Spectral Efficiency Analysis for Uplink Multicell Massive MIMO Cellular Communication System under Fading Channels

In multicell massive MIMO system, the maximum limit on area throughput can be achieved by improving spectral efciency and cell density, as well as bandwidth. In order to evaluate the area throughput for such scenarios, the spectral efciency (SE) that utilizes the linear zero forcing uplink combining scheme, can be modeled under the Rician fading channel and the BS in case of up-links, is responsible to estimate the channel. Diferent from existing work, the proposed model incorporates various estimators such as minimum mean square error (MMSE), element-wise minimum mean square error estimators under Rician fading. Te multicell scenarios with uplink (UL) massive MIMO has been analyzed using the proposed model under diferent cases such as pilot reuse factor, coherence block length, diferent number of antennas, and diferent estimators. Te simulation results and analysis are presented based on these parameters. It is found that the average summation of SE per cell can be improved by optimizing MMSE channel estimation using ZF UL combiner, installing multiple BS antennas, serving multiple number of UEs per cell, and using efcient pilot reuse factor. Te MMSE and ZF uplink combining are found to be more suitable in improving SE as compared to MMSE-MR. For example, the uplink SE of MMSE channel estimator for pilot reuse factors, 1, 3, and 4, is calculated as 22.5bit/s/Hz/cell, 22.3bit/s/Hz/cell, and 21bit/s/Hz/cell, respectively. Te uplink SE for EW-MMSE channel estimator with pilot reuse factors, 1, 3, and 4, is calculated as 22.5bit/s/Hz/cell, 22bit/s/Hz/cell, and 22bit/s/Hz/cell, respectively. For the uplink SE of LS channel estimators, it can be 17.9 bit/s/Hz/cell, 20.2bit/s/Hz/cell, and 20bit/s/Hz/cell with pilot reuse factors as f � 1, 3, and 4, respectively. So, for f � 3, the maximum calculated uplink SE for MMSE, EW-MMSE, and LS is 17.6bit/s/Hz/cell, 17.8bit/s/ Hz/cell, and 13bit/s/Hz/cell, respectively. It can be concluded that the improved performance is obtained by reducing the pilot contamination at a pilot reuse factor f � 3 with diferent values of SNR, coherence block length, number of UEs, and number of BS antennas. Tere is also trade-of between the pilot contamination mitigation and the larger SE. However, there is not much efect on coherence block as when it increases, then the SE increases as well.


