by Pˆon,dyn(CCj,k), that varies as per the dynamics of traffic. As Pˆon,min(CCj,k) is the constant corresponding to the handled traffic by CC, which could be excluded from remaining analysis. The linear function of RF output power is considered as Pˆon,dyn(CCj,k) that is needed for satisfying the requirements of QoS as requested by UEs that is connected to CC as such carried out in traditional process. Therefore, this could be expressed as:

Pˆon,dyn(CCj,k) = wj,k\(\sum _{i}{p}_{i,j,k}\) (9)

At which, Pi,j,k signifies the RF output power amount that is needed by CCj,k for satisfying the QoS that is requested by UE I and the constant wj,k is unique for each CCj,k. Rather than the value of wj,k, the value of Pˆon,min(CCj,k) is based on the internal components that is associated by CC operation with their interconnection.

*C. Adaptive Multi-Stream Carrier Aggregation*

The carrier aggregations CA’s are the next generation’s two distinct features of cellular network models. The 2-D model which is not appropriate for the dense urban environments, region of high rise as the vertical node component distributions are not be considered. So as to reduce the cross-tier interference and enhance the HetNets capacity, the adaptive multi-stream carrier aggregation is being applicable for HetNets. A model of Heterogeneous 3-D cellular Network (that consists of Microcell, Picocell, Femtocell and Macrocell) were exhibited for the manipulation of AMCA. The similar frequency resource was shared by PBSs along with the macrocells that leads to interference seriously. For reducing the rate of interference and to enhance the 3D HetNets capacity, the multi stream carrier aggregation is presented to 3-D HetNets. The cross-tier interference in the HetNets could be eradicated by means of scheduling various CCs intended for Pico-cell users (PUs) and Macro-cell user (MUs) correspondingly. The presented method aids in enhancing the of mobile base station’s (enodeB) EE.

The proposed network model performance could be analyzed by mean of computing several performance metrics. As mostly, semi-analytic expressions were derived intended for the ergodic channel capacity and the symbol error rate (SER), which enumerates the energy efficiency and reliability of IoT dependent model of HetNet with the service of AMCA.

Let us consider one 4G-LTE cell of mobile system which could be any of those NBS LTE Advanced BS with LUE UEs/mobiles and their two carriers. One such carrier is regarded as the LTE advanced carrier and another one is regarded as the MIMO radar carrier which is considered as the secondary carrier.

Each UE consists of their specified utility function Ui(ri) which corresponds to the running application on UE. It is assumed that the function of utility that is assigned to ith user is regarded as a strictly concave utility function one once the user is running in the application of delay-tolerant or sigmoidal means of utility function. Those utility functions have the corresponding properties:

Ui(0) = 0 and Ui(ri) is the enhancing function of ri.

Ui(ri) is differentiable twice continuously in ri and the above bounded one.

The sigmoidal-like normal utility function employed in this model is the similar one as employed in traditional method and is expressed as shown:

$$\text{U}\text{i}\left(\text{r}\text{i}\right)={c}_{i}\left(\frac{1}{1+{e}^{-{a}_{i}({r}_{i}-{b}_{i})}}-{d}_{i}\right)$$

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Here, \({c}_{i}=\frac{1+{e}^{{a}_{i}{b}_{i}}}{{e}^{{a}_{i}{b}_{i}}}\)and \({d}_{i}=\frac{1}{1+{e}^{{a}_{i}{b}_{i}}}\), this in turn makes it satisfy U(0)=0 and U(∞)=1. The normalized sigmoidal utility function inflection point is at the \({r}_{i}^{inf}={b}_{i}\). Moreover, the normalized logarithmic utility function employed could be expressed as:

$$\text{U}\text{i}\left(\text{r}\text{i}\right) =\frac{\text{l}\text{o}\text{g}(1 + {k}_{i}{r}_{i}) }{\text{l}\text{o}\text{g}(1 + {k}_{i}{r}_{max})}$$

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Here, rmaxis signified as the maximum rate needed for user for attaining 100% utilization and a constant is ki which alters from user to user. Therefore, this satisfies U (0) = 0 and U(rmax) = 1. The allocation of first resource optimization issue is regarded as the primary carrier i.e., the advanced LTE carrier optimization. The utility proportional fairness scheme is employed for allocating the primary carriers’ resources for guarantying that none other user is allocated as the zero resources.

The primary carrier’s optimization problem is expressed as follows:

$$\begin{array}{cc}\begin{array}{c}max\\ {r}_{radar}\end{array}& \prod _{i=1}^{{L}^{UE}}{U}_{i}({r}_{i,radar}+{r}_{i, LTE}^{opt}\end{array}$$

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Which is subjected to

$$\sum _{i=1}^{{L}^{UE}}{r}_{i,radar}\le {R}_{radar}$$

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0 ≤ ri,radar ≤ Rradar, i = 1, 2, ..., LUE

Here, rradar={\({r}_{1,radar}, {r}_{2,radar},\dots ,{r}_{{L}_{UE, radar}}\}\) and LUE is the UEs number in the total coverage area, R radar is denoted as the maximum attainable rate of \({r}_{i, LTE}^{opt}\) for each user and this in turn provides priority for the users that runs in the real-time application.

The aggregated rate of final optimal ri,agg for ith user is being attained by the optimization problem solution sum. The \({r}_{i, LTE}^{opt}\)can be expressed and written as \({r}_{i, agg}^{opt}={r}_{i, radar}^{opt}+{r}_{i, LTE}^{opt}\) so that, the \({ r}_{i, agg}^{opt}\) is regarded as the final solution that is optimum and gives each user LUE users the rate of optimal solutions from both MIMO radar carriers and LTE advanced carriers.

