## 1. Introduction

An exponential increase in mobile phone users and the inclusion of smart gadgets in daily-life affairs has overburdened the cellular networks. Quality-of-service, high data rate, energy efficiency, remote connectivity, and increased network capacity at affordable costs are the major requirements of future networks. The wireless communication technology has significantly changed the methods of information interchange. The use of satellites has provided liberty with wireless access to remote locations. Additionally, Wi-Fi-based Local Area Networks (LANs) and UMTS2, GSM1, and LTE3 based cellular Wide Area Networks (WANs) improved this area in all demanded aspects. Recently, wireless connectivity has been accepted as a basic necessity of society because of an exponential increase in services and applications. According to Martin cooper’s law [

1], the number of connections (both data and voice) doubled every 2.5 years. Moreover, Ericsson Mobility verifies a composite 12-monthly growth rate of 42% in transportable data traffic from 2016–2022 [

2] that is even quicker than the prediction made in [

1]. An imperative query for researchers is, how does one develop existing and/or new technologies to meet the increasing requirements, and thus evade the crisis of data traffic? The end-users expect wireless connectivity services at any place and at any time. The pervasive connectivity and exponential traffic growth urge the researchers to plan groundbreaking wireless technologies.

This paper provides an examination of massive MIMO technology to validate how and why it is a proficient solution to knob extra data traffic than existing wireless technology. The prominent aim of this work is to select appropriate values of

B,

D, and

$\phantom{\rule{3.33333pt}{0ex}}SE$ to optimize the area throughput with 1000x as shown in

Figure 1. A realistic method is to examine an appropriate value of SE that can be used together with increasing D and B to realize 1000x goal. Mobile networks were initially intended for voice communications; however, currently, data transmission has dominated [

3,

4]. Furthermore, video streaming is considered to be a key driver of the forecasted rise in data traffic demand [

5]. The area throughput is thus an extremely related performance parameter of modern wireless networks that is measured in bits/s/km

${}^{2}$ and modeled as Equation (

1).

The SE can be further defined as “total information transferred in one second by using 1 Hz bandwidth”. In (

1), parameters

$D,B,$ and

$SE$ are three key parameters to optimize the area throughput in a massive MIMO technology for future networks. In coverage prospects, a wireless network can be divided into two tiers described in

Figure 2 the coverage tier and hotspot tier. The definition of area throughput can be considered a principle for both tiers. The area throughput can be considered to be a volume of a rectangular container with coordinates of

$D,B,$ and

$SE$ [

6].

The parameters shown in

Figure 1 are dependent on each other as choosing cell density and frequency band influences broadcast environments. All three parameters can be treated independently for the 1st order approximation. This query can be settled by increasing bandwidth up to 1000-fold. Existing networks use approximately 1 GHz bandwidth i.e., in Sweden, mobile phone operators can use a 1 GHz spectrum, while approximately 650 MHz in the United States with a supplementary 500 MHz available for Wi-Fi [

7,

8]. A network intended with 1000-fold improvement would approximately use 1 THz that is unrealistic. Additionally, the frequency spectrum is a global resource used for different services, and it needs higher frequency bands that physically restrict the service range reliability.

The second option would be the densification of the network by deploying 1000x BS/km

${}^{2}$. In existing deployment scenarios, the distance between BSs is a few 100 m in the coverage tier, in which BSs are positioned at raising sites to circumvent from shadowing of huge buildings and objects. The scenario provided in

Figure 2 gives an illustration of the hotspot tier and coverage tier. It confines several sites for the deployment of BSs in coverage tier. Additionally, BS densification would be challenging unless the BSs are moved closer to User Equipment (UEs) that increases the risk of deep shadowing, in that way plummeting the coverage. However, the deployment of extra hotspots is comparatively a more feasible solution. The distance between BSs (in hotspot tier) can surely be reduced to a few meters in future network deployments. Even underneath much densification in hotspot tier, coverage tier still needs to duck coverage holes and provide mobility support. The technique for area throughput optimization is to optimize SE in future mobile networks. It is predominantly significant for BSs that can neither depend upon network densification nor uses mm-Wave band.