Introduction
Massive MIMO is one of the promising technologies for the next generation cellular systems.Each cell contains a central base station (BS) and many user equipment (UEs).Each base station contains a large number of antennas, approximately tens or hundreds of antennas that are used for communication with several singleantenna user equipment (UEs).Te base station processes the signal using its antennas on both the uplink and downlink transmission sides [1,2].Te MIMO technology is not new, and it already has a signifcant efect on both modern Wi-Fi networks and 4G LTE networks.Massive MIMO, on the other hand, is a recent improvement that was introduced for 5G new radio (NR) networks.Te number of antenna elements and the multiuser capability within the antenna array are the two key features of massive MIMO technology that set it besides standard MIMO.To ensure future high trafc demand, we need to design and deploy a 5G network, which must enhance the performance of the network in terms of capacity, spectral efciency (SE), energy efciency, latency, network security, and overall robustness [2,3].Due to the popularity of smart devices, the cellular network operators are facing challenges to satisfy the exponential trafc growth.To realize the attractive potential of massive MIMO system, a perfect match between the receiver and the actual channel is necessary, which can be best suitable for the cellular networks also [3][4][5].In addition, the time division duplexing (TDD) mode is an outstanding choice for the operation of massive MIMO system.It can reduce the overhead of CSI acquisition by producing channel reciprocity, which means that the channel response is identical in both uplink and downlink transmission [6][7][8][9][10].For cellular network scenarios, it can utilize available space resources, boosting channel capacity, and communication quality without requiring more spectrum resources and antenna transmission power [10][11][12], so that the need for new communication technology is motivated by the growing need for higher throughput in cellular wireless networks as well as the development of services such as the internet of things (IoT) and machineto-machine communications (M2M).Hence, the MIMO technique can be a strong candidate to deliver high data rates in mobile networks and is a key enabler of modern cellular systems that ofer less expensive ways to boost data rates, such as acquiring more bandwidth [11,13,14].
In terms of SE, one of the performance parameters is the area throughput that can be defned as an expression as Areathroughput � B × Nc × SE [7,9].Here, B is the channel bandwidth; Nc is the number of cells in the unit area (cells per); and SE is the spectral efciency per cell [3,6,8,10].So, the followings can be the criteria used to improve area throughput in massive MIMO system such as more (i) bandwidth allocation; (ii) cell density; and (iii) spectral efciency.However, the more bandwidth allocation has limitation due to the use of limited frequency availability, and another is the increasing cell density that becomes difcult due to additional installations and confgurations of base stations.So, the spectral efciency (SE) improvement can only be a criterion for improving the area throughput [7].
In this article, the followings are the contributions by the motivations from the above observations: (i) the proposed model as ZF combiner that incorporates various estimators to analyze the SE of massive MIMO system under Rician fading channel.Tese include the minimum mean square error (MMSE), the element-wise minimum mean square error estimators; (ii) a detailed analysis is given based on ZF combiners with multicell scenario in diferent cases; (iii) the impact of pilot reuse factor with diferent base station antennas is studied in detail; (iv) the impact of coherence block length on uplink spectral effciency of multicell massive MIMO system is also studied under diferent numbers of antennas and channel estimators.
Te rest of the paper is organized as follows.Te related work about massive MIMO system is described in Section 2. In Section 3, the proposed model design is described.Te results analysis and conclusion remarks are covered in Section 4 and Section 5, respectively.

Related Works
In this section, the recent research work on multicell massive MIMO communication system based on diferent channels, estimators, antennas, line of sight (LOS), and nonline of sight (NLOS) is discussed.In [8], the authors had modeled a zero-forcing beam-forming scheme to improve spectral efciency performance of the system.In [9], a Laplacian centralized scattering model was considered with a spatially correlated Rayleigh fading channel.Te authors also included estimators such as a multicell minimum mean square error (M-MMSE) combining and precoding to handle the reduction on pilot contamination.Results claimed that the improved area throughput can be achieved with the M-MMSE technique, including the channel models such as the Laplacian-centralized scattering spatially correlated Rayleigh fading, one-ring scattering correlated Rayleigh fading, and uncorrelated Rayleigh fading [9].In [13,15], the pilot-based channel estimators were used to generate the channel state information of the desired system to optimize the pilot assignment.Te authors had identifed the pilot contamination using the pilot-assisted estimation, but they eliminated the channel estimated.Hence, the pilot contamination is avoided when there are no pilots.In [16,17], the authors modeled a multicell MIMO system with favorable propagation conditions for a multicell massive MIMO network for the 5G cellular networks.Tey analyzed the SE performance on the efect of pilot contamination and several base station antennas.Tree linear combiners were used in SE performance analysis, which includes the maximum ratio combiner (MRC), the zero-forcing (ZF), and the pilot-zero forcing (P-ZF) combiners.In their work, the drawback can be that a specifed channel model is not considered to analyze spectral efciency, so the impact of the line of sight path on SE performance for a multicell massive MIMO system cannot be observed.In [18], the spectral efciency of a multiway massive MIMO system over a Rician fading channels is modeled for a single-cell massive MIMO system.However, there is no consideration of study on the efect of pilot contamination on spectral efciency and the study with multicell massive MIMO was not considered in their methods.In [14], using Rician fading channel, the spectral efciency analysis was also studied for the multicell massive MIMO system that is similar to references [19][20][21][22][23]. But, the only diference is that the results analysis is based on the linear maximal-ratio combining detector and Rician fading channel for diferent values of Rician factor and BS antennas.However, the authors did not consider the number of BS antennas and K-rice factors that are constantly growing unbound in case of the multicell massive MIMO system.A simple MMSE estimator can be used to eliminate the pilot contamination efects.In addition, the consideration of computational complexity in analysis should be studied as very much reasonable for spectral efciency analysis.For both uplink and downlink, the authors in [25][26][27] had used a model for single user massive MIMO system for the improvement in BER with two retransmission schemes.However, their work is independent of the number of cells.