**Algorithm 1: **Algorithm of Adaptive Multi-stream carrier Aggregation

**Initial stage of the algorithm**

**Step 1: **Initially, UEs and the primary carriers collaborate for the allocation of optimum rate of each UE.

**Step 2: **The algorithm’s first stage initiates with once the UE transmits the initial bid wi,LTE for the LTE advanced eNodeB. This eNodeB in turn checks the variation among received current bid and the older one, in case it is less than the threshold value of € it exists. Or else, in case the variation is higher than threshold €, the price of shadow is then computed by LTE advanced eNodeB.

**Step 3: **The price of shadow signifies the total price per unit bandwidth rate for the entire users. This in turn depends on users bids and the available eNodeB resources.

**Step 4: **The advanced LTE eNodeB in turn transmits the computed PLTE (n) for each UE at which this is employed for computing rate ri,LTE (n) which is regraded as the solution for the optimization problem

$${r}_{i,LTE}\left(n\right)=\text{arg}\begin{array}{c}max\\ {r}_{i,LTE}\end{array}\left(log{U}_{i}\left({r}_{i,LTE}\right)-{P}_{LTE}\left(\text{n}\right){r}_{i,LTE}\right)$$

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**Step 5: **The computed rate is employed then for estimating the new bid wi,LTE(n) for the LTE eNodeB.

**Step 6: **Once the first stage is being finalized, then UE in turn computes their rate allocated .

**Step 7: **Once the allocation rate is made, the LTE carrier begins to perform the second stage of the algorithm

**Second stage of the algorithm**:

**Step1: **To each UE communicates their initial bids wi,radar for the MIMO eNodeB radar.

**Step2: **This eNodeB radar in turn examines the variance among the received current bid and the old one once it is decreased than the value of threshold it exists.

**Step3: **Moreover, once the variance is higher than eNodeB MIMO radar which computes the price of shadow by Pradar(n)=

**Step 4: **The eNodeB radar in turn transmits the computed is then computed Pradar(n) by to the UEs.

**Step 5: **The rate LTE advanced eNodeB. The price of shadow in turn signifies the is computed by each UE which is the optimization problem solution

$${r}_{i,radar}\left(n\right)=\text{arg}\begin{array}{c}max\\ {r}_{i,radar}\end{array}\left(log{U}_{i}\left({r}_{i,radar}+{r}_{i, LTE}^{opt}\right)-{P}_{radar}\left(\text{n}\right){r}_{i,radar}\right)$$ 15

**Step 6: **The new bid wi,radar (n) is then computed by means of ri,radar(n), at which wi,radar(n) = Pradar(n)ri,radar(n).

**Step 7: **The entire UEs in turn analyze the condition of fluctuation and in turn send their new bid wi,radar(n) to the eNodeB radar.

**Step 8: **The algorithm’s second stage is then finalized by radar eNodeB. The allocated rate is then computed by each UEs by then UE in turn computes their rate allocated by means of eNodeB radar.

**Step 9: **the rate of final global optimum is being allocated for every UEs.

The Adaptive Multi-stream carrier Aggregation in different scenarios is depicted below:

(a) Scenario A:

Scenario ‘A’ covers two symmetric non-continuous CCs at 30 MHz of AMCA as depicted in figure provided below. Each CC consists of bandwidth of about 10 MHz that is signified as the symmetric AMCA. The primary CC consists of the center frequency at 15 MHz and the next or second CC consist of center frequency at 36 MHz. therefore, the center frequency spacing is about 21 MHz that realizes the multiples of 300 KHz.

(b) Scenario B:

Scenario ‘B’ offers two CCs Asymmetric non-continuous 60 MHz AMCA as depicted in figure. The initial CC consists of 10MHz bandwidth at 15 MHz center frequency. Whereas, another CC comprise bandwidth of about 20 MHz having60 MHz center frequency. Accordingly, the spacing of center frequency is about 45 MHz. This employed AMCA is signified as AMCA that are Asymmetric.

(c) Scenario C:

So as to enhance the system throughput, scenario C offers60 MHz AMCA of intra-band Asymmetric non-continuous through employing three CCs as revealed in figure given below. The primary two CCs take bandwidths of about 10 MHz having center frequency spacing of about 15 MHz. The 3rd CC with bandwidth of 20 MHz has 60 MHz center frequency.

(d) Scenario D:

The figure provided below depicts the 100MHz AMCA LTE-A bandwidth spectrum having four CCs, each consist of bandwidth of about 20 MHz. the first CC center frequency is at the 20 MHz, with second CC at 45 MHz, the third one at 74 MHz and the final or fourth one at 101 MHz.

(e) Scenario E:

The 100 MHz AMCA LTE-A bandwidth spectrum with five asymmetric CCs is represented in figure provided below. In this, all four CCs have 20MHz bandwidth and the fifth one having 10MHz bandwidth. The first CC center frequency is at 20 MHz, second CC at the 42 MHz, and third CC at the 63 MHz, fourth one at 87 MHz, and the final one at 105MHz. the spacing of center frequency among CC’s in turn satisfies the needed multiples of 300 KHz.

Therefore, the simulation outcomes attained by the requirements of LTE-A on employing five CCs extended the band of LTE to about 100 MHz. This approach can be applicable for m-Health IoT environment for transmitting and storing the data in IoT framework for further usage in healthcare application.