Furthermore, optimization of SE corresponds to use bandwidth and BSs, which are efficiently placed by using new multiplexing and modulation methods. Modulation and channel coding play a crucial part in the physical layer to enhance SE. Essentially, higher SE can be attained by implementing a higher-order modulation scheme and low-code rate with high SNR. In [

9], the authors have developed a novel approach to improve bit-error-rate (BER) performance of iterative detection and decoding (IDD) schemes by using a Low-Density Parity Check (LDPC) codes. Recently, a novel family of protograph LDPC codes also called Root-Protograph (RP-LDPC) codes are used in [

10]. The presented codes can realize highspeed decoding and encoding by quasi-cyclic structure. It can also achieve near-outage-limit performance in Block-Fading (BF) set-ups [

11,

12].

Last but not least, another aspect of SE augmentation in massive MIMO systems and antenna array elements is a mutual coupling. If mutual coupling increases it drastically affects the antenna characteristics by degrading the system’s performance [

13]. A lot of existing works presented novel way outs of reducing mutual coupling specifically, patch antennas using UC-EBG superstrate [

14], closely spaced microstrip MIMO antennas [

15,

16], mutual coupling in closed packed antennas [

17], and micro coupling in planner antennas by using a Simple Microstrip U-Section [

18]. The mutual coupling between closely packed antennas rises either by the large flow of surface current from the exciting ports or space radiation and surface waves. Additionally, the opposing effect of mutual coupling on reflection coefficients cannot be undervalued [

19]. Hence, limiting the mutual coupling is a challenging task within the recent miniaturized printed and other antennas in designing of massive MIMO antenna systems. In digital MIMO infrastructure, the higher mutual coupling effects error rate and channel capacity. An extensive range of coded modulation schemes is proposed to decrease this effect, such as partial swam optimization, genetic algorithms, and galaxy-based search algorithms.

#### Preliminaries

The 1000x area throughput is accomplished without using mm-Wave spectrum and/or any extensive densification since it would unavoidably result as a patchy in the coverage tier. To avoid pitchy coverage, improved SE is desired. In this work, we have established an argument that the massive MIMO is capable of providing enhanced SE. Contrarily, the hotspot tier reduces burden of coverage tier by unburdening a huge share of traffic from low mobility user equipment. Subsequently, hotspot tier has been boosted with cell-densification and by hefty bandwidth accessible in mm-Wave. The Shannon proposition of sampling infers that ‘the band-limited data communication signal transmitted through a channel with bandwidth ‘B’ can be completely recovered by ‘2B’ equal spaced and real value samples/s [

11] While considering the complex baseband signal, B complex-valued samples/s is in natural quantity [

12]. These samples are the degrees of freedom (DoF) offered to construct a communication signal. The SE is amount of information transferred reliably per complex-valued sample. For a fading channel between UE and BS, SE is the number of information bits transmitted reliably over communication channel measured as bits/s/Hz. Moreover, an information rate is the product of SE and B which is another associated metric measured in bit/s. For all channels from UEs to their particular BS in a cell, sum SE is measured in bit/s/Hz/cell. The channel between a

$Tx$ and

$Rx$ at specified locations can serve several UEs with respect to the used encoding and decoding scheme. According to Shannon’s channel capacity [

20,

21,

22], the max. SE can be calculated by channel capacity that is demonstrated in Equation (

2). Suppose, a communication channel with input and output are represented by random variables a and b, respectively. The channel capacity (C) can be calculated as Equation (

2) by taking the supremum concerning all possible

$f\left(x\right)$ input distributions.

whereas the

$H\left(b\right)$ and

$H(b\parallel a)$ represents the differential and conditional-differential entropies of the

b given the

a. The channel capacity in Equation (

2) can be calculated as in Equation (

3) [

11].

where

$n={N}_{c}$$(0,{\sigma}^{2})$ is independent noise,

$\mathbb{E}\left\{{\left|a\right|}^{2}\right\}\le p$ gives the power-limited input distribution and the

x describes the channel response

$\left(x\in C\right)$ that is a known value. The ergodic channel capacity can be attained as Equation (

3) by input

$a\sim {N}_{C}(0,p)$.