2
Journal of Electrical and Computer Engineering Diferent from this existing work, this article considers a multicell massive MIMO system with estimated channel state information at the receiver with three diferent types of channel estimators.Te efect of pilot contamination on the SE performance is also studied for multicell massive MIMO scenario.Furthermore, the efect of line-of-sight and nonline-of-sight communication over Rician fading channels is also considered for better analysis.Our work includes the detailed analysis on the spectral efciency with the pilot reuse factor, the number of users, the number of BS antennas, and the propagation condition of the system.Similar works given in [9,19] were based on M-MMSE combining and precoding for the pilot contamination reduction and cell throughput improvements for massive MIMO multicell system.In our proposed design, the LS, MMSE, and EW-MMSE channel estimator and ZF combining techniques are analyzed to evaluate the pilot contamination efects and spectral efciency performance.

The Proposed Model Design
In this section, a system model under TDD is described for a multicell massive MIMO system.In the process of developing a model of a multicell massive MIMO system, we choose and design channel models.Te system model shown in Figure 1 considers the realism of a multicell massive MIMO system over Rician fading.In this TDD system, the multicell massive MIMO is assumed which shares the same time-frequency resources.All user equipment simultaneously occupy the available frequency-time resources for uplink pilot and data transmission.
Te channel response h j li from users i in cell l to the BS within j th cell is modeled as Rician fading channels as follows: where β j li is the large-scale fading coefcient, which contains the path loss and the shadowing efect of cellular environment and g j li is the small-scale fading; Here, the g j li ∈ C M j are assumed to be complex Gaussian distribution with zero mean and unity variance, denoted by NC(0, I M ).
Te channel response between UE k in cell l and the base station in cell j is denoted by h j jk ∈ C M j ×1 .Based on these training sequences, the desired base station can estimate the channels to the user equipment with some estimation error.Te pilot sequence transmitted by user equipment is having a pilot length ⊺ p ≥ k ≈ ⊺ p using TDD protocol [1].In TDD mode, the channel response remains constant over a coherence block ⊺ c .Te size of ⊺ c is determined by the carrier frequency and the external factor such as the propagation environment and UE mobility.It represents the number of orthogonal training sequences available for signaling with consideration of the same pilot sequences in each cell and k th user in each cell has the same training sequences.To reduce interference in the transmission channel, a successful pilot assignment is a challenging task.Although it is necessary to assign more pilots for channel estimation in order to reduce pilot contamination, the spectral efciency is declined when more resources within the coherence interval are assigned to pilots for estimation rather than the payload for transmission.As a resultant, when the number of users per cell increases, the number of pilot sequences also increases, and it leads to decreasing the spectral efciency.Optimization on the resources is required for enhancing the spectral efciency, since it allows more pilots to be assigned to data transmission rather than channel estimation [2].In order to estimate the channel between user equipment (UE) of the diferent cell and the base station of desired cell channel, a model is designed as shown in Figure 1.It is only the system model for uplink multicell multiuser massive MIMO cellular network and the transmission process of uplink model.As shown in Figure 1, BS estimates the channel response from active UEs for making the efcient use of antennas.
Let ϕ jk be the pilot sequence for k th UE in j th cell.Te element of ϕ jk is scaled by the uplink transmit power as ��� p jk  and transmitted as the signal x jk over ⊺ p uplink samples leading to the received uplink signal, denoted as y pilot j ∈ C M j ×⊺ p at BS j.At j th BS, the received pilot signal can be expressed as follows: where y pilot j is denoted as j th BS received pilot signal; ��� p jk  h j jk ϕ T jk is denoted as desired pilot signal; li is denoted as intercell pilot; and n pilot j is denoted as AWGN.In this model, for the sake of argument, from an arbitrary i th UE in L th cell, the BS j estimates the channel h j li .Te BS is also multiplied or correlated y pilot j with this UE pilot sequence ϕ li to generate the processed received pilot signal y pilot j ∈ C M j , which is given as follows: (3)

Journal of Electrical and Computer Engineering
To get the estimation of channel using the abovementioned signal for the k th user within the cell, a projection of y pilot j on ϕ ⋆ jk to obtain y pilot jli is as follows: Note that for all, y pilot jjk � y pilot jli , as (l, i) ∈ ϑ jk , because of the same pilot for all these UEs.Also, we have n j ϕ ⋆ jk ∽NC(0M j σ 2 ul ⊺ p I Mj ).When inside its own cell, there is possibility of strongest interference, the pilot assignment for the desired cellular network is important to utilize the desired pilot sequence efciently.Te value of ϑ jk is given as follows: ( Considering the same pilot sequences for k th user j th cell, the (l, i) ∈ ϑ jk implies the same, so (j, k) ∈ ϑ jk .

Te Least Square (LS) Estimator.
Assuming that from user equipment to base station, the transmitted data rate and the pilots are denoted by x.We have where y pilot is the received pilot signal, h is the unknown channel from UEs to BS antenna, and x denotes both the data rate and pilot length.
Using the received pilot signal, the estimation of the unknown channels from UEs to BS antennas is as follows: In LS algorithm, only frst-order statistics are assumed.In this algorithm, channel statistics are not considered beyond the frst order.To estimate the unknown parameter h using an observed variable of  y pilot , we get To estimate the desired channel between UEs and BS antennas of home cell using LS algorithm is as follows: By substituting the value of y pilot jjk , the following is the simplifed expression: If the desired cellular system-performing pilot is reused to increase the system capacity and to reduce pilot contamination, it simplifes the following expression:  Journal of Electrical and Computer Engineering

Minimum Mean Square Error (MMSE) Estimator.
Te aim of any channel estimator is to estimate an unknown channel parameter h from observed pilot signals  y pilot .To fnd the value of estimated channel, the estimated value will be defned as  h � E h/ y pilot  .Te aim of designing the MMSE channel estimator is to generate channel state information (CSI) at the receiver and minimize the error due to interference.So, the estimation  h is expressed as follows: Te weighted vector W is used to fnd a better channel estimation.Te W can be estimated in a better way using MMSE channel estimation by minimizing the MSE.According to orthogonality principle, the error on estimation, e � h −  h, is orthogonal to LS(  h) estimation.So, we obtain the following expression: Finally, MMMSE channel estimation according to algorithm in [3] is given as follows: where and h j li is the mean corresponding to the LOS component.

Element-Wise-MMSE (EW-MMSE) Channel Estimator.
Te EW-MMSE channel estimator is a special type of MMSE channel estimators used to minimize the computational complexity of MMSE.It does not consider the spatial correlation matrix completely, but a diagonal element of the covariance matrix is considered.Based on literature [14], the complexity is found in calculation of MMSE estimation.So, using EW-MMSE, the reasonable performance can be obtained by minimizing the computational complexity of MMSE.According to [5], the EW-MMSE channel estimator is written as follows: where At j th BS, the received signal during the uplink data transmission (y j ∈ C M j ) is defned as follows: where n j ∈ Nc(0 mj , σ 2 ul I Mj ) is the AWGN, the uplink data from k th UE in L th cell is x lk ∈ C, and it has a power of 3.4.Spectral Efciency of the System.Spectral efciency can be increased by using the radio network resources efectively that will result in increase of throughput.Te most basic and common factors that control the spectral efciency and throughput of cellular network are the signal to interference plus noise ratio (SINR) [24].If the SINR of the network is not up to a limit, then the throughput degradation can happen.
Te BS can restore the original signal from data signal received from users to improve the SE.For this, a linear detector combination of ZF combining is used as follows: where y j is the desired signal from its k th UE acting as interference.So, after doing the maximized ratio processing, the user signal can be expressed as follows: In general, we have the following expression: Journal of Electrical and Computer Engineering Based on the above expressions, we analyze the achievable spectral efciency of the uplink massive MIMO using these three diferent channel estimators.We have the signal y uplink j ∈ C Mj received at BS j and the uplink signal in cell L from user equipment k th UE x uplink jk .As per literature [8,21], the ergodic uplink capacity of k th UE in cell j is lower bounded, and fnally, we get the following expressions: where .