In Equation (

3),

$p{\left|x\right|}^{2}/{\sigma}^{2}$ is an actual compute-able SNR for a channel response

$\left(x\right)$, where it is an instantaneous SNR for a specified channel realization with random value of channel response. From Equation (

3), the average SNR has been defined as

$p\mathbb{E}{\left|x\right|}^{2}/{\sigma}^{2}$ while

$\mathbb{E}{\left|x\right|}^{2}$ is an average channel gain and expectation has been calculated according to the channel realizations. In wireless networks, the information signals tainted by interference occurred in the same and other cells. This interference is modeled at the output of a memory-less channel. The interference is reliant on input and channel response and it is challenging to realize the precise channel capacity of interference channels; however, expedient lower-bounds are calculated. By using [

23,

24,

25,

26], the lower-bound capacity of a channel with input and output calculated as Equation (

4).

If

x is deterministic and the interference

y has mean equals to zero, a known value of variance

${p}_{y}\in {\mathbb{R}}_{+}$ and uncorrelated input (i.e.,

$\mathbb{E}\{a\ast y\}=0$), in this way the lower-bounded channel capacity can be calculated as Equation (

4)

while the bound is realized employing

$a={N}_{C}(0,p)$. Suppose

x as an alternative is a realization of a random variable and that is random variable by

r’ the realization that disturbs the interference variance. If

n is independent of

y given

x and

r, mean equals to

$\mathbb{E}\left\{y|x,r=0\right\}$ and variance is

${p}_{y}\left(x,r\right)=\mathbb{E}\left\{{\left|y\right|}^{2}|x,v\right\}$. Hence, the interference is uncorrelated with the given input

$\left(\mathrm{i}.\mathrm{e}.,\phantom{\rule{4.pt}{0ex}}\mathbb{E}\{a\ast y|x,r\}=0\right)$ and lower-bound ergodic capacity can be determined as Equation (

5)

The capacity attained in Equation (

5) is accomplished by less complex signal processing at the receiver, in which the interference is considered to be noise. Moreover, the Signal to Interference Noise Ratio (SINR) can be given as Equation (

6)

## 3. Results And Discussion

This section provides the details of the simulation setup and results of previously discussed methods to increase SE. We have considered a 2-cell scenario for simulation to keep it simple, in which the typical channel gain between every UE and BS is identical in each cell. Moreover, Monte Carlo realizations of the Rayleigh fading has been considered.

Table 2 provides the list of simulation parameters.

Figure 6 shows the results for LoS and NLoS signal arrival in which, the spectral efficiency has been plotted against the increasing values of signal to noise ratio. According to the plot, the SNR is taken as a transmit power

p. In the simulation, the interference among cells have been represented by

$\overline{g}\in \left[-10,-20,-30,-40\phantom{\rule{4.pt}{0ex}}\mathrm{dB}\right]$. In

Figure 6a,b, SE for both LoS and NLoS is calculated against the SNR as modeled in

Section 3.

Figure 6a illustrates the results for LoS at interference of

$-10$ dBs, 20 dBs,

$-30$ dBs and

$-40$ dBs. The SE approaches to its maximum converge quickly that is around

$3.8$ bit/s/Hz at

$-10$ dBs. The NLoS with similar

$SNR$ of

$-10$ dB in

Figure 6b reaches its limit value

$3.7$ bit/s/Hz. For LoS at 40 dBs, the SE approaches to its maximum converge slowly that is around

$12.79$ bit/s/Hz and the NLoS reaches its limit value

$12.79$ bit/s/Hz. It has been noticed from the following figure that the increasing

$SN{R}_{0}$ from 20 dB to 40 dB increases the SE with the same ratio. It is also observed that LoS provides slightly higher SE as compared to NLoS for most values of SNR due to the haphazard changes channel response value

${\left|{x}_{0}\right|}^{2}$.