Results and Discussion
In this section, the performance analysis of the proposed model is presented.A step-by-step procedure is described in fowchart as shown in Figure 2. Te simulation parameters used for analysis are listed in Table 1.

Journal of Electrical and Computer Engineering
Increasing the number of orthogonal pilot sequence is a straight forward way to decrease pilot contamination but it reduces the data rate; another mechanism is required to negotiate the pilot contamination problem and required data [13,15,[18][19][20].Pilot reuse factor is a mechanism to improve the required throughput by reducing the pilot contamination.Te pilot reuse factor can be defned as f � ⊺ p /k as per TDD protocol.It also leads to SE performance improvement where f is the chosen integer and k denotes per cell number of UE. f � 1 is called as universal pilot reuse factor while f > 1 is named as nonuniversal pilot reuse factor.For analysis, three diferent pilot reuse factors are considered to evaluate the performance in equations ( 22)-( 24) and are shown in Figure 3.

Efect of Diferent Pilot Reuse Factors and Number of BS Antennas at Diferent SNR Values on Uplink Spectral Efciency of Multicell Massive MIMO Networks under Fading
Channels.In Figure 4, the low SNR with BS antennas and its efect on the spectral efciency are plotted for the multicell massive MIMO networks.In our proposed model with a BS antenna M ∈ 0 − 800 { } having minimum SNR and users per cell, k ≥ 10, the maximum SE is found to be 54 bit/s/Hz/cell with MMSE channel estimators and zero forcing uplink combining.As shown in Figure 4, the graph shows four times more SE.A pilot reuse factor f � 3 has a better spectral efciency than other pilot reuse factors.Similarly, Figures 5(a) and 5(b) show the uplink spectral efciency graph of multicell massive MIMO networks with diferent pilot reuse factors as a function of BS antenna numbers for 5 dB and 10 dB SNR.Te graphs show the linear efect of the SNR and the BS antennas.In Figure 5, SE performance is improved than that of Figure 4 with SNR of 5 dB.For any value of SNR, BS, and antenna numbers, a pilot reuse factor f � 3 has higher spectral efciency than other pilot reuse factors f ∈ 1, 4 { }.Based on the above observations, MMSE estimator and ZF uplink combining indicate reasonable performance; for example, the proposed work using MMSE-ZE with a pilot reuse factor f � 3 has 58 bit/s/Hz/cell uplink spectral efciency.Tis shows a great improvement of UL SE of a cellular network under the efect of shadowing and coherence interference.
As shown in Figures 4 and 5, the uplink SE averaged over a diferent number of BS antennas and shadow fading realization under high SNR and low SNR validate the theoretical results.As seen from fgures, a pilot reuse factor f � 3 has better SE than the other two pilot reuse factors.Generally, increasing the number of BS antennas and SNR of the system yields a better SE.Te potential pilot reuse factor f � 3 shows a maximum SE and a pilot reuse factor f � 4 also has a better performance than a universal pilot reuse factor, which is f � 1.
Table 2 shows the more detailed results of the uplink spectral efciency of multicell massive MIMO cellular networks under fading environment.

Efect of Diferent Pilot Reuse Factors and Number of UEs at Diferent Coherence Block Lengths on Uplink Spectral Effciency of Multicell Massive MIMO Networks under Rician
Fading Channels.Here, we consider MR combining to detect the desired signal received from the estimated channels.Choosing a pilot reuse factor with MR combining is another way to reduce pilot contamination and improve the uplink spectral efciency.In this analysis, the efect of the pilot reuse factor, coherence block, and number of UEs on the UL spectral efciency over Rician fading channels is presented.Figures 6(a) and 6(b) show the uplink spectral efciency of multicell massive MIMO systems vs the number of UEs within the cells for different pilot reuse factors with a coherence block length of S � 400 and S � 500.As shown in Figure 6(a), the spectral efciency for pilot reuse factors f ∈ 3, 4 { } is saturated for UEs ranging from 50 to 70, due to the presence of interference.For UEs, the ranges from 0 to 55 have improved SE as stated in IMT-advanced.Te saturated SE for UEs ranging from 0 to 55 is 145, 181, and 155 for pilot reuse factors f ∈ 1, 3, 4 { }, respectively.As shown in Figure 7, pilot reuse factor f � 3 can improve the spectral efciency of our desired systems with UEs up to 70.
As shown in Figure 6(b), the higher values of coherence block length make it easy to allocate the pilot sequences for channel estimation and uplink data transmission.As shown in Figure 6(b), a UE ranges from 0 to 40, and the maximum SE of each pilot reuse factor f ∈ 1, 3, 4 { } is 125,135.5, and 150, respectively.However, for large number of users, still a universal pilot reuse factor f � 1 is dominant with higher spectral efciency, while pilot reuse factors f ∈ 3, 4 { } become minimum for higher number of UEs.
As shown in Figure 6, a cellular system with k ≤ 30 and a pilot reuse factor f � 3 have a maximum SE than the other pilot reuse factors with diferent number of coherence block lengths.In order to design a particular network having a multicell and k ≤ 30, f � 3 has a great role to improve the uplink SE and hence improvement in its area throughput, while a pilot reuse factor f � 1 has a linear efect on the uplink SE of multicell massive MIMO networks with an increased number of UE, especially for a UE k > 30.It is shown in Table 3 that as the number of user equipment are increased, the interference within a desired network will be increased.So, using a universal pilot reuse factor, f � 1 has a positive efect on the SE of multicell massive MIMO networks when we consider large number of users within desired cellular networks.Table 3 shows the numerical results for Figures 7-9.It can show the efect of pilot reuse factors f ∈ 1, 3, 4 { }, code block length, and UEs on the uplink spectral efciencies of multicell massive MIMO networks under fading channels.Te table shows that a pilot reuse factor f � 3 for k ≤ 30 and code block length S ∈ 200, 400, 500 { } and M � 1000 have an enhanced uplink SE than f � 1 and f � 4. Furthermore, the SE performance with less number of UE is reasonable for f � 4 as compared to that of the pilot reuse factor f � 1.