Nevertheless, at higher values of SNR, the NLoS provides slightly better results since the interference is frailer as compared to the desired signal. It happens because the interference signal cannot be separated from the desired signal in one reflection. In existing networks, this is known as an interference-limited regime, in which the coverage tier operates.

Figure 6b presents the spectral efficiency vs SNR of the proposed scheme. If we compare the results of

Figure 6b with the results presented in [

38] in which, the authors have used an ideal adaptive detector for different SNR and SIR scenarios. A significant improvement can be observed in our proposed results and results of [

38]. According to

Figure 6b, the proposed scheme shows around 12.7 bits/s/Hz of SE by considering a multicell scenario while modeling inter-cell and inter-user interferences. However, the authors in [

38] have considered only one cell scenario that misses the interference factor from other cells and the maximum achieved value is around 8.5 bits/s/Hz. The proposed SE augmentation method shows around a

$25\%$ increase in comparison with existing work. Moreover, while we are considering IUI and ICI interferences, we have also modeled the incident and interfering angles of interfering and desired users presented in

Figure 7. That is not provided in the existing literature.

The range of spectral efficiency given in

Figure 6b can be compared with [

39,

40,

41,

42], in which a temporary network deployed that delivers 0 to 5 bits/s/Hz in similar values of interference. Conclusively, it was observed a simple approach for power scaling is not appropriate to realize optimized SE. The interfering degrees concerning BS antennas or

$\overline{g}g({\theta}_{0},{\theta}_{1})$ is plotted in

Figure 7, in which

${\theta}_{0}$ for desired UE has been fixed at

${45}^{\circ}$ and

${\theta}_{1}$ for interfering UE varies from

$\pm 180$ degrees where

${d}_{H}$ is half of the wavelength. In case of single antenna,

$g({\theta}_{0},{\theta}_{1})$ is 1 regardless of incident angles of signals.

Figure 7 shows the interference peaks when the desired and interfering both UEs signals arrive at the same angle

${\theta}_{0}$ of

${45}^{\circ}$ and when angles of both are mirror reflections of each other such as

${\theta}_{1}={180}^{\circ}-{45}^{\circ}={135}^{\circ}$. The SE expression Equation (

17) for NLoS is complex as it consists of special functions and summations. The lower bound for

$N\ge 1$ is modeled Equation (

20).

The array gain in Equation (

17) for calculated for LoS case and NLoS case is calculated in Equation (

20) that ended the desired signal-scale as

$(N-1)$ instead of

N.

Figure 8 deliberates the LoS cases with

$N=15,100$, and displays the cumulative distribution function at UE angles from 0 to

$2\pi $ and interference gain.

Figure 8 provides an avg. SE realized against the antennas deployed at the BS if the desired user

$SN{R}_{0}$ is considered to be constant 0 dB,

${d}_{H}$ is fixed at

$-10$ dB and

${d}_{H}$ is

$12$. In

Figure 8 for LoS from

$(N=1\phantom{\rule{4.pt}{0ex}}\mathrm{to}\phantom{\rule{4.pt}{0ex}}10)$, SE shows rapid improvement from

$0.85$ to

$3.5$ bits/s/Hz. This sharp improvement is due to array gain and MR combining. Moreover, after

$N>10$, the SE increases as a monotonic function of

N that increases as

$N\to \infty $. Yet again, it is because of MR combining, that gathers extra signal energy (from an array), deprived of amassing energy of interference signal.

Figure 8 illustrate the results of LoS scenario at

$-10$ dBs and

$-40$ dBs, in which SE is an increasing function of

N.

Figure 9 shows that there is a slight difference in NLoS and LoS as channel fading puts lesser influence on mutual-information among the signals transmitted and received from extra antennas deployed at BS (N has larger value) [

43]. The existing literature [

41,

44,

45,

46], on multi-antenna BSs focused on combating channel fading reception focused on combating channel fading, however, our proposal has been attributed with extra DoF and spatial-diversity that spot sovereign fading-realizations. The term channel hardening has been used in [

47] to describe a fading channel that behaves almost deterministically due to spatial diversity.