Efect of Diferent Pilot Reuse Factors and Number of BS Antennas Diferent UES on Uplink Spectral Efciency of Multicell Massive MIMO Networks under Fading Channels.
In this subsection, we consider pilot reuse factors with diferent number of users within a cell, which can efciently enhance the spectral efciency of multicell massive MIMO networks.
Figure 7 shows the uplink spectral efciency of multicell massive MIMO networks under fading channels for diferent pilot reuse factors with varying BS antenna numbers with a UE of k � 10.In Figure 10, we consider BS antennas ranging from 0 to 1000 and UEs of k � 10 for three diferent pilot reuse factors of f ∈ 1, 3, 4 { }.As the graph indicates in Figure 10, a pilot reuse factor f � 3 has a greater potential to enhance the spectral efciency of the overall system.It can be seen from the graph that the spectral efciency with pilot reuse factor f ∈ 3, 4 { } indicates little diference.So, these pilot reuse factors show the more efcient and maximum spectral efciency with small number of users.Figure 8 shows the corresponding spectral efciency of our desired system for three diferent pilot reuse factors of f ∈ 1, 3, 4 { } for UEs of k � 20 and k � 35 with coherence block length τ c � 200.As the number of users increase within the cell of a desired cellular network, the spectral efciency of a universal pilot reuse factor f � 1 becomes maximal.In Figure 11, the spectral efciency of pilot reuse factors f ∈ 1, 4 { } has a little diference for less number of antennas.However, they have same spectral efciency for higher number of BS antennas.A pilot reuse factor f � 3 still has a maximum spectral efciency as compared with other pilot reuse factors.For UEs k � 20 and BS antennas ranging from 0 to 1000, the maximum spectral efciency of diferent pilot reuse factors f ∈ 1, 3, 4 { } becomes 60 bit/s/Hz/cell, 70 bit/s/Hz/cell, and Pilot reuse factor f=1 Pilot reuse f=3 Pilot reuse factor f=4  4, the optimal spectral efciency of these pilot reuse factors f ∈ 1, 3, 4 { } is 87 bit/s/Hz/ cell, 70 bit/s/Hz/cell, and 47 bit/s/Hz/cell, respectively.

Efect of Diferent Number of BS Antennas and UEs at Diferent Values of Coherence Block Length on Uplink Spectral Efciency of Multicell Massive MIMO Networks under Fading
Channels.Te following fgures show the efect of number of equipment and diferent BS antenna numbers and coherence block length.Te value of coherence block length S depends mainly on mobility of users, frequency of operation, and propagation environment.
Figure 9 shows the uplink SE of multicell massive MIMO systems vs number of UEs under fading channels with a coherence block length of S � 800.As shown in fgure, the number of BS antenna have a great potential to improve the SE of multicell massive MIMO networks.Due to the technique of spatial multiplexing between the UEs and BS antennas, the SE can be improved.Te maximum uplink spectral efciency of multicell massive MIMO network for diferent antenna numbers M ∈ 100, 200, 500 { } is 55 bit/s/ Hz/cell, 100 bit/s/Hz/cell, and 170 bit/s/Hz/cell, respectively.
As indicated in Table 5, for a coherence block length of S � 500, the maximum spectral efciency for diferent number of BS antennas M ∈ 100, 200, 500 { } is 45 bit/s/Hz/ cell, 80 bit/s/Hz/cell, and 138 bit/s/Hz/cell, respectively.Generally, as the value of coherence block increases, the spectral efciency also increases, as shown in Table 5.

Efect of Diferent Pilot Reuse Factors and Tree Diferent Channel Estimators with Diferent Values of Coherence Block
Length on Uplink Spectral Efciency of Multicell Massive MIMO Networks under Fading Channels.In this subsection, we consider three diferent channel estimators with three diferent pilot reuse factors, for analyzing their efciencies with three diferent pilot reuse factors.At the receiver, we consider ZF combining used to detect the desired signals from desired users.As we discuss in the previous section, the channel is estimated by frst sending pilot sequences from diferent users to BS antennas.BS estimates the channels between users and BS antennas.
Figure 10 shows the uplink spectral efciency of multicell massive MMIMO network for MMSE and EW-MMSE LS with f � 3, using ZF uplink combining scheme.Te uplink spectral efciency of MMSE-ZF for a pilot reuse factor of f � 3 is 43.5 bit/s/Hz/cell.Te uplink spectral efciency of EW-MMSE-ZF for a pilot reuse factor of f � 3 is 35 bit/s/Hz/ cell and the uplink spectral efciency of LS-ZF with a pilot reuse factor of f � 3 is 35 bit/s/Hz/cell.Tis behaviour shows that the ZF uplink combining technique can suppress the coherence interference.As a resultant, the average sum spectral efciency is enhanced with MMSE and f � 3 with ZF uplink combining.
Figure 11 shows the uplink spectral efciency of multicell massive MMIMO network for MMSE and EW-MMSE LS with f � 4 using ZF uplink combining.Te uplink spectral efciency of MMSE-ZF for a pilot reuse factor of f � 4 is 37.5 bit/s/Hz/cell.Te uplink spectral efciency of EW-MMSE-ZF for a pilot reuse factor of f � 4 is 34.5 bit/s/Hz/cell and the uplink spectral efciency of LS-ZF with a pilot reuse        Figure 12 shows the uplink spectral efciency of multicell massive MMIMO network using MMSE, EW-MMSE, and LS channel estimators with zero forcing uplink combining and a pilot reuse factor of f � 1.As shown in fgure, the uplink spectral efciency of MMSE-ZF for a pilot reuse factor of f � 1 is 38 bit/s/Hz/cell and for EW-MMSE-ZF with pilot reuse factor of f � 1 is 36 bit/s/Hz/cell and for LS-ZF with a pilot reuse factor of f � 1 is 36 bit/s/Hz/cell.

Conclusions
In this paper, the UL spectral efciency with the MMSE, EW-MMSE, and LS and the pilot reuse factor (i.e., f � 1, 2, 3) with uplink ZF combining are analyzed.Te expression of uplink spectral efciency of each channel estimator is derived to model the behaviour under the Rician fading channel.Trough simulations, we analyzed the efect of SNR value, code block length, number of UEs, and BS antenna numbers.It is concluded that the multicell, massive MIMO networks considering an efcient pilot reuse factor and highly qualifed channel estimator have achieved the enhanced spectral efciency and area throughput.Te MMSE and ZF uplink combining are found to be more suitable in improving SE as compared to MMSE-MR.In addition, SE depends on the number of UEs within cells.It becomes saturated for number of UEs ranging 145, 181, and 155 for the given pilot reuse factors.However, there is not much efect on coherence block as when it increases, then the SE increases as well.It is also observed based on results that the ZF uplink combining technique can suppress the coherence interference and hence the average sum SE is enhanced with MMSE channel estimator and a pilot reuse factor of f � 3 with ZF uplink combining.In additional, the results indicate that the uplink spectral efciency of multicell massive MIMO networks for a pilot reuse factor f � 3 has a better performance than the other pilot reuse factors f ∈ 1, 4 { } with a considerable number of UEs, SNR values, code block length, and BS antenna numbers.

Figure 5 :
Figure 5: Uplink SE of multicell massive MIMO system under fading channels with diferent number of BS antennas and pilot reuse factor at (a) SNR � 5 dB and (b) SNR � 10 dB.

Figure 6 :
Figure 6: Uplink SE of multicell massive MIMO system under fading channels with diferent number of users and diferent pilot reuse factors at coherence block length of (a) S � 400 and (b) S � 500.

Figure 7 :
Figure 7: Efect of diferent pilot reuse factors and number of BS antennas on the uplink SE of multicell massive MIMO network under fading channels at k � 10.

Figure 8 :Figure 9 :Figure 10 :Figure 11 :
Figure 8: Efect of diferent pilot reuse factors and number of BS antennas on the uplink SE of multicell massive MIMO network under fading channels at (a) k � 20 and (b) k � 35.

Figure 12 :
Figure12: Average UL sum SE of multicell massive MIMO network when using MMSE, EW-MMSE LS channel estimators, and a pilot reuse factor of f � 1, using the ZF uplink combining scheme.
p ≥ k ≈ ⊺ p � k for universal pilot reuse ⊺ p � fk if pilot reuse factor is greater than one

Table 2 :
Efect of SNR and number of BS antennas on SE of multicell massive MIMO over fading channels.

Table 3 :
Efect of code block length and UEs on SE of multicell massive MIMO system under fading channels.

Table 4 :
Numerical results of uplink spectral efciency of three diferent pilot reuse factors.

Table 5 :
Efect of code block length, UE, and BS antenna on SE under fading channels.